A comprehensive mathematical approach to exotic option pricing

This work illustrates how several new pricing expressions for exotic options can be derived within a Levy framework by employing a unique pricing expression. To the purpose, a unifying formula is obtained by solving some nested Cauchy problem for pseudodifferential equations generalizing BlackScholes PDE. The main result extends (Agliardi R. The quintessential option pricing formula under Levy processes. Applied Mathematics Letters 2009; 22:1626-1631) and is a powerful tool for generating new valuation expressions. Several examples of pricing formulas under the Levy processes are provided to illustrate the flexibility of the method. Some of them are new in the financial literature. Finally, many existing pricing formulas of the traditional Gaussian model are easily obtained as a by-product. Copyright (c) 2012 John Wiley & Sons, Ltd.