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A hybrid pricing method for multi-asset options
Yongsik Kim,Hyeong-Ohk Bae,Tae-Chang Jo 한국산업응용수학회 2012 한국산업응용수학회 학술대회 논문집 Vol.7 No.1
A hybrid numerical method is studied for pricing options that linked to several equities. Instead of imposing artificial boundary condition for the multi-dimensional Black-Scholes equation, we calculate certain low-dimensional model equation at each time-step using pre-simulated Monte-Carlo(MC) time series. With standard finite difference method using nine point stencil, our method reduce the computational domain of the governing equation (the two dimensional Black-Scholes equation) exceedingly.As benchmark tests,we consider the call on themaximum option which has an analytic solution, and a complicated structured note from the derivative market.
COMPARISON OF NUMERICAL SCHEMES ON MULTI-DIMENSIONAL BLACK-SCHOLES EQUATIONS
Jo, Joonglee,Kim, Yongsik Korean Mathematical Society 2013 대한수학회보 Vol.50 No.6
In this paper, we study numerical schemes for solving multi-dimensional option pricing problem. We compare the direct solving method and the Operator Splitting Method(OSM) by using finite difference approximations. By varying parameters of the Black-Scholes equations for the maximum on the call option problem, we observed that there is no significant difference between the two methods on the convergence criterion except a huge difference in computation cost. Therefore, the two methods are compatible in practice and one can improve the time efficiency by combining the OSM with parallel computation technique. We show numerical examples including the Equity-Linked Security(ELS) pricing based on either two assets or three assets by using the OSM with the Monte-Carlo Simulation as the benchmark.