The Pricing and Hedging of Options in Finitely Elastic Markets

Standard derivative pricing theory is based on the assumption of the market for the underlying asset being infinitely elastic. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative contract. Our analysis extends a prior work of Jarrow who has analyzed this question in a binomial setting to economies with continuous security trading. We characterize the solution to the hedge problem in terms of a nonlinear partial differential equation and provide results on existence and uniqueness of this equation. Simulations are used to compare the hedge ratio in our model to standard Black-Scholes strategies. Moreover, we discuss how standard option pricing theory can be extended to finitely elastic markets.