Analytical Valuation of Lookback and Russian Options in a Double-Exponential Jump-Diffusion Model

Abstract:     
We derive explicit formulas for pricing a number of lookback options under a double-exponential jump diffusion. Assuming risk-neutrality, the value of a lookback option satisfies the generalized Black-Scholes equation with the appropriate boundary and final conditions. We take the Laplace transform of this equation in time and solve it explicitly. Option price and risk parameters are computed via the numerical inversion of the corresponding solution in Laplace domain. Numerical examples reveal that the pricing formulas are easy to implement and they result in accurate prices and risk parameters. Proposed formulas allow fast computing of smile-consistent prices of floating/fixed strike lookback call and put options.

Number of Pages in PDF File: 18

Keywords: jump diffusion processes, exponential jumps, volatility smile, option pricing, path-dependent options, lookback options, Russian options, Laplace transform

JEL Classification: C00,G00

working papers series