Calibration of the temporally varying volatility and interest rate functions

초록

In this study, we develop a calibration method of the temporally varying volatility and interest rate functions using the Black-Scholes (BS) partial differential equation and the observed market option prices with different strikes and expiries. The proposed method uses the piecewise linear interpolations between data points which are defined at the middle points of maturity dates. When we construct the volatility and interest rate, we use the exponential function so that the interpolated values are always positive. Numerical experiments with synthetic and real market data demonstrate the superior performance of the proposed method.

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