1. Traditional investment theory versus the options approach

Size: px
Start display at page:

Download "1. Traditional investment theory versus the options approach"

Transcription

1 Econ 659: Real options and investment I. Introduction 1. Traditional investment theory versus the options approach - traditional approach: determine whether the expected net present value exceeds zero, ENPV>0 - This rule is the basis for neoclassical investment theory Econ 659, I Introduction Page 1

2 o Two equivalent approaches of neoclassical investment theory (i) Compare the MP of capital with an equivalent per period rental cost or user cost that can be computed from the purchase price of capital, interest, depreciation rates, and applicable taxes (ii) Compare the expected present value of future revenue with the PV of investment cost This second approach can be put in the context of Tobin (1969) compare the capitalized value of marginal investment to the purchase cost The capitalized value can be found directly if the ownership of the investment can be traded in a market; otherwise the Econ 659, I Introduction Page 2

3 value can be imputed from the expected present value of the future stream of profits Tobin s q ratio of capitalized value to purchase price - should undertake the investment if Tobin s q exceeds 1. Econ 659, I Introduction Page 3

4 - The traditional ENPV approach implicitly assumes o an investment is reversible in that expenditures can be recovered if the market turns out to be worse than expected, or o if the expenditures are irreversible, it cannot be delayed if not undertaken now it cannot be undertaken in the future - Many investments can be delayed, and this can affect investment decision - There are also other options available in many investment projects which are often ignored by traditional analysis management has the flexibility to expand, contract, shut down etc as time unfolds - Ex. Decision to drill in an Arctic wildlife refuge o We are considering whether to develop oil reserves in an area that has previously been protected because of sensitive herds of caribou and other wildlife. Econ 659, I Introduction Page 4

5 o There is a non-zero probability that great damage will be done to the wildlife. o Suppose the ENPV>0 i.e. (Expected PV oil revenues costs of production Expected PV of damages to caribou herd) >0 o Does that mean you should begin drilling right away? What are some reasons you might want to delay? Get more info about caribou through a study or just observing information over time could avoid the worst case scenario completely Wait to see trends in oil demand and development of energy substitutes. Econ 659, I Introduction Page 5

6 o Suppose over the next five years time you can do a study that will tell you whether the caribou herd will be harmed or not. We have an option to delay development to wait for more information o Your ENPV might be higher if you delay your decision and undertake this study o If you were correctly valuing this investment you would take into account the fact that the investment can be delayed, or even started and halted part way through Econ 659, I Introduction Page 6

7 - Extending the example: The option to shut down the investment midstream o Consider again our Arctic drilling example, and suppose the ENPV (naively calculated) is negative. o Suppose the ENPV of oil development (not including environmental damage) is $200 million o You estimate the expected value of damages to the caribou as follows. Note that all amounts are present values. Econ 659, I Introduction Page 7

8 5 % -$5 billion 50 % -$3 million 45 % 0 EV(damages) = 0.05(-5000 million)+0.5(-3 million) = -$251.5 million ENPV of oil development including environmental damage= $200 million - $251.5 million = -$51.5 million Conclusion: Do not undertake the project Econ 659, I Introduction Page 8

9 Now suppose you recognize that if the worst case scenario appears to be happening to the caribou, you could suspend development in time for the herd to recover. A correct analysis of the project would take this into account. Suppose if your biologists notice that the herd is being damaged and you suspend development the damages will only be $500 million instead of $5 billion. To correctly calculate the option to suspend production you create the following decision tree for caribou damage: Econ 659, I Introduction Page 9

10 continue -$5 billion 5 % 50 % suspend -$3 million -$500 million 45 % 0 o The EV of damages is now: 0.05 Max[-5 bil, -500 mil]+ 0.5(-$3 million)=-$26.5 million - We also need to recalculate the ENPV of the oil production because of the possibility that production will be shut down. Econ 659, I Introduction Page 10

11 - Suppose if production is shut down the ENPV from the oil development alone will be -$10 million (an assumption) - ENPV of oil production = 0.95($200 million) (-10) = $189.5 million - ENPV of oil development including EV of damages is: $189.5 million - $26.5 million = $163.0 million. - Conclusion: We should go ahead with the project o The simplest ENPV approach ignores these issues o The real options approach focuses on correctly valuing all important embedded options in a project like the option to delay or the option to shut down. Econ 659, I Introduction Page 11

12 - A firm with an investment opportunity is holding an option like a financial call option - If you treat an investment opportunity like a call option, then you explicitly deal with the optimal timing of investment and optimal decisions regarding other embedded options. Econ 659, I Introduction Page 12

13 2. Introduction to Financial options A derivative is a financial instrument whose value depends on the value of other underlying variables usually other traded assets. Futures and forward contracts and options are all derivatives. Also credit derivatives, electricity derivatives, weather derivatives, insurance derivatives Traded on derivatives exchanges or over-the-counter market See Hull ch 1 for a good introduction to derivatives Econ 659, I Introduction Page 13

14 2.1 Call options A financial call option: gives you the right, but not the obligation, to buy a financial asset at some future date. o Example: An investor buys European call option to purchase 100 shares of a particular stock. strike price (or exercise price) = $100 current price of the stock is $98 options expires in 4 months price of an option to purchase one share is $5 The investor spends $5 X 100 on options = $500 A European option can only be exercised at the expiry date. (An American option can be exercised at any time up to the expiry date.) Econ 659, I Introduction Page 14

15 o If in four month s time the price of the stock is less than $100, the investor will not exercise the option and loses $500 (initial investment) o If in four months time the stock price exceeds $100, he will exercise the option. o Suppose stock price in 4 months time is $120. By exercising the option investor can buy the stock at $100 and sell immediately for a gain of $20 per share = $2000. o Deducting initial investment of $500, the net profit is $1500. o Draw a diagram showing the profit from buying this call option versus the stock price at the expiry of the option. (the hockey stick diagram) Econ 659, I Introduction Page 15

16 o Note that holder of a call option benefits if the stock price rises o Profit per share = max[stock price exercise price, 0 ] option price Econ 659, I Introduction Page 16

17 2.2 Put options o Purchaser of a put option benefits if the price of the asset falls o A put option gives the right but not the obligation to sell an asset at a given price at a date specified by the option contract. o Consider an investor who buys a European put option to sell 100 shares of a particular stock for $70 per share (strike price or exercise price). The current price of the stock is $65 and the option expires in three months time. o Price of an option to sell one share is $7. o Initial investment: - Profit per share = max[e-s,0] op price Econ 659, I Introduction Page 17

18 o Suppose the price in three months time is $50. o The investor s gain is: o Draw a diagram showing the profit from buying this European put option versus the stock price at the expiry date. Econ 659, I Introduction Page 18

