Author:

Keywords:

Black & Scholes, Basket options, Pricing and hedging, Comonotonicity, Partial differential equations, Finite difference method, Least-Squares Monte-Carlo, Social Sciences, Science & Technology, Physical Sciences, Business, Finance, Economics, Mathematics, Interdisciplinary Applications, Social Sciences, Mathematical Methods, Business & Economics, Mathematics, Mathematical Methods In Social Sciences, ACTUARIAL SCIENCE, COMONOTONICITY, SIMULATION, SCHEMES, FINANCE, BOUNDS, 01 Mathematical Sciences, 14 Economics, 15 Commerce, Management, Tourism and Services, Finance, 35 Commerce, management, tourism and services, 38 Economics, 49 Mathematical sciences

Abstract:

We consider the pricing of American-type basket derivatives by numerically solving a partial differential equation (PDE). The curse of dimensionality inherent in basket derivative pricing is circumvented by using the theory of comonotonicity. We start with deriving a PDE for the European-type comonotonic basket derivative price, together with a unique self-financing hedging strategy. We show how to use the results for the comonotonic market to approximate American-type basket derivative prices for a basket with correlated stocks. Our methodology generates American basket option prices which are in line with the prices obtained via the standard Least-Square Monte-Carlo approach. Moreover, the numerical tests illustrate the performance of the proposed method in terms of computation time, and highlight some deficiencies of the standard LSM method.