Reconstructing the Local Volatility Surface from Market Option Prices

We present an efficient and accurate computational algorithm for reconstructing a local volatility surface from given market option prices. The is dependent on the values of both time underlying asset. use generalized Black–Scholes (BS) equation finite difference method (FDM) to numerically solve BS equation. reconstruct function, which provides best fit between theoretical prices by minimizing cost function that quadratic representation two This inverse problem in we want calculate consistent with observed To achieve robust computation, place sample points unknown middle expiration dates. perform various numerical experiments confirm simplicity, robustness, accuracy proposed function.