FNCE4830 Investment Banking Seminar Introduction on Derivatives What is a Derivative? A derivative is an instrument whose value depends on, or is derived from, the value of another asset. Examples: Futures Forwards Swaps Options Exotics
Why Derivatives Are Important Key role in transferring risks in the economy Underlying assets include stocks, currencies, interest rates, commodities, debt instruments, electricity, insurance payouts, weather, etc. Many financial transactions have embedded derivatives The real options approach to assessing capital investment decisions has become widely accepted How Derivatives Are Traded On exchanges such as the Chicago Board Options Exchange In the over-the-counter (OTC) market where traders working for banks, fund managers and corporate treasurers contact each other directly
Growth of OTC Market by Product How Derivatives are Used To hedge risks e.g. you are a producer of oil or a consumer of soy beans, or are paid in a different currency To speculate (take a view on the future direction of the market) To lock in an arbitrage profit To change the nature of a liability To change the nature of an investment without incurring the costs of selling one portfolio and buying another
Speculation Example You have $2,000 to invest You believe that a stock price will increase over the next 2 months The current stock price is $20 The price of a 2-month call option with a strike of 22.50 is $1 What are the alternative strategies? Arbitrage Example A stock price is quoted both in London and in New York. The prices are: 100 in London $160 in New York The current exchange rate is 1.55 (ask yourself what are the units of that figure) Is there an arbitrage opportunity? If so what is it? (get the direction right!)
Dangers Traders can switch from being hedgers to speculators or from being arbitrageurs to speculators It is important to set up controls to ensure that trades are using derivatives in for their intended purpose SocGen is an example of what can go wrong Linear payout Forwards
Forward Price DEFINITION: the delivery price that would be applicable to the contract if negotiated today (i.e. the delivery price that would make the contract worth exactly zero today) The forward price may (and will likely) be different for contracts of different maturities Some Terminology (more to come) The party that has agreed to buy has a long position The party that has agreed to sell has a short position Selling a derivative is sometimes referred to writing a derivative (forwards, options, etc.) The contract delivery date is sometimes referred to expiration date, or maturity date
Forward Example The treasurer of a corporation enters into a long forward contract to buy 1 million in six months at an exchange rate of 1.6115 This contract obligates the corporation to pay $1,611,500 for 1 million on the maturity date (July 10, 2013) What are the possible outcomes? Profit from a Long Forward K = delivery price = forward price at time contract was entered into Profit K Price of Underlying at Maturity,
Profit from a Short Forward K = delivery price = forward price at time contract was entered into Profit K Price of Underlying at Maturity, PV of a Forward K delivery price that was agreed F current forward price for that maturity r continuously compounded interest rate T maturity of the forward Long forward Short forward
Linear payout Futures Contracts Futures Contracts Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract, but there are Differences: A forward contract is traded OTC, a futures contract is traded on an exchange A futures contract requires daily settlement of the value of the contract, a forward contract has a cash flow only a maturity WARNING This is what the book says but it is not strictly true. More on this later.
