| Summary: | 碩士 === 國立中央大學 === 統計研究所 === 100 === Along with the rapid development of financial instruments, pricing options correctly and efficiently remains a critical issue both in industry and in academy. However, closedform
formulas for exotic or complicated options price rarely exist even under the standard Black-Scholes assumptions, and consequently additional numerical techniques are required. Among them, Monte Carlo approaches are invaluable tools and are easy to implement, but Monte Carlo estimators usually suffer from large variances. To tackle this problem, we propose an importance sampling procedure with an exponentially tilted measure to minimize the variance of Monte Carlo estimators. We apply our method to calculate both the price and the Greek letters for several popular options, such as spread and maximum options.
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