19 2.3 Valuing financial options For derivatives that are traded in markets, we can observe their market price For new types of derivatives, analysts will need to estimate their fair market value. Ex. An analyst may want to determine whether a new derivative offered by an insurance company is being priced fairly. There is a very large literature on the pricing of financial derivatives can get very complex- due to the proliferation of exotic options as opposed to vanilla options - Bermudan options, chooser options, knock-out options Econ 659, I Introduction Page 19

20 2.4 A firm s opportunity to acquire a real asset There is an analogy between a firm s investment opportunity and a call option. A firm with an investment opportunity has the right but not the obligation to buy an asset at some future time of its choosing. - Consider the Arctic drilling example again: Econ 659, I Introduction Page 20

21 Analogy between financial and real options Financial option Real option Call option on a stock Opportunity to develop an oil field Exercise price Cost of the investment drilling the wells etc Option price sometimes Value of the right to drill and extract oil observable in the market from the reservoir what you would other times must be need to pay to acquire that right calculated sometimes observable in the market, other times must be calculated Expiration date of option May be infinite, or have a fixed time American or European Most real options are American-type types Option price depends on the price of the underlying asset the price of the stock options Value of the investment opportunity depends on the price of underlying uncertain variables the price of oil, the caribou herds Econ 659, I Introduction Page 21

22 Irreversibility: Once you have exercised the option, you don t have the right to reverse your decision. Irreversibility: Once you begin spending on the oil field a certain portion of your investment cannot be recovered a sunk cost. For American style options (both financial and real) we are interested in finding the optimal time to exercise the option a critical threshold of the underlying asset at which it is optimal to exercise the option. Makes American style options more complex than European style. Econ 659, I Introduction Page 22

23 When we exercise an option, we lose opportunity to wait for a time when the investment might be more profitable we kill the option. This lost option value should be included as an investment cost when determining the optimal time to invest. Modify the traditional investment rule - From o Invest if the expected present value of the net revenue from capital purchase cost - To o Invest if the expected present value of revenue from capital purchase cost + value of keeping investment option alive - The value of keeping the option alive may also be considered the opportunity cost of exercising the option. Econ 659, I Introduction Page 23

24 - Investment decisions can be very wrong if this opportunity cost is ignored - Optimal investment rules for irreversible investment under uncertainty can be obtained using methods that have been developed for pricing options in financial markets contingent claims approach - Dixit and Pindyck also present an equivalent approach dynamic programming an approach from the theory of optimal sequential decisions under uncertainty - The problem with the dynamic programming approach is an inadequate treatment of the discount rate for problems involving embedded options and a finite time horizon. Econ 659, I Introduction Page 24

25 - In this course we will focus on the methodologies from finance, but we will also discuss the dynamic programming approach and why it is problematic Econ 659, I Introduction Page 25

26 3. A two period example of valuing an investment under uncertainty This example is a variation on one in Dixit and Pindyck, chapter 2. A firm is considering whether to invest in a widget factory. An irreversible investment Investment can be built instantly for a cost of I=$1600 and will produce one widget per year forever with zero operating costs. Price of widget today, P 0 =$200. Price next year and forever after: P 1 = $340 with probability q = 0.5 P 1 = $100 with probability (1-q) = 0.5 Econ 659, I Introduction Page 26

27 Discount rate = 10% (Assume for the moment that risk in investing in widgets is fully diversifiable i.e. it can be completely eliminated in a diversified portfolio. Hence we are able to use the risk-free interest rate, which we assume is 10%.) Should the firm invest now or would it be better to wait until next year to see whether the price of widgets goes up or down? What is the value of this investment opportunity? There are two ways to answer these questions. In the calculations we assume revenues and costs occur at the beginning of each period. Econ 659, I Introduction Page 27

28 3.1 Method 1: Compare the ENPV of investing immediately, versus waiting until next year. Show that the ENPV of investing immediately is $800 while the ENPV of investing a year from now is $973. EPNV(of immediate investment) = EP ( 1 ) $ Econ 659, I Introduction Page 28

29 What if our choice was to invest today or never? How much is it worth to have the flexibility to make the investment decision next year, rather than having to invest either now or never? Answer: $173 How high would the cost of the flexible investment have to be to make us indifferent between the flexible versus the now-or-never investment? Answer: $1980 Econ 659, I Introduction Page 29

30 3.2 Method 2: Using option pricing methods creating a hedging portfolio An aside on short sales Short selling or shorting an asset: selling an asset that is not owned. Short selling is possible for some, but not all, investment assets. Eg. (see Hull page 100) An investor tells his broker to short 500 shares of RBC. The broker borrows these shares from another client and sells them in the market and gives the revenue to the investor. The investor can maintain the short position as long as the broker has shares that he can borrow. The investor must pay the broker any dividends or income that accrue to the shares during the time the shares are shorted. When the investor wants to close out his position he will purchase 500 shares of RBC and return them to the broker. The investor profits if the stock has fallen in price in the meantime. Econ 659, I Introduction Page 30

31 Suppose the original price of the stock is $200 and when the short position is closed out the price has fallen to $ shares are shorted in April and the position is closed out in July. Cash flow from short sale of shares: April Borrow 500 shares and sell at $200 per share $100,000 May Pay dividend, $2 per share -$1000 July Buy 500 shares for $150 per share -$75,000 Net profit $24,000 Econ 659, I Introduction Page 31

32 The cash flows from a short sale are the mirror image of the cash flow from purchasing the shares in April and selling in July. Cash flow from purchase of shares: April Purchase 500 shares at $200 per share -$100,000 May Receive dividend, $2 per share $1000 July Sell 500 shares for $150 per share $75,000 Net profit -$24,000 Econ 659, I Introduction Page 32

33 3.2.2 Creating a hedging portfolio In finance, options are typically valued by creating a portfolio of the option and a sufficient number of another related asset so that the risk from holding the option is eliminated i.e. the portfolio is riskfree By setting the portfolio s return equal to the riskfee rate we can back out the value of the option. We can use this same approach for valuing an investment opportunity. Econ 659, I Introduction Page 33

34 Let: F 0 : the value today of the investment opportunity what we would be willing to pay for the opportunity to build a widget factory This is what we want to determine. F 1 : the value of the investment opportunity next year, a random variable which depends on the price of widgets (1 r) If P 1 =$340, F 1 If P 1 =$100, F1 max ,0 $2140 r (1 r) max ,0 0 r The value of the investment opportunity depends on the price of widgets. We can eliminate the risk of our investment opportunity by shorting an appropriate number of widgets Econ 659, I Introduction Page 34

35 We create a portfolio hold the investment opportunity and sell short n widgets. We choose the number of widgets so that the portfolio is riskfree and therefore must earn a return equal to the riskfree rate. Econ 659, I Introduction Page 35

