Numerical methods for pricing passport option

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Passport option is a financial derivative with the contingent claim being dependent on the value of a trading account. The valuation of the passport option can be obtained through the solution of a nonlinear backward pricing partial differential equation (PDE). In this thesis, we examine the numerical approaches to pricing the passport option, by solving the pricing PDE for both the symmetric case as well as the non-symmetric case. A general introduction and description of the passport option, both theoretical and numerical, along with the pricing PDE and the holder's optimal trading strategy for European passport option is presented. In the symmetric case (when the cost of carry is identical to the risk-free rate), it is observed that the pricing PDE becomes linear parabolic for which a closed form solution exists.The absence of the same in the non-symmetric case motivated the focus on the numerical approaches as presented in this thesis.
Supervisor: Siddhartha Pratim Chakrabarty