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option_price_example - U NIVERSITY OF E SSEX D EPARTMENT OF...

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U NIVERSITY OF E SSEX D EPARTMENT OF E CONOMICS EC372 Economics of Bond and Derivatives Markets Option Pricing How to Derive an Option Price Formula 1. Make assumptions, most importantly about: (i) frictionless markets, (ii) about deter- mination of the underlying asset price in the future. 1 2. Propose an arbitrage portfolio, comprising options, the underlying asset and risk-free borrowing (or lending): (a) zero initial outlay, and (b) non-negative payoff in every eventuality (state of the world). 3. In market equilibrium, the arbitrage portfolio has a zero payoff in every state. 2 4. Derive an option price formula from the conditions that define an arbitrage portfolio together with the absence of arbitrage opportunities: c = f ( S, X, τ, R, σ ) (see chapter 19 of Economics of Financial Markets for notation). Numerical Example 1. Assume: frictionless markets, that today’s underlying asset price, S = 80 ; that S will change after one time period to exactly one of two values uS = 128 (state 1) or dS = 48
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