Seminar by Siddhartha Pratim Chakrabarty

Title: Pricing of Passport Option
Time and Date: 12 noon, 20th March 2019,
Venue: Committee Room

The problem of pricing the passport option, whose contingent claim is dependent on the balance of a trading account, is considered. For the European passport option, a closed form solution exists for the symmetric case, when the risk-free rate is identical to the cost of carry. However, in absence of an explicit solution for the non-symmetric case, we need to use numerical methods in order to solve the corresponding pricing partial differential equation. In addition, we derive the Greeks, namely, Delta and Gamma for the symmetric case, since the optimal holding strategy is dependent on them. The key result is the improvement in the pricing of the option, as well as estimation of these Greeks, with significantly better results being observed near zero accumulated gain (in the symmetric case), by using the three time level scheme, which is then extended to estimate the price and the Greeks in the non-symmetric case. For the American passport option, the pricing is done by presenting the free boundary problem as a sequence of linear complementarity problems, with the numerical implementation being carried out using the three time level scheme. The key result is the usage of lesser number of grid points as compared to the numerical approaches used previously for this problem, while maintaining the accuracy of the option prices obtained.