UNIVERSITY OFESSEXDEPARTMENT OFECONOMICSEC372 Economics of Bond and Derivatives MarketsOption PricingHow to Derive an Option Price Formula1. Make assumptions, most importantly about: (i) frictionless markets, (ii) about deter-mination of the underlying asset price in the future.12. Propose an arbitrage portfolio, comprising options, the underlying asset and risk-freeborrowing (or lending): (a) zero initial outlay, and (b) non-negative payoff in everyeventuality (state of the world).3. In market equilibrium, the arbitrage portfolio has azeropayoff in every state.24. Derive an option price formula from the conditions that define an arbitrage portfoliotogether with the absence of arbitrage opportunities:c=f(S, X, τ, R, σ)(see chapter 19 ofEconomics of Financial Marketsfor notation).Numerical Example1. Assume: frictionless markets, that today’s underlying asset price,S= 80; thatSwill change after one time period to exactly one of two valuesuS= 128(state 1) ordS= 48
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