Option Pricing Problem when Stock Price Returns Have Hyperbolic Distribution

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.