Analysis And Simulation Of The Option Pricing Under Stochastic Interest Rate Model

In advance of the interest rate liberalization, the risks of fluctuations in interest rates affecting the financial markets of countries are growing, and that putting the interest rate risk into consideration is particularly necessary. In the classic B-S formula, we assume that interest rates are deterministic, and thus under the above backdrop, considering the problems with the classical B-S formula,errors will be relatively high, in some cases there may be a serious danger.In this article, we still take the classic B-S formula as the basis for discussion, supposing additionally that the interest rate satisfy the Hull-White model (Several advantages are introduced in the text why to use this interest rate model), i.e. formula (4.1), this coupled with the underlying assets also satisfying a SDE.we then have two Brownian motions Wt and Wt0. The main ideas of this paper start here. Because there are no other assumptions on the two Brownian motions, we begin to discuss the following three cases.But in advance we define the quadratic variation of two processes, namely formula (4.2). Respectively, from the next three aspects ρ=0, ρ=1, and the other cases, we get the new B-S formula. The first two cases, we have the products corresponding in practice, so it is easy to understand. For the discussion of other situations, although in practice we do not have an intuitive product,simple and beautiful result of its pricing process can be used to construct a new financial product.With these new B-S formula, we find that there are lots of similarities to the classic one, so we would further expect that they may also have a numerical simulation method similar to the classic binary tree. So in the last chapter, we focused on the two cases mentioned earlier,(due to the third case in practice there is no corresponding products, it will not be discussed). At last, under the assumption of stochastic interest rates, we conclude that there indeed are simulation methods which are similar to the classic binary tree, we use Matlab to simulate and get satisfactory results.