Integral price formulas for lookback options. (English) Zbl 1186.91222

Summary: We derive an integral representation of the price formulas for European options whose terminal payoff involves path-dependent lookback variable. The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. We also derive a parity relation between the price functions of the floating strike and fixed strike lookback options.


91G20 Derivative securities (option pricing, hedging, etc.)
26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
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