The Valuation Of Binary Option Under Stochastic Interest Rates

In resent years, the market of financial derivatives has rapidly developed. In special, the development of options, is far-reaching impact on the field of venture evading, venture investment and value directions etc. Option pricing has been one of the important parts of modern financial mathematics.Nowadays, a large number of new financial derivatives are derived in finan-cial derivative markets. The binary option is a typical one. People have done a lot of researches on pricing of binary option when the interest rate is a constant and obtained some results. But the realistic situation is not in such case, affected by lots of uncertain factors, the interest rate is always one variable and it changes randomly.In this paper, the pricing of binary option under stochastic interest rate is discussed by means of the no-arbitrage theory and changing the numeraire etc, and the main conclusions as follows:(1) when the underlying asset is stock, we discuss the one-dimensional and multi-dimensional binary option pricing model under stochastic interest rate re-spectively, and we obtain the pricing formula of binary option. As a corollary, it discusses the relationship between the value of European call option and binary option. In addition, a pricing formula of European call option is exhibited.(2) The pricing of binary option on bond is displayed in next part. It gives a explicit pricing formula when the underlying asset is zero coupon bond. Then, the pricing method of binary option on coupon bond is also presented.