FBE459_3_7_Exotic_Options

FBE459_3_7_Exotic_Options - FBE 459 Financial Derivatives...

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FBE 459 – Financial Derivatives Prof. Pedro Matos Lecture 3.7. : “Non-Vanilla”/ Exotic Options Extensions of Black-Scholes: Options on Dividend-paying Stocks, Currency and Futures Exotic Options Readings: HULL chapter 15, 24
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2 Lecture Outline Extension of Black-Scholes formula: - Option on Dividend-paying Stocks - Options on Stock Indices - Currency Options - Options on Futures Exotic Options: - Compound, Barrier, Lookback, … Interest Rate Options: - Callable Bonds - Swaptions
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3 Extensions on Black-Scholes Formula
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4 Options on Dividend-Paying Stocks . Example: A European call on the S&P 500 index has a strike of 900 and matures in 77 days. The S&P 500 index has a current price of 1076, a dividend yield of 1.23% and a volatility of 35%. The riskless rate is 2.20% (all rates are annualised and continuously compounded). What is the option’s price?
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5 Options on Dividend-Paying Stocks . Ex. (cont.): Using Black-Scholes d 1 = d 2 = N(d 1 ) = N(d 2 ) = c =
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6 Options on Dividend-Paying Stocks Ex. (cont.): sheet “Black_Scholes (2)” of FBE459_3_5_BlackScholes.xls
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7 Options on Dividend-Paying Stocks . Ex. (cont.): What would be the value of American put on the S&P 500 index with a strike of 900 and maturing in 77 days? -> use Binomial model !
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8 Options on Dividend-Paying Stocks . Ex. (cont.): Valuing American put using Binomial model -> Build n=4 binomial tree: - time increment T = (77/365)/4 = 0.05 ( n = 4) - up and down steps (* see lecture 3.4 *) - compute risk-neutral probabilities
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9 Options on Dividend-Paying Stocks . Ex. (cont.): Valuing American put using Binomial model -> tree for S&P500 index -> tree for American put (optimal not to exercise early) see FBE459_3_7_American_Put_w_Dividends.xls
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10 Options on Dividend-Paying Stocks If lumpy dividends (known in advance) : . Extending the Black-Scholes formula: Subtract the PV(dividends in life of option) from the underlying price: S* = S - PV(D). Then apply the B-S formula to S*. . Extending the Binomial risk-neutral pricing formula:
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FBE459_3_7_Exotic_Options - FBE 459 Financial Derivatives...

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