The 'fair price' and Greeks of option is a highly sensitive issue in financial service in-dustry for derivatives which has no closed-form solutions in Black-Scholes framework. We improve a popular numerical scheme for pricing ELS by modeling the multi dimensional exit-probabilities with copula. Numerical examples show our method is superior than the conventional methods in numerical accuracy and computational cost. The new method can be practically used to calculate the price and the Greeks of any option whose payoff determined by multi-dimensional hitting conditions.
Keywords: Black-Scholes Equation, Multi-Dimensional Exit-Probability, Equity-Linked Securities, Copula