Option pricing in continuous time

Le résumé fourni par la source

This chapter showed how to determine the fair value of derivative securities whose payoff depends on the future value of an underlying asset. The central principle is that we can construct a self-financing portfolio that matches this payoff. Then, in a well-functioning market with no-arbitrage opportunities, the value of this portfolio should equate to the derivative price at all times. The outcome is the risk-neutral pricing formula where the derivative price is the discounted expected payoff under the risk-neutral measure. The risk-neutral measure is the measure under which the discounted asset price is a martingale. Girsanov’s theorem tells us how to find this probability measure. Then the discounted derivative price is also a martingale and the risk-neutral pricing formula follows. In the Black-Scholes model, there is a unique risk-neutral measure and hence one unique price for all options. This is not true in all mathematical models for option pricing. There may be multiple risk-neutral measures and hence multiple option prices for some derivatives. Another possibility is that there is no risk-neutral measure and no option price.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.