L3 Pricing of Futures and Forwards

L3 Pricing of Futures and Forwards - 1 Determination of...

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Unformatted text preview: 1 Determination of Forward and Futures Prices Chapters 4.1, 4.2 and Chapter 5 2 AGENDA: Short selling strategy; Measuring interest rates; Determination of forward price for assets: that do not have an interim cash flow; that have a known interim cash flow; that provide a know yield; Valuing a forward contract; Futures on commodities; Future prices and expected spot prices. 3 Consumption vs. Investment Assets Investment assets are assets held by significant numbers of people purely for investment purposes (Examples: gold, silver, stocks, bonds) Consumption assets are assets held primarily for consumption (Examples: copper, oil, corn) 4 Short sale Short sale means selling of securities borrowed from your broker; Your broker borrows the securities from another client and sells them in the market in the usual way; Investors profit from price declines in short sales. Short-sellers must replace the shares as well as any dividends paid during the short period. Short-sellers may have to replace the shares on demand. ( 29 Dividend price Ending price Initial Profit +- = Example on short sale: Suppose you borrowed 100 Morgan Stanley (MS) shares from your broker and sold them for $16.04 a share at the end of 2008. Your broker requires 50% initial margin in short sales which you covered using the T-bills in your account. MS paid a dividend of $0.437 a share during 2009. (a) What was your profit if you covered your short position at the end of 2009 when MS was trading at $29.60 a share? (b) If your broker had a 30% maintenance margin requirement, how far could MS rise to before you received a margin call? (c) How much money would you have to put into your account in order to satisfy the maintenance margin requirement if MS suddenly jumped to $23 a share? 5 Example on short sale 6 ( 29 ( 29 ( 29 584 $ Add % 30 100 23 $ Add 100 23 $ 802 $ 100 04 . 16 $ (c) 51 . 18 $ * % 30 100 * 100 * 802 $ 100 04 . 16 $ 802 $ 5 . 100 04 . 16 $ bills- T of Value (b) 70 . 399 , 1 $ 100 437 . $ 60 . 29 $ 04 . 16 $ Profit (a) Dividend price Ending price Initial = = + - + = = - + = =- = +- = P P P 7 Measuring Interest Rates The difference between quarterly and annual compounding is analogous to the difference between miles and kilometers; A(1+R) n A(1+R/m) mn 8 Measuring Interest Rates The compounding frequency used for an interest rate is the unit of measurement; A(1+R) n A(1+R/m) mn A amount, R Interest rate, n years, m- times per year Example: m = 1 100$(1.1) = 110$ m = 2 100$ (1.05) 2 = 110.25$ m = 4 100$(1.025) 4 = 110.38$ m = 360 100$(1.1/360) 360 = 110.52$ Continuous compounding can be thought of as being equivalent to daily compounding . 9 Continuous Compounding In the limit as we compound more and more...
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L3 Pricing of Futures and Forwards - 1 Determination of...

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