earticle

영어

Since the crash of 1987, researcher have realized that the Black-Scholes model can no longer explain the observed volatility smile in the option markets. These conditions have led to renewed interest in parametric extension of the Black-Scholes model that incorporate stochastic volatility and stochastic jumps. An alternative approach is to use observed option prices in order to learn more about the stochastic process of the asset price. Given a set of option prices with specific times to expiration, we can find risk-neutral probability distributions that support theses prices. Different methods to estimate of the implied risk-neutral probability distribution have been proposed, among which we distinguish two different approaches. Parametric methods, such as the mixture method and the expansion method, postulate a particular form for the probability distribution and fit the parameters to observed prices. Non-parametric methods, such as the maximum-entropy method, the kernel method, and the curve fitting method, do not make any specific assumption on the form of the probability distribution but require a lot of data. A number of studies assess the change in these probability distributions due to news events. The implied risk-neutral probability distribution expected by investors in the future underlying asset price distribution is a crucial information in option market. In other words, the implied risk-neutral probability distribution helps to real “market sentiment,” which could be useful for the policy stance of monetary authorities or for contrarian investors who disagree with the consensus shape of the distribution. Consequently, it is necessary to systematic study on use of the implied risk-neutral probability distribution.