Research On Pricing American Callable Bonds Based China Money Market Rates

Options are financial contracts that give holder the right to purchase or sell underlying assets at certain strike price with the absence of obligation. The unequal feature of options makes them an efficient tool for investors to hedge risk, or to speculate. Thus the accurate price of American options remains a hot and key point in financial mathematics areas. But few researches concentrate on American option pricing model based on interest rate model.Firstly, this paper introduces GMM methods to estimates the parameter of two interest rate model——Vasicek model and CIR model, with the data come from seven-day repurchase interest rate of China interbank financial market. Result suggests both model are applicable due to all their significant parameters. Comparisons with domestic literature and foreign literature are also made, which result in that seven-day repurchase interest rate is more useful and stable.Secondly, this paper utilizes two interest rate pricing models, one is trigeminal tree, the other is Monte-Carlo MLE method. Trigeminal tree suits interest model better than binary tree because of its additional degree of freedom and this paper develop specific trees for each model. Monte-Carlo MLE method use MLE to find optimal stopping time. The paper simulation interest rate pathways by Milstream Method and construct regression model with weighted Lagrange polynomials.Finally, the paper price the American callable bonds through above two methods based on Vasicek model and CIR model. The parameters selected come from GMM estimate. Result shows, for trigeminal tree method, price become more stable when steps increase and bond price is lower under Vasicek model than CIR model. While for Monte-Carlo MLE, bond price rise a certain level with the increase of steps. Probably more steps failed to reflect more pathway information, thereby underestimating the option price.