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Unformatted text preview: EC372 Bond and Derivatives Markets Options II: Price determination R. E. Bailey Department of Economics University of Essex University week 21 EC372 Bond and Derivatives Markets Options II Topic #6 Outline 1 Option prices: fundamentals 2 Twostate optionpricing model Numerical example: call option Multiple time periods to expiry 3 The BlackScholes model Volatility 4 Contingent claims analysis Reading: Economics of Financial Markets , chapter 19 EC372 Bond and Derivatives Markets Options II Topic #6 Outline Option prices: fundamentals Option prices: fundamentals I Goal: a formula for the option price: c = f ( S , X , τ, R , σ ) I c = European call option premium I S = underlying asset (stock) price I X = exercise price I τ = time to expiry ( T t ) I R = interest factor, typically written R = e r τ I σ = volatility of the underlying asset’s rate of return I The formula links c with S : it provides a partial theory I Assumptions: I Frictionless markets 1 Zero transactions costs 2 Unlimited borrowing and lending at riskfree interest rate 3 No restrictions on shortselling 4 Perfect divisibility of underlying asset I Options contracts 1 Stock pays no dividends and is protected against stock splits 2 Option is European EC372 Bond and Derivatives Markets Options II Topic #6 Outline Option prices: fundamentals Option prices: fundamentals I Goal: a formula for the option price: c = f ( S , X , τ, R , σ ) I c = European call option premium I S = underlying asset (stock) price I X = exercise price I τ = time to expiry ( T t ) I R = interest factor, typically written R = e r τ I σ = volatility of the underlying asset’s rate of return I The formula links c with S : it provides a partial theory I Assumptions: I Frictionless markets 1 Zero transactions costs 2 Unlimited borrowing and lending at riskfree interest rate 3 No restrictions on shortselling 4 Perfect divisibility of underlying asset I Options contracts 1 Stock pays no dividends and is protected against stock splits 2 Option is European EC372 Bond and Derivatives Markets Options II Topic #6 Outline Option prices: fundamentals Option prices: fundamentals I Goal: a formula for the option price: c = f ( S , X , τ, R , σ ) I c = European call option premium I S = underlying asset (stock) price I X = exercise price I τ = time to expiry ( T t ) I R = interest factor, typically written R = e r τ I σ = volatility of the underlying asset’s rate of return I The formula links c with S : it provides a partial theory I Assumptions: I Frictionless markets 1 Zero transactions costs 2 Unlimited borrowing and lending at riskfree interest rate 3 No restrictions on shortselling 4 Perfect divisibility of underlying asset I Options contracts 1 Stock pays no dividends and is protected against stock splits 2 Option is European EC372 Bond and Derivatives Markets Options II Topic #6 Outline Option prices: fundamentals Option prices: fundamentals I Goal: a formula for the option price: c = f ( S ,...
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 Spring '12
 R.E.Bailey
 Economics, Options, Strike price, Derivatives Markets

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