Density Estimation Through Kernel Density Method:Asian Options Arbitrage With Transaction Costs

In recent decades, derivatives has become actively in financial markets, at the same time, options trading has been paid more and more attention by investors and managers. As an important option in the financial derivatives market, Asian options play an irreplaceable role in cost savings, hedge risk and arbitrage.In this paper, I study the density estimation through Kernel density method:Asian options arbitrage with transaction costs. Considering the complexity of Asian option, I convert the arithmetic average Asian option pricing to European option pricing through asymptotic difference method. Then produce a series of random stock price path and calculate the arbitrage profit on each path, soon I get density distribution of Asian option arbitrage without transaction costs by MTLAB programming and get the parameters which have an effect on aribitrage profit distribution. Further, build the parameter sets include bid-ask, brokerage commission and discrete price. On this basis, I get the density distribution of Asian option arbitrage with transaction costs by Monte Carlo simulation. The central feature is choosing appropriate window width and Kernel function, thus get the density function under conditional distribution through Kernel density method. Finally, I show balances transaction costs and risk exposure can be optimal when the hedge ration changes by 0.25. Then choose the optimal hedging strategy for the risk aversion investors.