Analytical Green's Function Approximation and Option Pricing - Cheng, Wen
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Closed-form solutions to Kolmogorov type equations are very important in many application areas, such as derivative pricing, quantum mechanics, statistical physics, etc. However, they are only available for some very special equations. This book considers general second order parabolic equations with coefficients that are dependent on both time and space. It extends the recently developed Dyson-Taylor commutator method for autonomous equations to non-autonomous equations. Closed-form approximations of the Green's functions that are accurate to any prescribed order are obtained. Consequently,…mehr

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Produktbeschreibung
Closed-form solutions to Kolmogorov type equations are very important in many application areas, such as derivative pricing, quantum mechanics, statistical physics, etc. However, they are only available for some very special equations. This book considers general second order parabolic equations with coefficients that are dependent on both time and space. It extends the recently developed Dyson-Taylor commutator method for autonomous equations to non-autonomous equations. Closed-form approximations of the Green's functions that are accurate to any prescribed order are obtained. Consequently, the solutions to second order parabolic equations can be obtained by integrating the approximated Green's functions against initial data. For applications, this book considers Local Volatility models and Stochastic Volatility models that appear in option pricing theory, gives explicit formulas for European option prices, and carries out numerical tests for such formulas.
Autorenporträt
Wen Cheng received her Master of Science and Doctor of Philosophy in Experimental Psychology from the University of Texas at Arlington in 2008 and 2011 respectively. She currently works as a postdoctoral research fellow at the Center for Learning Assessment Service in National Tsing Hua University in Hsinchu, Taiwan.