Lecture23

Lecture23 - Investor writes one call and buys H shares of...

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Lecture 23 : Options Markets Economics 252, Spring 2008 Prof. Robert Shiller, Yale University
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Put-Call Parity Relation • Put option price – call option price = present value of strike price + present value of dividends – price of stock • For European options, this formula must hold (up to small deviations due to transactions costs), otherwise there would be arbitrage profit opportunities
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Binomial Option Pricing S = current stock price u = 1+fraction of change in stock price if price goes up d = 1+fraction of change in stock price if price goes down r = risk-free interest rate
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Binomial Option Pricing, Cont. C = current price of call option C u = value of call next period if price is up C d = value of call next period if price is down E = strike price of option H = hedge ratio, number of shares purchased per call sold
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Hedging by writing calls
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Unformatted text preview: Investor writes one call and buys H shares of underlying stock If price goes up, will be worth uHS-C u If price goes down, worth dHS-C d For what H are these two the same? Binomial Option Pricing Formula One invested HS-C to achieve riskless return, hence the return must equal (1+ r) ( HS-C ) (1+ r )( HS-C )= uHS-C u = dHS-C d Subst for H , then solve for C Black-Scholes Option Pricing Call T the time to exercise, 2 the variance of one-period price change (as fraction) and N(x) the standard cumulative normal distribution function (sigmoid curve, integral of normal bell-shaped curve) =normdist(x,0,1,1) Excel (x, mean,standard_dev, 0 for density, 1 for cum.) Black-Scholes Formula Actual S&P500 Volatility Monthly July1871- April 2008 Implied and Actual Volatility Monthly Jan 1986-April 2008...
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This note was uploaded on 02/08/2012 for the course ECON 252 taught by Professor Robertshiller during the Spring '08 term at Yale.

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Lecture23 - Investor writes one call and buys H shares of...

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