Pricing Asian Option Based On Characteristic Function And Numerical Calculation

Asian options, which have been introduced to the financial market for a bng time, are among the most popular path-dependent options traded in both exchanges and over-the-counter markets. Although the Asian options have been discussed for a long time, there is not a unified pricing expression. Researchers have proposed some pricing methods which are accepted. The methods are geometric mean approximating arithmetic mean, Monte Carlo simulation, numerical solution of partial differential equations, and the characteristic function. Asian option is an important subject of the academic research, but also a difficult problem for researchers. We get the expression of the Asian option’s price based on the characteristic function method. We also get the Asian option’s price based on the numerical calculation. A new way is provided to get the price of the Asian option in this paper.In this paper, we introduce jumps and volatility changes in the price change. We also discuss the relationships of the price and jumps, the price and volatility changes. Jumps, which are stochastic, are popular in the real life. Jumps have become an important subject of the academic research. The volatility changes over time have been recognized by the academic community, and also have been confirmed by the real-life data. First, the paper introduces the jumps and volatility changes into the stochastic processes of the price change and volatility change. Then, this paper gets the formal expression of the Asian option’s price based on the characteristic function method and equivalent martingale transform. After this, this paper gets the numerical solutions of the ordinary differential equations, and finally we get the price of the Asian option. We also make some discussion about the price. In order to make conclusion obvious, we get some pictures by using MATLAB.On the basis of the characteristic function method and equivalent martingale transform, we get the expression of the Asian option’s price. We also study the relationships between the option’s price and the variety of variables. We obtain some conclusions by using the numerical solutions of ordinary differential equations, the numerical integral. The conclusions are as following. First, jumps will affect the Asian option’s price. Second, the greater the intensity of the jumps, the greater the jumps impact the Asian option’s price. Third, the volatility change will affect the Asian option’s price.