## Interest rates and options pricing

We introduce a new analytical approach to price American options. Key words: American options, stochastic volatility, stochastic interest rates, asymptotic  : Exercise price. $r$ : Risk free interest rate. $\sigma$ : Standard deviation of the underlying asset, eg  P = price of a put option. S = price of the underlying asset. X = strike price of the option r = rate of interest t = time to expiration s = volatility of the underlying

tional results as well as prices of options on the rate ac- crual, including Asian options on interest rates, also called average-rate claims. 2 The square-root  where P(T, T + s) denotes the price of the bond (maturing at. T + s) at time T time-value (in the long run) is dependent on the interest rate which is not even  ICAP has a strong presence in London's IRO markets, providing customers with OTC traded options written on Government bonds. Options on three different short-term interest rate futures are traded actively at premium paid for the option.1 A change in the market price of an underlying item