36 The value of this portfolio today (Φ 0 ) is F0 np0 The value of this portfolio next year is: F np n F np 0 100n (1.1) We want to choose n (the number of widgets to sell short) so that the value of the portfolio next year is the same whether the price of widgets rises or falls. Show that n= If price rises our portfolio in period 1 is worth: Econ 659, I Introduction Page 36

37 If price falls our portfolio in period 1 is worth: What is the return from holding this portfolio? The return will be capital gains less any payments needed to hold the short position. Capital gain is: ( F ) Payments to hold the short position: assumed to be zero (contrary to the Dixit and Pindyck example) Return from holding the portfolio over the year is therefore. Econ 659, I Introduction Page 37

38 F0 (1.2) The return must equal the riskfree rate. So we can calculate F 0 as follows. r F 0 0 Substituting for 0and solving for F 0 we get F 0 =$ Econ 659, I Introduction Page 38

39 The value of the investment opportunity calculated in this manner is the same as using the previous approach. Using this latter approach how do we decide whether or not to exercise the option to invest? The payoff from investing immediately is $800, found earlier. But if we invest immediately we kill the option and lose a value of $973. Hence it is better to delay. Econ 659, I Introduction Page 39

40 Another way to look at this: The full cost of investing today is the $1600 capital cost plus the $973 lost value of the option to invest next period. Full cost = $2573 We invest today only if the PV of revenues from investing today exceeds the full cost of investment. Expected PV revenues = $200+$220/.1=$2400. Since $2400<$2573, we delay our investment. The rule is to invest immediately if V 0 I F 0 where V 0 refers to the present value of revenues from widgets. Note that this approach requires that we can trade widgets hold long or short positions. If this is not possible, we could look for Econ 659, I Introduction Page 40

41 another asset, or combination of assets, the price of which is perfectly correlated with widgets. Alternately we could use Method 1 if all price risk is diversifiable and we can use the riskfree rate. If this does not hold, then we have to find a way to determine an appropriate risk premium. This will be discussed further in future classes. Econ 659, I Introduction Page 41

42 3.2.3 Hedging strategy for previous example At beginning of year: - sell widgets short and receive X$200=$ use proceeds to purchase the investment opportunity for $ (=F 0 ) - this leaves $1783-$973 = $810, which can be put in a riskfree bank account and earn 10% At end of the year: - How much do we have in the bank? $810 X (1.10)=$891 - If P our investment opportunity ( 1 F ) is worth zero. - To pay back the short position requires 100 X = $891.66, which is what we have in our bank account Econ 659, I Introduction Page 42

43 - If P 1 340, F 1 $ To close out the short position we have to buy shares for a total cost of 340 X = $ This can be financed by selling our investment opportunity for $2140 and using the bank account of $892 for a total of $ Hence whether the price of widgets rises or falls, we end up with zero dollars. - Since I put up zero dollars of my own money initially, I must just break even in the end. Otherwise there is an arbitrage opportunity. Econ 659, I Introduction Page 43

44 3.2.4 An aside on the no-arbitrage assumption and risk The no-arbitrage assumption A key assumption in economics and finance. An arbitrage opportunity refers to an opportunity to make an instantaneous riskless profit. The assumption of no arbitrage opportunities means that there is no free lunch. More correctly, it is assumed that arbitrage opportunities cannot persist for long as changes in prices will eliminate them. Econ 659, I Introduction Page 44

45 Finance theory assumes the existence of risk-free investments that give a guaranteed return with no chance of default. One approximation would be a Canadian government short term bond or a bank deposit in a sound bank. Under the no-arbitrage assumption the greatest risk-free return you could make on a portfolio of assets is the riskless return one would get on a bank deposit. To see why, suppose you can purchase a portfolio of assets for $V and that these assets earn a guaranteed return in the form of a dividend, $D per year. Suppose that the dividend yield (D/V) is 10% while the risk-free rate on a bank account is only 5%. Econ 659, I Introduction Page 45

46 No one would hold the bank account and everyone would try to buy the portfolio of assets. This would push up the price of the portfolio. V would rise until the return on V equalled the risk-free rate of 5%. Anyone who wants a return greater than the risk-free rate must accept some risk. An implication is that if a portfolio requires no investment and is riskless, then its terminal value must be zero. We demonstrated this in the previous example of buying an asset using the proceeds of the short sale of widgets. Econ 659, I Introduction Page 46

47 A note on risk Risk is commonly classified as either specific or non-specific. (Non-specific risk is also sometimes called systematic risk, or market risk.) Specific risk is due to the specific characteristics of a particular asset. For example, if a company operates in an area prone to earth quakes, its stock is subject to that specific risk. A non-specific risk refers to risks that affect all assets, such as a change in interest rates or inflation. It is possible to diversify away specific risk by having a portfolio of assets from different sectors of the economy. A diversified portfolio implies that your wealth is not significantly affected by the specific risk faced by any individual asset. Econ 659, I Introduction Page 47

48 In theory, an individual will only be rewarded with extra return in the market by taking on non-specific risk. One popular definition of risk is the variance of return. There are other definitions as well. Econ 659, I Introduction Page 48

49 3.2.5 Impact of changing investment cost, I Recall our equilibrium condition that the return to our portfolio must equal the riskfree rate. 1 0 r 0 State F 0 as a function of I for our example. Sketch a graph of F 0 and the value of investing right away, V 0 -I, versus I. Show the critical I* at which one is indifferent between investing now or delaying for a year. Note: I*=1283, given V 0 =2400-I Econ 659, I Introduction Page 49

50 3.2.6 Changing the initial price P 0 Specify F 0 as a function of P 0. Sketch a graph of F 0 and V 0 -I as functions of P 0. Observe that there are three regions in this graph. P P * 0 0 * ** ** 0 0 Never invest P P P Delay to period 1 and invest if price goes up. P P Invest immediately Note we can write the expected value of net revenues from investing immediately in terms of P 0 as follows: V 0 =12P 0 The upper and lower critical values are: P*=$85.56 and P**=$ Econ 659, I Introduction Page 50

51 3.2.7 Increasing uncertainty over price Suppose we keep P 0 fixed but increase the size of upward and downward movements in period 1. How is the value of F 0 changed? What about the critical price P* above which you will delay investing until period 1? Try an example on your own. Econ 659, I Introduction Page 51

52 4. Extending the example to more periods We could extend the previous example to three periods so that the price could rise or fall in period 1 as well as period 2, and then remain constant thereafter. This would increase the complexity of the problem in at least two ways. (i) The number of investment strategies to choose from depending on P 0 will increase to 5: Econ 659, I Introduction Page 52

