股票收益为双曲分布时的欧式期权定价问题

Option Pricing Problem when Stock Price Returns Have Hyperbolic Distribution

本文考虑的是股票收益为双曲分布下欧式期权的定价问题．在只有一种无风险资产和一种风险资产的 光滑市场上，通过自融资策略，得到权价格所满足的ＰＤＥ方程，并给出了特定情况下期权价格的显示形式．此 外，还从方程的角度说明了股票的波动越大，以其为标的资产的期权价格就越高．

In this paper, we consider European option pricing problem when stock returns have hyperbolic distribution. In the market where two securities are traded one of which is riskless and the other is risky, by self-financing strategy, we obtain the PDE option price satisfies and explicit expression of option price under the special conditions. On the other hand, we also find that the larger the volatility of stock price is, the higher the price is for this option.