| Summary: | 碩士 === 東吳大學 === 財務工程與精算數學系 === 103 === Foreign exchange option implied volatility of market information is quoted. Implied volatility have volatility smile. Dupire (1994) propose local volatility model explain volatility smile. Local volatility was the volatility of the underlying asset. It was a function of time and the underlying assets. Dupire (1994) has also been a function of local volatility and European option price. Andersen and Ratcliffe (1998) and Gatheral (2006) were two further local volatility functions, as a function of the local volatility function and the implied volatility of the relationship. In this paper, we used foreign exchange option implied volatility in market data, and Andersen and Ratcliffe (1998) or Gatheral (2006) approach, with the cubic spline interpolation, calibration local volatility function. Reduce variance with the practice of the use of Monte Carlo simulation. Calculated option of the local volatility model prices and implied volatility. Compare with the actual implied volatility verification. The results show that the results of Andersen and Ratcliffe (1998) and Gatheral (2006) practice of insignificant, reduce variance approach is more precise and effective computing option prices and implied volatility of the local volatility model.
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