A Universal Model for Pricing All Options

Abstract

This paper presents a new option pricing approach for all underlying assets that precisely fits the market data. We obtain the probability density function of the underlying asset without any external parameter. The density function for a given expiration date is uniquely determined by the prices of three options with different strikes but the same expiration. Our approach allows for the calculation of path dependent options as we are able to calculate the contingent density function of the underlying asset between subsequent expiries as a function of the underlying asset price. The new model accurately matches market option prices in all asset classes (currencies, interest rates, equities and commodities) including exotic options.

Keywords: Volatility smile, volatility surface, implied volatility, valuation of path dependent options, option pricing, exotic options, option valuation, implied stochastic process, conditional density function, path integral representation of options, continuous time finance

JEL Classification: C51, C52, C58, C61, G12, G13