Overview. Greek Letters Finite i differences and PDEs Estimating volas and correlations FFT and Moment generating functions

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1 Overview Basics of Forwards, Futures, and Options Introduction to C++, basic facilities Properties of Stock Option Prices & trading strategies Trees for Option Pricing Classes in C++ C++ && Random Number Generation Model of Stock Price Behavior and Black Scholes Implementing Trees and dmonte Carlo Methods in C++ Greek Letters Finite i differences and PDEs Estimating volas and correlations FFT and Moment generating functions

2 Mechanics of ffutures Markets Chapter 2 Derivatives, 7th Edition, Copyright 2

3 Futures Contracts Available on a wide range of assets Exchange traded Specifications need to be defined: What can be delivered, Where it can be delivered, & When it can be delivered Settled daily 3

4 Margins A margin is cash or marketable securities deposited by an investor with his or her broker The balance in the margin account is adjusted d to reflect daily settlement t Margins minimize the possibility of a loss through h a default on a contract t 4

5 Example of a Futures Trade (page 26-28) An investor takes a long position in 2 December gold futures contracts on June 5 contract size is 100 oz. futures price is US$600 margin requirement is US$2,000/contract (US$4,000 in total) maintenance margin is US$1,500/contract (US$3,000 in total) 5

6 A Possible Outcome Table 2.1, Page 28 Daily Cumulative Margin Futures Gain Gain Account Margin Price (Loss) (Loss) Balance Call Day (US$) (US$) (US$) (US$) (US$) ,000 5-Jun (600) (600) 3, Jun (420) (1,340) 2,660 1, Jun (1,140) (2,600) 2,740 1, Jun (1,540) 5,060 0 = 4,000 < 3,000 = 4,000 6

7 Other Key Points About Futures They are settled daily Closing out a futures position involves entering into an offsetting trade Most contracts are closed out before maturity 7

8 Collateralization in OTC Markets It is becoming increasingly common for contracts to be collateralized in OTC markets They are then similar to futures contracts in that they are settled regularly (e.g. every day or every week) 8

9 Futures Prices for Gold on Jan 8, 2007: Prices Increase with Maturity (Figure 2.2a, page 33) 650 oz) Futures Price ($ per Contract Maturity Month 600 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 9

10 Futures Prices for Orange Juice on January 8, 2007: Prices Decrease with Maturity (Figure 2.2b, page 33) Futures Pr rice (cents per lb) Contract Maturity Month 170 Jan-07 Mar-07 May-07 Jul-07 Sep-07 Nov-07 10

11 Delivery If a futures contract is not closed out before maturity, it is usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. A few contracts (for example, those on stock indices and Eurodollars) are settled in cash 11

12 Some Terminology Open interest: the total number of contracts outstanding equal to number of long positions or number of short positions Settlement price: the price just before the final bell each day used for the daily settlement process Volume of trading: the number of trades in 1 day 12

13 Convergence of Futures to Spot (Figure 2.1, page 26) Futures Price Spot Price Spot tprice Futures Price (a) Time (b) Time 13

14 Questions When a new trade is completed what are the possible effects on the open interest? Can the volume of trading in a day be greater than the open interest? 14

15 Regulation of Futures Regulation is designed to protect the public interest Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups 15

16 Accounting & Tax Ideally hedging g profits (losses) should be recognized at the same time as the losses (profits) on the item being hedged Ideally profits and losses from speculation should be recognized on a mark-to-market basis Roughly speaking, this is what the accounting and tax treatment of futures in the U.S. and many other countries attempts to achieve 16

17 Forward Contracts vs Futures TABLE 2.3 (p. 39) Contracts FORWARDS Private contract between 2 parties Non-standard contract FUTURES Exchange traded Standard contract Usually 1 specified ed delivery date Range of delivery dates Settled at end of contract Delivery or final cash settlement usually occurs Some credit risk Settled daily Contract usually closed out prior to maturity Virtually no credit risk 17

18 Foreign Exchange Quotes Futures exchange rates are quoted as the number of USD per unit of the foreign currency Forward exchange rates are quoted in the same way as spot exchange rates. This means that GBP, EUR, AUD, and NZD are quoted as USD per unit of foreign currency. Other currencies (e.g., CAD and JPY) are quoted as units of the foreign currency per USD. 18

19 Homework 1. C++ Program zur Bewertung eines Futures: Eingabe von Spot, Zinsrate, Future price. Gibt es ein Arbitragemoeglichkeit? 2. Beruecksichtigung von Lagerungskosten 3. Bewertung von Futures in einer anderen Waehrung mit unterschiedlichen h Zinsraten. Teilen sie die Aufgaben sinnvoll in unterschiedliche Funktionen auf und verwenden Sie struct.

MBF1243 Derivatives Prepared by Dr Khairul Anuar. Lecture 2 Mechanics of Futures Markets

MBF1243 Derivatives Prepared by Dr Khairul Anuar Lecture 2 Mechanics of Futures Markets Specification of Futures Contracts Available on a wide range of assets Exchange traded Specifications need to be