Uncertain Volatility Model Under Static Hedging Method

Option pricing and risk measurement are the most important questions about the research of options among academic and practice. The Black-Scholes model is the cornerstone of option pricing, but there're two strict assumptions:the volatility of the underlying asset and risk-free interest rate is pre-assumed to be constant during the contract period. In practice, volatility is inevitable to change over contract period. Many scholars have proposed improvements. One of the most important improvements is that the volatility uncertainty (assuming that the volatility under a certain interval). The questions can be solved by BSB, and get the envelopes of option. When we use the BSB model, the envelopes of option is larger than market price. The idea of static hedge has been proposed based on above. This method can effectively reduce the envelopes, and get a reasonable price, and promote the market liquidity.This paper studied the static hedging method under the uncertain volatility model systematically. The main research as below: One:the comparison between the envelopes of options with and without static hedge under volatility uncertainty; Two:the static hedge approach relative advantages of other hedging methods under volatility uncertainty.The main innovation of this paper is as follows: Previous studies assume that the shares of hedge portfolio are given when narrowing the envelopes of option. In my paper, we assume the shares of hedge portfolios are laid in an interval and the result is better than the former. This shows it is reasonable. This is the innovation of this paper.For simplicity, the structure of the paper is as follows:Chapter I: the background and status of static hedging method under the volatility uncertainty;Chapter II: the uncertain volatility theory and the advantage of BSB compare to BS;Chapter III: the comparison between the envelopes of options with and without static hedge under volatility uncertainty; the static hedge approach relative advantages of other hedging methods under volatility uncertainty;Chapter IV: conclusion.