53 T=0 T=1 T=2 P0 P1 + P1 - P2 + P2 - Never invest Delay delay never invest - Delay invest never continue - Delay invest delay invest or continue don t invest Invest continue continue continue continue (ii) Also the number of widgets to sell short would need to change in period 2 when the price of widgets changes. A dynamic hedging strategy is required. If the price of widgets is assumed to be able to change to any value and is described as a continuous time stochastic process, then F 0 will be a smooth, continuous function of P 0. Econ 659, I Introduction Page 53

54 5. Other common types of real options The ability to delay investment is the most common type of option considered in the literature. Other important options (See Table 1.1 of Trigeorgis, pages 2-3, for references.) (i) option to alter operating scale expand or contract; shut down and restart (ii) time to build options (staged investment) (iii) option to abandon (iv) option to switch outputs or inputs eg switch energy source of power plant (v) growth options an early investment is a prerequisite for future growth opportunities eg R&D or industries with multiple product generations (vi) multiple interacting options collection of various options combined value may differ from the sum of separate values Econ 659, I Introduction Page 54

Economic Risk and Decision Analysis for Oil and Gas Industry CE School of Engineering and Technology Asian Institute of Technology

Economic Risk and Decision Analysis for Oil and Gas Industry CE School of Engineering and Technology Asian Institute of Technology Economic Risk and Decision Analysis for Oil and Gas Industry CE81.98 School of Engineering and Technology Asian Institute of Technology January Semester Presented by Dr. Thitisak Boonpramote Department

More information

Corporate Valuation and Financing Real Options. Prof. Hugues Pirotte

Corporate Valuation and Financing Real Options. Prof. Hugues Pirotte Corporate Valuation and Financing Real Options Prof. Hugues Pirotte Profs H. Pirotte & A. Farber 2 Typical project valuation approaches 3 Investment rules Net Present Value (NPV)» Discounted incremental

More information

, the nominal money supply M is. M = m B = = 2400

, the nominal money supply M is. M = m B = = 2400 Economics 285 Chris Georges Help With Practice Problems 7 2. In the extended model (Ch. 15) DAS is: π t = E t 1 π t + φ (Y t Ȳ ) + v t. Given v t = 0, then for expected inflation to be correct (E t 1 π

More information

LECTURES ON REAL OPTIONS: PART III SOME APPLICATIONS AND EXTENSIONS

LECTURES ON REAL OPTIONS: PART III SOME APPLICATIONS AND EXTENSIONS LECTURES ON REAL OPTIONS: PART III SOME APPLICATIONS AND EXTENSIONS Robert S. Pindyck Massachusetts Institute of Technology Cambridge, MA 02142 Robert Pindyck (MIT) LECTURES ON REAL OPTIONS PART III August,

More information

*Efficient markets assumed

*Efficient markets assumed LECTURE 1 Introduction To Corporate Projects, Investments, and Major Theories Corporate Finance It is about how corporations make financial decisions. It is about money and markets, but also about people.

More information

Appendix A Financial Calculations

Appendix A Financial Calculations Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options, Second Edition By Andrew M. Chisholm 010 John Wiley & Sons, Ltd. Appendix A Financial Calculations TIME VALUE OF MONEY

More information

University of Victoria. Economics 325 Public Economics SOLUTIONS

University of Victoria. Economics 325 Public Economics SOLUTIONS University of Victoria Economics 325 Public Economics SOLUTIONS Martin Farnham Problem Set #5 Note: Answer each question as clearly and concisely as possible. Use of diagrams, where appropriate, is strongly

More information

Hull, Options, Futures & Other Derivatives Exotic Options

Hull, Options, Futures & Other Derivatives Exotic Options P1.T3. Financial Markets & Products Hull, Options, Futures & Other Derivatives Exotic Options Bionic Turtle FRM Video Tutorials By David Harper, CFA FRM 1 Exotic Options Define and contrast exotic derivatives

More information

CHAPTER 12 APPENDIX Valuing Some More Real Options

CHAPTER 12 APPENDIX Valuing Some More Real Options CHAPTER 12 APPENDIX Valuing Some More Real Options This appendix demonstrates how to work out the value of different types of real options. By assuming the world is risk neutral, it is ignoring the fact

More information

Irreversibility, Uncertainty, and Investment. Robert S. Pindyck. MIT-CEPR WP March 1990

Irreversibility, Uncertainty, and Investment. Robert S. Pindyck. MIT-CEPR WP March 1990 Irreversibility, Uncertainty, and Investment by Robert S. Pindyck MIT-CEPR 90-007WP March 1990 4 IRREVERSIBILITY, UNCERTAINTY, AND INVESTMENT* by Robert S. Pindyck Massachusetts Institute of Technology

More information

Overview:Time and Uncertainty. Economics of Time: Some Issues

Overview:Time and Uncertainty. Economics of Time: Some Issues Overview:Time and Uncertainty Intertemporal Prices and Present Value Uncertainty Irreversible Investments and Option Value Economics of Time: Some Issues Cash now versus cash payments in the future? Future

More information

Real Options and Game Theory in Incomplete Markets

Real Options and Game Theory in Incomplete Markets Real Options and Game Theory in Incomplete Markets M. Grasselli Mathematics and Statistics McMaster University IMPA - June 28, 2006 Strategic Decision Making Suppose we want to assign monetary values to

More information

Theme for this Presentation

Theme for this Presentation Types of Flexibility = Options Richard de Neufville Professor of Engineering Systems and of Civil and Environmental Engineering MIT Option Concepts Slide 1 of 43 Theme for this Presentation To place Concept

More information

DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY

DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY DUALITY The essence of duality is that in managing risks one can: Address the cause of the risk i.e. remove the risk Address the effect of the risk -

More information

Real Options. Katharina Lewellen Finance Theory II April 28, 2003

Real Options. Katharina Lewellen Finance Theory II April 28, 2003 Real Options Katharina Lewellen Finance Theory II April 28, 2003 Real options Managers have many options to adapt and revise decisions in response to unexpected developments. Such flexibility is clearly

More information

3/15/2018 DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY DUALITY

3/15/2018 DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY DUALITY DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY DUALITY The essence of duality is that in managing risks one can: Address the cause of the risk i.e. remove the risk Address the effect of the risk -

More information

15 American. Option Pricing. Answers to Questions and Problems

15 American. Option Pricing. Answers to Questions and Problems 15 American Option Pricing Answers to Questions and Problems 1. Explain why American and European calls on a nondividend stock always have the same value. An American option is just like a European option,

More information

Chapter 22: Real Options

Chapter 22: Real Options Chapter 22: Real Options-1 Chapter 22: Real Options I. Introduction to Real Options A. Basic Idea => firms often have the ability to wait to make a capital budgeting decision => may have better information

More information

Real Options. Bernt Arne Ødegaard. 23 November 2017

Real Options. Bernt Arne Ødegaard. 23 November 2017 Real Options Bernt Arne Ødegaard 23 November 2017 1 Real Options - intro Real options concerns using option pricing like thinking in situations where one looks at investments in real assets. This is really