Exchanges Trading Futures CME Group (formerly Chicago Mercantile Exchange and Chicago Board of Trade) NYSE Euronext BM&F (Sao Paulo, Brazil) TIFFE (Tokyo) and many more (see list at end of Hull book) Examples of Futures Contracts You think gold will appreciate during the year: Buy 100 oz. of gold @ 1108 $/oz in Dec. You will receive GBP in March but want USD: Sell 62,500 @ 1.55 US$/ in March You are an oil producer and want to hedge: Sell 1,000 bbl. of oil @ 48 $/bbl in April You are a soybean buyer looking to lock your input costs: Buy 1mm bushels of soybean in 6m
Types of Traders Hedgers use derivatives to mitigate the risk they are already exposed to, coming from their business or assets/liabilities Speculators use derivatives to express a view often with leverage on a financial sector/asset Arbitrageurs use derivatives to lock in a specific payout for a risk-free profit Linear payout (caveat) Swaps
Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules Typically swaps have two legs as there are two parties swapping cash flows Counterparty A Cash flow Cash flow Counterparty B Vanilla Interest Rate Swap An agreement to swap fixed rate cash flows for floating cash flows over a specified period of time Tenor determines how often payments are made In the US floating payments are generally every 3 months Fixed payments are made every 6 months Floating cash flows reference a trusted benchmark rate e.g. LIBOR Generally the reference rate is fixed at the beginning of a period and paid at the end
Typical Uses of an Int. Rate Swap Converting a liability from fixed rate to floating rate floating rate to fixed rate Converting an investment from fixed rate to floating rate floating rate to fixed rate E.g. Plain Vanilla Int. Rate Swap An agreement by Microsoft to receive 6-month LIBOR pay a fixed rate of 5% per annum every 6 months Start date: tomorrow Maturity: 3 years Notional: $100m
Microsoft swap Fixed for Floating Microsoft enter an interest rate swap Notional: 100m Maturity: 3 years Semi-annual payments Receive Fixed: 5% Pay Floating: 6 Month USD LIBOR 2.5% 2.5% 2.5% 2.5% 2.5% 2.5% 0.5y 1y 1.5y 2y 2.5y 3y 6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR Confirmations Confirmations specify the terms of a transaction The International Swaps and Derivatives Association (ISDA) has developed Master Agreements that can be used to cover all agreements between two counterparties Governments now require central clearing to be used for most standardized derivatives
Interest Rate Swaps Valuation Initially, interest rate swaps are often worth zero (caveats) At later times, they can be valued as the difference between the value of a fixed-rate bond, and that of a floating-rate bond The fixed rate bond is valued in the usual way The floating rate bond is valued by noting that it is worth par immediately after the next payment date Other types of swaps Credit Default Swaps (CDS, more on this later in the course) Currency Swaps Commodity Swaps Mortgage Swaps Equity Swaps (on price or dividends) Variance Swaps Etc.
Non-linear payout Options Basic Option Terminology An option gives the holder the right but not the obligation to buy(sell) the underlying asset at some time or times in the future.
Futures/Forwards vs. Options A futures/forward contract gives the holder the obligation to buy or sell at a certain price An option contract gives the holder the right to buy or sell at a certain price Hedging Examples (pages 10-12) A US company will pay 10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract An investor owns 1,000 Microsoft shares currently worth $43 per share. A two-month put with a strike price of $40 costs $1. The investor decides to hedge by buying 10 contracts
Underlying Assets Stocks Currencies Stock Indices (not indexes) Futures Commodities (individual and index) Interest Rates (swaptions) Credit products (credit default swaptions) Etc. Option Types A Call option is an option to buy a certain asset by a certain date for a certain price (the strike price) A Put option is an option to sell a certain asset by a certain date for a certain price (the strike price)
Options Style An American option can be exercised at any time during its life A European option can be exercised only at maturity A Bermudan option can be exercised only at fixed times before maturity (e.g. monthly) Options Specs Expiration date Strike price (or Exercise price) European or American (option style) Call or Put (option class or type) Delivery details Cash or Physical delivery
Warrants Warrants are options that are issued by a corporation or a financial institution They are often issued as a sweetener during a bond issue They are options that can be exchanged into shares of the company Generally American style Typically companies issue new shares when warrants are exercised There is a dilution effect when warrants are exercised as the company issues new shares Dilution effect Assume a company has n shares outstanding at a price of S Assume the company has m warrants outstanding with an exercise price of K If all warrants are exercised then the number of shares outstanding will become m+n The expected share price will be: n S m K n m
Corporate Actions For equity options corporate actions can change the terms of an option contract The general principal is that things that are known and predictable do not affect the terms of an option Events that are not expected are handled so as to minimize the impact on option holders Generally dividends do not affect the terms of an option contract Note: dividends do affect the value of the option Special Dividends If a company announces a special dividend the strike of an option is generally adjusted down to reflect the amount of the dividend For example, on July 20, 2004 Microsoft announced a $3 special dividend If you were holding a $30 call then the strike would be adjusted to $27 The distribution of a regular dividend would not translate into a strike adjustment
