| Summary: | 碩士 === 銘傳大學 === 財務金融學系碩士班 === 96 === Two major disadvantages in the conventional Black-Scholes model include that the underlying asset follows the log normal distribution and that volatility of underlying asset does not vary over time. To overcome these disadvantages, speed up option valuation and obtain call pricing function be a square-integrable function, this study employs fast Fourier transform in three modified call option valuation models, i.e., the jump-diffusion (Merton) model, stochastic volatility (Heston) model, and stochastic volatility with jump (SVJ, Bates) model. These models are utilized to assess TAIEX options and to formulate option hedging strategy. The traditional Delta neutral and Delta-Gamma neutral option hedging strategies are used to hedge the underlying assets. Furthermore, the minimizing hedge risk and optimal Conditional VaR methods are used to hedge the portfolio of derivative assets.
The empirical results of option hedging on spot market indicate that the Delta Neutral strategy of hedging in-the-money TAIEX options obtains better hedging effectiveness. When at-the-money and out-of-the-money TAIEX options with large volatility are used as hedging instruments, Delta-Gamma Neutral strategy obtains better hedging effectiveness. Moreover, the hedging effectiveness of various models and strategies increases as hedging horizon increases. As to options hedging on derivative assets, the hedging effectiveness of minimizing hedge risk outperformed that of optimal Conditional VaR hedge. The higher the confident level, the higher the hedging effectiveness of optimal Conditional VaR Hedge.
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