More information

The Binomial Approach

The Binomial Approach W E B E X T E N S I O N 6A The Binomial Approach See the Web 6A worksheet in IFM10 Ch06 Tool Kit.xls for all calculations. The example in the chapter illustrated the binomial approach. This extension explains

More information

Practice of Finance: Advanced Corporate Risk Management

Practice of Finance: Advanced Corporate Risk Management MIT OpenCourseWare http://ocw.mit.edu 15.997 Practice of Finance: Advanced Corporate Risk Management Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

More information

Motivating example: MCI

Motivating example: MCI Real Options - intro Real options concerns using option pricing like thinking in situations where one looks at investments in real assets. This is really a matter of creative thinking, playing the game

More information

Option Properties Liuren Wu

Option Properties Liuren Wu Option Properties Liuren Wu Options Markets (Hull chapter: 9) Liuren Wu ( c ) Option Properties Options Markets 1 / 17 Notation c: European call option price. C American call price. p: European put option

More information

The investment game in incomplete markets

The investment game in incomplete markets The investment game in incomplete markets M. R. Grasselli Mathematics and Statistics McMaster University Pisa, May 23, 2008 Strategic decision making We are interested in assigning monetary values to strategic

More information

Capital structure I: Basic Concepts

Capital structure I: Basic Concepts Capital structure I: Basic Concepts What is a capital structure? The big question: How should the firm finance its investments? The methods the firm uses to finance its investments is called its capital

More information

WEB APPENDIX 12F REAL OPTIONS: INVESTMENT TIMING, GROWTH, AND FLEXIBILITY

WEB APPENDIX 12F REAL OPTIONS: INVESTMENT TIMING, GROWTH, AND FLEXIBILITY WEB APPENDIX 12F REAL OPTIONS: INVESTMENT TIMING, GROWTH, AND FLEXIBILITY In Chapter 12, Section 12-7, we presented an overview of real options and discussed how to analyze abandonment options. However,

More information

ECON4510 Finance Theory Lecture 10

ECON4510 Finance Theory Lecture 10 ECON4510 Finance Theory Lecture 10 Diderik Lund Department of Economics University of Oslo 11 April 2016 Diderik Lund, Dept. of Economics, UiO ECON4510 Lecture 10 11 April 2016 1 / 24 Valuation of options

More information

Portfolio Management Philip Morris has issued bonds that pay coupons annually with the following characteristics:

Portfolio Management Philip Morris has issued bonds that pay coupons annually with the following characteristics: Portfolio Management 010-011 1. a. Critically discuss the mean-variance approach of portfolio theory b. According to Markowitz portfolio theory, can we find a single risky optimal portfolio which is suitable

More information

2 The binomial pricing model

2 The binomial pricing model 2 The binomial pricing model 2. Options and other derivatives A derivative security is a financial contract whose value depends on some underlying asset like stock, commodity (gold, oil) or currency. The

More information

1.1 Basic Financial Derivatives: Forward Contracts and Options

1.1 Basic Financial Derivatives: Forward Contracts and Options Chapter 1 Preliminaries 1.1 Basic Financial Derivatives: Forward Contracts and Options A derivative is a financial instrument whose value depends on the values of other, more basic underlying variables

More information

Sample Chapter REAL OPTIONS ANALYSIS: THE NEW TOOL HOW IS REAL OPTIONS ANALYSIS DIFFERENT?

Sample Chapter REAL OPTIONS ANALYSIS: THE NEW TOOL HOW IS REAL OPTIONS ANALYSIS DIFFERENT? 4 REAL OPTIONS ANALYSIS: THE NEW TOOL The discounted cash flow (DCF) method and decision tree analysis (DTA) are standard tools used by analysts and other professionals in project valuation, and they serve

More information

Web Extension: Abandonment Options and Risk-Neutral Valuation

Web Extension: Abandonment Options and Risk-Neutral Valuation 19878_14W_p001-016.qxd 3/13/06 3:01 PM Page 1 C H A P T E R 14 Web Extension: Abandonment Options and Risk-Neutral Valuation This extension illustrates the valuation of abandonment options. It also explains

More information

Derivative Instruments

Derivative Instruments Derivative Instruments Paris Dauphine University - Master I.E.F. (272) Autumn 2016 Jérôme MATHIS jerome.mathis@dauphine.fr (object: IEF272) http://jerome.mathis.free.fr/ief272 Slides on book: John C. Hull,

More information

CHAPTER 17 OPTIONS AND CORPORATE FINANCE

CHAPTER 17 OPTIONS AND CORPORATE FINANCE CHAPTER 17 OPTIONS AND CORPORATE FINANCE Answers to Concept Questions 1. A call option confers the right, without the obligation, to buy an asset at a given price on or before a given date. A put option

More information

Lecture 1 Definitions from finance

Lecture 1 Definitions from finance Lecture 1 s from finance Financial market instruments can be divided into two types. There are the underlying stocks shares, bonds, commodities, foreign currencies; and their derivatives, claims that promise

More information

Keywords: Digital options, Barrier options, Path dependent options, Lookback options, Asian options.

Keywords: Digital options, Barrier options, Path dependent options, Lookback options, Asian options. FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Exotic Options These notes describe the payoffs to some of the so-called exotic options. There are a variety of different types of exotic options. Some of these

More information

Corporate Finance, Module 21: Option Valuation. Practice Problems. (The attached PDF file has better formatting.) Updated: July 7, 2005

Corporate Finance, Module 21: Option Valuation. Practice Problems. (The attached PDF file has better formatting.) Updated: July 7, 2005 Corporate Finance, Module 21: Option Valuation Practice Problems (The attached PDF file has better formatting.) Updated: July 7, 2005 {This posting has more information than is needed for the corporate

More information

Department of Mathematics. Mathematics of Financial Derivatives

Department of Mathematics. Mathematics of Financial Derivatives Department of Mathematics MA408 Mathematics of Financial Derivatives Thursday 15th January, 2009 2pm 4pm Duration: 2 hours Attempt THREE questions MA408 Page 1 of 5 1. (a) Suppose 0 < E 1 < E 3 and E 2

More information

CHAPTER 17. Payout Policy

CHAPTER 17. Payout Policy CHAPTER 17 1 Payout Policy 1. a. Distributes a relatively low proportion of current earnings to offset fluctuations in operational cash flow; lower P/E ratio. b. Distributes a relatively high proportion

More information

Chapter 11 Cash Flow Estimation and Risk Analysis ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 11 Cash Flow Estimation and Risk Analysis ANSWERS TO END-OF-CHAPTER QUESTIONS Chapter 11 Cash Flow Estimation and Risk Analysis ANSWERS TO END-OF-CHAPTER QUESTIONS 11-1 a. Project cash flow, which is the relevant cash flow for project analysis, represents the actual flow of cash,

