Comparison of L1 and L2 Approximation in Estimating the Implied Volatility Surface

Abstract

In this paper, we approximate the implied volatility surface of KOSPI200 call option in the assumption that the implied volatility surface can be ap- proximated by bivariate polynomial function of degree 4. In the approxima- tion , we adopt two dierent methods, L1 approximation and L2 approxima- tion. Finally, We discuss about the accuracy of the approximation methods by comparing the numerical results of them.