Developing a Risk-Based Approach for American Basket Option Pricing

Options are one of the important financial contracts for reducing the risk of investors. Many active practitioners in the financial markets really believe that mispricing or incorrect valuation of these securities would be the main reason of collapse of some financial institutions. The complexity of option pricing/valuation, especially in the case of American basket options, as high dimensional options, has motivated many researchers to develop numerical and simulation-based models. In this paper, a new simulation-based approach for pricing/valuation of American basket option with risk consideration is proposed. Having the prices obtained through Longstaff–Schwartz methodology, which is based on Approximate Dynamic Programming as a risk-neutral approach, we propose a new approach for pricing the American basket option according to the worst-case (pessimistic/risk-averse) and the best-case (optimistic/risk-taking) scenarios. Furthermore, for scenarios generation, we use a Monte Carlo simulation technique using a t-student copula-GARCH method and Extreme Value Theory to handle the nonlinearity of dependencies between variables. To verify the computational efficiency and the accuracy of the proposed methodology, we compare the results of prices obtained through the proposed models with those achieved through the Monte Carlo simulation and the method developed by Ju for European basket options. Moreover, the developed models are tested using out-sample scenarios to explore what would happen if investors bought the option with the obtained prices through three different strategies: risk-averse, risk-neutral, and risk-taking approaches.