More information

Debt. Firm s assets. Common Equity

Debt. Firm s assets. Common Equity Debt/Equity Definition The mix of securities that a firm uses to finance its investments is called its capital structure. The two most important such securities are debt and equity Debt Firm s assets Common

More information

Practical Hedging: From Theory to Practice. OSU Financial Mathematics Seminar May 5, 2008

Practical Hedging: From Theory to Practice. OSU Financial Mathematics Seminar May 5, 2008 Practical Hedging: From Theory to Practice OSU Financial Mathematics Seminar May 5, 008 Background Dynamic replication is a risk management technique used to mitigate market risk We hope to spend a certain

More information

Appendix: Basics of Options and Option Pricing Option Payoffs

Appendix: Basics of Options and Option Pricing Option Payoffs Appendix: Basics of Options and Option Pricing An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (called a strike price or an exercise

More information

Graduate Macro Theory II: Two Period Consumption-Saving Models

Graduate Macro Theory II: Two Period Consumption-Saving Models Graduate Macro Theory II: Two Period Consumption-Saving Models Eric Sims University of Notre Dame Spring 207 Introduction This note works through some simple two-period consumption-saving problems. In

More information

Dynamic Strategic Planning. Evaluation of Real Options

Dynamic Strategic Planning. Evaluation of Real Options Evaluation of Real Options Evaluation of Real Options Slide 1 of 40 Previously Established The concept of options Rights, not obligations A Way to Represent Flexibility Both Financial and REAL Issues in

More information

Econ 422 Eric Zivot Fall 2005 Final Exam

Econ 422 Eric Zivot Fall 2005 Final Exam Econ 422 Eric Zivot Fall 2005 Final Exam This is a closed book exam. However, you are allowed one page of notes (double-sided). Answer all questions. For the numerical problems, if you make a computational

More information

FNCE 302, Investments H Guy Williams, 2008

FNCE 302, Investments H Guy Williams, 2008 Sources http://finance.bi.no/~bernt/gcc_prog/recipes/recipes/node7.html It's all Greek to me, Chris McMahon Futures; Jun 2007; 36, 7 http://www.quantnotes.com Put Call Parity THIS IS THE CALL-PUT PARITY

More information

Arbitrage Pricing Theory (APT)

Arbitrage Pricing Theory (APT) Arbitrage Pricing Theory (APT) (Text reference: Chapter 11) Topics arbitrage factor models pure factor portfolios expected returns on individual securities comparison with CAPM a different approach 1 Arbitrage

More information

Fixed Income and Risk Management

Fixed Income and Risk Management Fixed Income and Risk Management Fall 2003, Term 2 Michael W. Brandt, 2003 All rights reserved without exception Agenda and key issues Pricing with binomial trees Replication Risk-neutral pricing Interest

More information

Lecture Quantitative Finance Spring Term 2015

Lecture Quantitative Finance Spring Term 2015 and Lecture Quantitative Finance Spring Term 2015 Prof. Dr. Erich Walter Farkas Lecture 06: March 26, 2015 1 / 47 Remember and Previous chapters: introduction to the theory of options put-call parity fundamentals

More information

B. Combinations. 1. Synthetic Call (Put-Call Parity). 2. Writing a Covered Call. 3. Straddle, Strangle. 4. Spreads (Bull, Bear, Butterfly).

B. Combinations. 1. Synthetic Call (Put-Call Parity). 2. Writing a Covered Call. 3. Straddle, Strangle. 4. Spreads (Bull, Bear, Butterfly). 1 EG, Ch. 22; Options I. Overview. A. Definitions. 1. Option - contract in entitling holder to buy/sell a certain asset at or before a certain time at a specified price. Gives holder the right, but not

More information

Decision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to:

Decision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to: CHAPTER 3 Decision Analysis LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. List the steps of the decision-making process. 2. Describe the types of decision-making environments.

More information

Lecture 5. Trading With Portfolios. 5.1 Portfolio. How Can I Sell Something I Don t Own?

Lecture 5. Trading With Portfolios. 5.1 Portfolio. How Can I Sell Something I Don t Own? Lecture 5 Trading With Portfolios How Can I Sell Something I Don t Own? Often market participants will wish to take negative positions in the stock price, that is to say they will look to profit when the

More information

Forwards, Futures, Options and Swaps

Forwards, Futures, Options and Swaps Forwards, Futures, Options and Swaps A derivative asset is any asset whose payoff, price or value depends on the payoff, price or value of another asset. The underlying or primitive asset may be almost

More information

Martingale Pricing Theory in Discrete-Time and Discrete-Space Models

Martingale Pricing Theory in Discrete-Time and Discrete-Space Models IEOR E4707: Foundations of Financial Engineering c 206 by Martin Haugh Martingale Pricing Theory in Discrete-Time and Discrete-Space Models These notes develop the theory of martingale pricing in a discrete-time,

More information

ECON DISCUSSION NOTES ON CONTRACT LAW. Contracts. I.1 Bargain Theory. I.2 Damages Part 1. I.3 Reliance

ECON DISCUSSION NOTES ON CONTRACT LAW. Contracts. I.1 Bargain Theory. I.2 Damages Part 1. I.3 Reliance ECON 522 - DISCUSSION NOTES ON CONTRACT LAW I Contracts When we were studying property law we were looking at situations in which the exchange of goods/services takes place at the time of trade, but sometimes

More information

16 MAKING SIMPLE DECISIONS

16 MAKING SIMPLE DECISIONS 247 16 MAKING SIMPLE DECISIONS Let us associate each state S with a numeric utility U(S), which expresses the desirability of the state A nondeterministic action A will have possible outcome states Result

More information

FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.

FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015. FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 2 1. Consider a zero-sum game, where

More information

CHAPTER 4 SHOW ME THE MONEY: THE BASICS OF VALUATION

CHAPTER 4 SHOW ME THE MONEY: THE BASICS OF VALUATION 1 CHAPTER 4 SHOW ME THE MOEY: THE BASICS OF VALUATIO To invest wisely, you need to understand the principles of valuation. In this chapter, we examine those fundamental principles. In general, you can

More information

Midterm Review. P resent value = P V =

Midterm Review. P resent value = P V = JEM034 Corporate Finance Winter Semester 2017/2018 Instructor: Olga Bychkova Midterm Review F uture value of $100 = $100 (1 + r) t Suppose that you will receive a cash flow of C t dollars at the end of

More information

Problem Set #2. Intermediate Macroeconomics 101 Due 20/8/12

Problem Set #2. Intermediate Macroeconomics 101 Due 20/8/12 Problem Set #2 Intermediate Macroeconomics 101 Due 20/8/12 Question 1. (Ch3. Q9) The paradox of saving revisited You should be able to complete this question without doing any algebra, although you may