Stock Splits Suppose you own N options with a strike price of K: When there is an n-for-m stock split: the strike price changes to K x m/n the number of options changes to N x n/m Consider a call option to buy 100 shares for $20/share How should terms be adjusted for a 2-for-1 stock split? Mergers and Acquisitions This can be very complicated Suppose an all cash offer is made for XYZ corporation at $10 per share If you own a call option to buy 1 share of XYZ at $6 that expires after the merger date then you will receive $10-$6 =$4
Principal Protected Note Allows investor to take a risky position without risking any principal Example: $1000 instrument consisting of 3-year zero-coupon bond with principal of $1000 3-year at-the-money call option on a stock portfolio currently worth $1000 Principal Protected Notes (continued) Viability depends on Level of dividends Level of interest rates Volatility of the portfolio Variations on standard product Out of the money strike price Caps on investor return Knock outs, averaging features, etc
Mechanics of Options Markets Diagrams A common technique for understanding options is to draw a payoff diagram This will usually show the value of the option at maturity Note you will see payoff diagrams that deduct the the premium paid from the payoff Many diagrams in the Hull book do this Generally this is frowned upon in the industry, because you are adding values at different times The following slides will chart just payoffs
Long Call Option 6 for a European Call option with a strike of $5 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Terminal Asset Price Short Call Option for a European Call option with a strike of $5 0 0 1 2 3 4 5 6 7 8 9 10-1 -2-3 -4-5 -6 Terminal Asset Price
Long Put Option 6 for a European Put option with a strike of $5 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Terminal Asset Price Short Put Option for a European Put option with a strike of $5 0 0 1 2 3 4 5 6 7 8 9 10-1 -2-3 -4-5 -6 Terminal Asset Price
s from Options What is the option position? K = Strike price, = Price of asset at maturity K K K K Terminology Moneyness: At-The-Money (ATM) option The underlying is trading at the strike price In-The-Money (ITM) option The underlying is trading above the strike price Out-of-The-Money (OTM) option The underlying is trading below the strike price
Long Call Option at Maturity is 6 for a European Call option with a strike of $5 5 4 3 2 In the money 1 Out of the? money At the money 0 0 1 2 3 4 5 6 7 8 9 10 Terminal Stock Price More Trading Strategies Involving Options
Strategies to be Considered Bond + option principal protected note Underlying asset, plus option Two or more options of the same type (a spread) Two or more options of different types (a combination) Two (or more) options of same type at different maturities (a calendar spread) Option + Underlying The resulting payoff is represented in red K K (a) +Stock Call (b) Stock + Call K K (c) +Stock +Put (d) Stock Put
Option + Forward The resulting payoff is represented in red K K (a) +Fwd Call (b) Fwd + Call K K (c) +Fwd +Put (d) Fwd Put Bull Spread Using Calls The resulting payoff is represented in red =? K 1 K 2
Bull Spread Using Puts The resulting payoff is represented in red K 1 K 2?= Bear Spread Using Puts The resulting payoff is represented in red?= K 1 K 2
Bear Spread Using Calls The resulting payoff is represented in red K 1 K 2 =? Box Spread A Bull Call Spread + a Bear Put Spread of European options. Price = PV(K 2 K 1 ) K 2 K 2 -K 1 = const = K 2 K 1 -K 1 K 1 K 2 The resulting payoff is represented in red
Butterfly Spread Using Calls NOTE: K 2 = Average(K 1, K 3 ) You need to short 2 calls @ K 2 Max payout =? K 1 K 2 K 3 The resulting payoff is represented in red Butterfly Spread Using Puts NOTE: K 2 = Average(K 1, K 3 ) You need to short 2 puts @ K 2 Max payout =? K 1 K 2 K 3 The resulting payoff is represented in red
Other Patterns When the strike prices are close together a butterfly spread provides a payoff consisting of a small spike If options with all strike prices were available any payoff pattern could (at least approximately) be created by combining the spikes obtained from different butterfly spreads A Straddle Combination?= K
A Strangle Combination?= Payout K 1 K 2 Test your understanding Build the following strategies by combining puts and calls
Build the strategy below 12 Portfolio 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Build the strategy below 0 Portfolio 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10 12
Build the strategy below 20 Portfolio 15 10 5 0 5 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 10 15 20 Build the strategy below 15 Portfolio 10 5 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 5 10 15
Build the strategy below 6 Portfolio 4 2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 Build the strategy below 10 Portfolio 5 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 5 10 15 20
Build the strategy below 6 Portfolio 5 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Build the strategy below 6 Portfolio 5 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Build the strategy below 1.2 Portfolio 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Build the strategy below 1.2 Portfolio 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30