Research And Application Of Option Pricing Under Stochastic Interest Rate

Option pricing is an important branch of the financial mathematics research, which is mainly to solve the various cases of option pricing models. The usual option pricing is based mainly on classical assumptions, while in reality; many conditions under classical assumptions are not satisfied. As a result, we should consider the option pricing questions under other cases. The traditional option pricing models assume that interest rates are constant risk-free investment rates, and don't consider the situation of the stock dividend. In this article, we mainly study the option pricing under the stochastic interest rate. Meanwhile, we also solve the corresponding call and put European option pricing formulas and the compound option response pricing formulas under the situation of the stock dividend payments.This article is divided into four parts; the first chapter is devoted to the backgrounds of financial mathematics and the backward stochastic differential equations and also the current situations of the option studies. In the second chapter, we study the relevant option pricing theories based on the stochastic interest rates under the stock dividends payments, which finally leads to the call option pricing model, the put option pricing model and the compound option pricing model. In this chapter, we adopt a bond of random price to represent the case of stochastic interest rates. Under which case, we improve our theories according to the changes of the options. At the same time, we derive the option pricing models under the stock dividends payments. In the third chapter, we solve the corresponding changes of options considering the two current market interest rates-- deposit and loan interest rates --hich are random and not equal, under which assumptions, we study the option pricing questions. In the last chapter, we find the way to evaluate the development potential of SME using the real options theory based on the financial option theory. Meanwhile, we price the real option using the option pricing model got in the second chapter.