More information

CHAPTER 22. Real Options. Chapter Synopsis

CHAPTER 22. Real Options. Chapter Synopsis CHAPTER 22 Real Options Chapter Synopsis 22.1 Real Versus Financial Options A real option is the right, but not the obligation, to make a decision regarding an investment in real assets, such as to expand

More information

A Beginners Guide To Making Money Trading Binary Options

A Beginners Guide To Making Money Trading Binary Options A Beginners Guide To Making Money Trading Binary Options What Are Binary Options? A binary option has now become a fairly common term amongst traders. A Binary Option deals with a kind of purchased asset

More information

CHAPTER 2 LITERATURE REVIEW

CHAPTER 2 LITERATURE REVIEW CHAPTER 2 LITERATURE REVIEW Capital budgeting is the process of analyzing investment opportunities and deciding which ones to accept. (Pearson Education, 2007, 178). 2.1. INTRODUCTION OF CAPITAL BUDGETING

More information

MATH 425 EXERCISES G. BERKOLAIKO

MATH 425 EXERCISES G. BERKOLAIKO MATH 425 EXERCISES G. BERKOLAIKO 1. Definitions and basic properties of options and other derivatives 1.1. Summary. Definition of European call and put options, American call and put option, forward (futures)

More information

Web Extension: The Binomial Approach

Web Extension: The Binomial Approach 19878_06W_p001-009.qxd 3/10/06 9:53 AM Page 1 C H A P T E R 6 Web Extension: The Binomial Approach The example in the chapter illustrated the binomial approach. This extension explains the approach in

More information

MBF1243 Derivatives. L9: Exotic Options

MBF1243 Derivatives. L9: Exotic Options MBF1243 Derivatives L9: Exotic Options Types of Exotics Packages Nonstandard American options Forward start options Compound options Chooser options Barrier options Lookback options Shout options Asian

More information

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Decision Analysis

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Decision Analysis Resource Allocation and Decision Analysis (ECON 800) Spring 04 Foundations of Decision Analysis Reading: Decision Analysis (ECON 800 Coursepak, Page 5) Definitions and Concepts: Decision Analysis a logical

More information

MORAL HAZARD PAPER 8: CREDIT AND MICROFINANCE

MORAL HAZARD PAPER 8: CREDIT AND MICROFINANCE PAPER 8: CREDIT AND MICROFINANCE LECTURE 3 LECTURER: DR. KUMAR ANIKET Abstract. Ex ante moral hazard emanates from broadly two types of borrower s actions, project choice and effort choice. In loan contracts,

More information

MA300.2 Game Theory 2005, LSE

MA300.2 Game Theory 2005, LSE MA300.2 Game Theory 2005, LSE Answers to Problem Set 2 [1] (a) This is standard (we have even done it in class). The one-shot Cournot outputs can be computed to be A/3, while the payoff to each firm can

More information

NBER WORKING PAPER SERIES SUNK COSTS AND REAL OPTIONS IN ANTITRUST. Robert S. Pindyck. Working Paper

NBER WORKING PAPER SERIES SUNK COSTS AND REAL OPTIONS IN ANTITRUST. Robert S. Pindyck. Working Paper NBER WORKING PAPER SERIES SUNK COSTS AND REAL OPTIONS IN ANTITRUST Robert S. Pindyck Working Paper 11430 http://www.nber.org/papers/w11430 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue

More information

LET S GET REAL! Managing Strategic Investment in an Uncertain World: A Real Options Approach by Roger A. Morin, PhD

LET S GET REAL! Managing Strategic Investment in an Uncertain World: A Real Options Approach by Roger A. Morin, PhD LET S GET REAL! Managing Strategic Investment in an Uncertain World: A Real Options Approach by Roger A. Morin, PhD Robinson Economic Forecasting Conference J. Mack Robinson College of Business, Georgia

More information

Class Notes on Chaney (2008)

Class Notes on Chaney (2008) Class Notes on Chaney (2008) (With Krugman and Melitz along the Way) Econ 840-T.Holmes Model of Chaney AER (2008) As a first step, let s write down the elements of the Chaney model. asymmetric countries

More information

Valuation of Options: Theory

Valuation of Options: Theory Valuation of Options: Theory Valuation of Options:Theory Slide 1 of 49 Outline Payoffs from options Influences on value of options Value and volatility of asset ; time available Basic issues in valuation:

More information

Corporate Control. Itay Goldstein. Wharton School, University of Pennsylvania

Corporate Control. Itay Goldstein. Wharton School, University of Pennsylvania Corporate Control Itay Goldstein Wharton School, University of Pennsylvania 1 Managerial Discipline and Takeovers Managers often don t maximize the value of the firm; either because they are not capable

More information

Real Options: Creating and Capturing the Option Value in Regulated Assets

Real Options: Creating and Capturing the Option Value in Regulated Assets STRATEGIC CONSULTING Energy Real Options: Creating and Capturing the Option Value in Regulated Assets White Paper The fundamental insight is recognizing that faced with uncertainty, flexibility has value.

More information

Advanced Topics in Derivative Pricing Models. Topic 4 - Variance products and volatility derivatives

Advanced Topics in Derivative Pricing Models. Topic 4 - Variance products and volatility derivatives Advanced Topics in Derivative Pricing Models Topic 4 - Variance products and volatility derivatives 4.1 Volatility trading and replication of variance swaps 4.2 Volatility swaps 4.3 Pricing of discrete

More information

Corporate Finance, Module 3: Common Stock Valuation. Illustrative Test Questions and Practice Problems. (The attached PDF file has better formatting.

Corporate Finance, Module 3: Common Stock Valuation. Illustrative Test Questions and Practice Problems. (The attached PDF file has better formatting. Corporate Finance, Module 3: Common Stock Valuation Illustrative Test Questions and Practice Problems (The attached PDF file has better formatting.) These problems combine common stock valuation (module

More information

Option Pricing. Simple Arbitrage Relations. Payoffs to Call and Put Options. Black-Scholes Model. Put-Call Parity. Implied Volatility

Option Pricing. Simple Arbitrage Relations. Payoffs to Call and Put Options. Black-Scholes Model. Put-Call Parity. Implied Volatility Simple Arbitrage Relations Payoffs to Call and Put Options Black-Scholes Model Put-Call Parity Implied Volatility Option Pricing Options: Definitions A call option gives the buyer the right, but not the

More information

CHAPTER 1 Introduction to Derivative Instruments

CHAPTER 1 Introduction to Derivative Instruments CHAPTER 1 Introduction to Derivative Instruments In the past decades, we have witnessed the revolution in the trading of financial derivative securities in financial markets around the world. A derivative

