| Summary: | 碩士 === 南台科技大學 === 財務金融系 === 99 === As the popularity of basket options continues to rise over the past years, the accurate pricing method for basket options has been of interest to academic researchers and practitioners. Basket options are multi-factor options which belong to exotic options. They are among the most difficult to price and hedge both analytically and numerically due to the fact that the sum of log-normally distributed random variables is not log-normal. Several analytical approaches have been proposed in the literature, among which Ju’s analytical approximation is the most accurate (Krekel et al., 2003). Since constant volatility assumption is violated by many empirical investigations (Finnerty (1978), MacBeth and Merville (1979), Rubinstein (1985)), several stochastic models have been developed. Among these, Heston (1993) model is the most popular one due to its fast and easily implemented closed form solution for European options.
The first step is to use Heston closed form formula to get the individual asset’s price and then use Black Scholes formula to derive the implied correlation for each asset in different strike price. Next step, we price basket option with various combinations of correlations by implementing Heston model with Monte Carlo simulation. Finally, we use these implied volatilities and prices as input in the Ju’s basket approximation formula to derive the IC. We investigate which combination of correlations can fit the implied correlation smile. We have found one set of combination which fit the implied correlation smile.
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