Pricing Research On Discrete Asian Options

The Asian option has always been the focus of academic researches. It is a path-dependent option. And its price is related to the average of underlying asset, so the pricing of Asian option has a great difficulty. According to the execution date can be advanced or not, Asian options are divided into European Asian option and American Asian option. There are some differences between the two kinds of options. Researching on the pricing of Asian option mostly chooses continuous Asian option as the research object. But in the actual financial derivatives market, the Asian option is generally in the discrete state. Therefore, this paper will select discrete Asian option as the research object. It’s more in line with the needs of the development of Chinese financial market, and is closer to the actual market.This paper mainly studies the approximate pricing method of arithmetic average European Asian option. First it introduces the history of the development of financial derivatives market at home and abroad, and the research status of Asian option pricing. Then it introduces two kinds of the basic models of Black-Scholes-Merton pricing model of option pricing and binomial tree pricing model. For the European Asian option, it uses the risk neutral pricing theorem and the Taylor expansion to get the approximate pricing formula of arithmetic average European Asian option. Then it compares the results of approximate analytical pricing formula with the results of Monte Carlo simulation. The results show that the approximate pricing formula for in the money option and at the money option performs well. The errors between the two methods can be controlled within 5%. For the out of the money option, errors of the approximate pricing formula are big. In addition, for any option, the errors of the approximate pricing method will increase with the increasing of volatility. This shows that the approximate pricing method has some limitations in application scope, but it still has great practicality. First, it gives the approximate display solution of the European Asian option pricing formula. Second, compared with Monte Carlo method, it spends less time and high efficiency. For in the money option and at the money option, in the situation of precision approaching, choosing the approximate pricing formula is more efficient and convenient. This paper also discusses binomial tree pricing model for American Asian option. American Asian option can be converted into European Asian option for pricing. However, the expiry date of American Asian option is uncertain. So, using the binomial tree pricing method has bigger error.