More information

16 MAKING SIMPLE DECISIONS

16 MAKING SIMPLE DECISIONS 253 16 MAKING SIMPLE DECISIONS Let us associate each state S with a numeric utility U(S), which expresses the desirability of the state A nondeterministic action a will have possible outcome states Result(a)

More information

Binomial Trees. Liuren Wu. Zicklin School of Business, Baruch College. Options Markets

Binomial Trees. Liuren Wu. Zicklin School of Business, Baruch College. Options Markets Binomial Trees Liuren Wu Zicklin School of Business, Baruch College Options Markets Binomial tree represents a simple and yet universal method to price options. I am still searching for a numerically efficient,

More information

ECON4510 Finance Theory

ECON4510 Finance Theory ECON4510 Finance Theory Kjetil Storesletten Department of Economics University of Oslo April 2018 Kjetil Storesletten, Dept. of Economics, UiO ECON4510 Lecture 9 April 2018 1 / 22 Derivative assets By

More information

Module 3: Factor Models

Module 3: Factor Models Module 3: Factor Models (BUSFIN 4221 - Investments) Andrei S. Gonçalves 1 1 Finance Department The Ohio State University Fall 2016 1 Module 1 - The Demand for Capital 2 Module 1 - The Supply of Capital

More information

LECTURE 12. Volatility is the question on the B/S which assumes constant SD throughout the exercise period - The time series of implied volatility

LECTURE 12. Volatility is the question on the B/S which assumes constant SD throughout the exercise period - The time series of implied volatility LECTURE 12 Review Options C = S e -δt N (d1) X e it N (d2) P = X e it (1- N (d2)) S e -δt (1 - N (d1)) Volatility is the question on the B/S which assumes constant SD throughout the exercise period - The

More information

Lecture 13: The Equity Premium

Lecture 13: The Equity Premium Lecture 13: The Equity Premium October 27, 2016 Prof. Wyatt Brooks Types of Assets This can take many possible forms: Stocks: buy a fraction of a corporation Bonds: lend cash for repayment in the future

More information

CHAPTER 11. Proposed Project Data. Topics. Cash Flow Estimation and Risk Analysis. Estimating cash flows:

CHAPTER 11. Proposed Project Data. Topics. Cash Flow Estimation and Risk Analysis. Estimating cash flows: CHAPTER 11 Cash Flow Estimation and Risk Analysis 1 Topics Estimating cash flows: Relevant cash flows Working capital treatment Inflation Risk Analysis: Sensitivity Analysis, Scenario Analysis, and Simulation

More information

1.1 Interest rates Time value of money

1.1 Interest rates Time value of money Lecture 1 Pre- Derivatives Basics Stocks and bonds are referred to as underlying basic assets in financial markets. Nowadays, more and more derivatives are constructed and traded whose payoffs depend on

More information

Binomial Trees. Liuren Wu. Options Markets. Zicklin School of Business, Baruch College. Liuren Wu (Baruch ) Binomial Trees Options Markets 1 / 22

Binomial Trees. Liuren Wu. Options Markets. Zicklin School of Business, Baruch College. Liuren Wu (Baruch ) Binomial Trees Options Markets 1 / 22 Binomial Trees Liuren Wu Zicklin School of Business, Baruch College Options Markets Liuren Wu (Baruch ) Binomial Trees Options Markets 1 / 22 A simple binomial model Observation: The current stock price

More information

General Examination in Macroeconomic Theory. Fall 2010

General Examination in Macroeconomic Theory. Fall 2010 HARVARD UNIVERSITY DEPARTMENT OF ECONOMICS General Examination in Macroeconomic Theory Fall 2010 ----------------------------------------------------------------------------------------------------------------

More information

The Value of Petroleum Exploration under Uncertainty

The Value of Petroleum Exploration under Uncertainty Norwegian School of Economics Bergen, Fall 2014 The Value of Petroleum Exploration under Uncertainty A Real Options Approach Jone Helland Magnus Torgersen Supervisor: Michail Chronopoulos Master Thesis

More information

IMPA Commodities Course: Introduction

IMPA Commodities Course: Introduction IMPA Commodities Course: Introduction Sebastian Jaimungal sebastian.jaimungal@utoronto.ca Department of Statistics and Mathematical Finance Program, University of Toronto, Toronto, Canada http://www.utstat.utoronto.ca/sjaimung

More information

Valuation of Exit Strategy under Decaying Abandonment Value

Valuation of Exit Strategy under Decaying Abandonment Value Communications in Mathematical Finance, vol. 4, no., 05, 3-4 ISSN: 4-95X (print version), 4-968 (online) Scienpress Ltd, 05 Valuation of Exit Strategy under Decaying Abandonment Value Ming-Long Wang and

More information

Introduction to Real Options

Introduction to Real Options IEOR E4706: Foundations of Financial Engineering c 2016 by Martin Haugh Introduction to Real Options We introduce real options and discuss some of the issues and solution methods that arise when tackling

More information

Reading map : Structure of the market Measurement problems. It may simply reflect the profitability of the industry

Reading map : Structure of the market Measurement problems. It may simply reflect the profitability of the industry Reading map : The structure-conduct-performance paradigm is discussed in Chapter 8 of the Carlton & Perloff text book. We have followed the chapter somewhat closely in this case, and covered pages 244-259

More information

Additional Lecture Notes

Additional Lecture Notes Additional Lecture Notes Lecture 3: Information, Options, & Costs Overview The purposes of this lecture are (i) to determine the value of information; (ii) to introduce real options; and (iii) begin our

More information

ECONOMICS 103. Topic 7: Producer Theory - costs and competition revisited

ECONOMICS 103. Topic 7: Producer Theory - costs and competition revisited ECONOMICS 103 Topic 7: Producer Theory - costs and competition revisited (Supply theory details) Fixed versus variable factors; fixed versus variable costs. The long run versus the short run. Marginal

More information

Investments Background and Introduction. I. Course Objectives to address the following Questions:

Investments Background and Introduction. I. Course Objectives to address the following Questions: Investments Background and Introduction I. Course Objectives to address the following Questions: A. Basic questions: Why do people and firms invest? What investments are available? How do you choose? How

More information

Math 5760/6890 Introduction to Mathematical Finance

Math 5760/6890 Introduction to Mathematical Finance Math 5760/6890 Introduction to Mathematical Finance Instructor: Jingyi Zhu Office: LCB 335 Telephone:581-3236 E-mail: zhu@math.utah.edu Class web page: www.math.utah.edu/~zhu/5760_12f.html What you should

More information

SAMPLE FINAL QUESTIONS. William L. Silber

SAMPLE FINAL QUESTIONS. William L. Silber SAMPLE FINAL QUESTIONS William L. Silber HOW TO PREPARE FOR THE FINAL: 1. Study in a group 2. Review the concept questions in the Before and After book 3. When you review the questions listed below, make

More information