Stochastic Stock Process and Its Option Pricing for a Risk Aversion Stock Market

In this paper, we consider the contingent claim pricing and hedging of European call option. The theory of stock trading volume is applied to describe and study the fluctuations of stock prices in a stock market, and we obtain the formula for pricing a European call option. Then we discuss the range of parameters of the formula in a risk-averse market, and give the corresponding option pricing bounds. In this work, stochastic analysis and stopping theory are used to study and show the risk- neutral probability distribution for the financial model, further we study the European call option for a risk-averse stock market.