THE INVERSE PROBLEM OF OPTION PRICING

Valuation of options and other financial derivatives critically depend s on the underlying stochastic process specified for a particular mark et. An inverse problem of option pricing is to determine the nature of this stochastic process, namely, the distribution of expected asset r eturns implied by current market prices of options with different stri kes. We give a rigorous mathematical formulation of this inverse probl em, establish uniqueness, and suggest an efficient numerical solution. We apply the method to the S&P 500 Index and conclude that the index is negatively skewed with a higher probability of the sudden decline o f the US stock market.