Option pricing and hedging with transaction costs
- The traditional Black-Scholes theory on pricing and hedging of European call options has long been criticized for its oversimplified and unrealistic model assumptions. This dissertation investigates several existing modifications and extensions of the Black-Scholes model and proposes new data-driven approaches to both option pricing and hedging for real data. The semiparametric pricing approach initially proposed by Lai and Wong (2004) provides a first attempt to bridge the gap between model and market option prices. However, its application to the S& P 500 futures options is not a success, when the original additive regression splines are used for the nonparametric part of the pricing formula. Having found a strong autocorrelation in the time-series of the Black-Scholes pricing residuals, we propose a lag-1 correction for the Black-Scholes price, which essentially is a time-series modeling of the nonparametric part in the semiparametric approach. This simple but efficient time-series approach gives an outstanding pricing performance for S& P 500 futures options, even compared with the commonly practiced and favored implied volatility approaches. A major type of approaches to option hedging with proportional transaction costs is based on singular stochastic control problems that seek an optimal balance between the cost and the risk of hedging an option. We propose a data-driven rule-based strategy to connect the theoretical approaches with real-world applications. Similar to the optimal strategies in theory, the rule-based strategy can be characterized by a pair of buy/sell boundaries and a no-transaction region in between. A two-stage iterative procedure is provided for tuning the boundaries to a long period of option data. Comparing the rule-based strategy with several other existing hedging strategies, we obtain favorable results in both the simulation studies and the empirical study using the S& P 500 futures and futures options. Making use of a reverting pattern of the S& P 500 futures price, we refine the rule-based strategy by allowing hedging suspension at large jumps in futures price.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Statistics
|Lai, T. L
|Lai, T. L
|Statement of responsibility
|Submitted to the Department of Statistics.
|Thesis (Ph.D.)--Stanford University, 2010.
- © 2010 by Ling Chen
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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