I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are nonrandom, i.e. known): Merton [2] considered dividend and stochastic interest rate into the option pricing model. Cox and Rose [4] used the alte[3] r- native stochastic process to discuss the option pricing model and considered the expanded formula of stock price that not include contidoes nuous sample path. In this section, we shall discuss the new option price, the Europe call option price, based on investment strategy with the stochastic interest rates under the Vasicek short model. Using daily data of the Nikkei 225 index, call option prices and call money rates of the Japanese financial market,a comparison is made of the pricing performance of stock option pricing modelsunder several stochastic interest rate processes proposedby the existing term structure literature.The results show that (1) one option pricing modelunder a specific stochastic interest ratedoes not significantly outperformanother option pricing model under an alternative stochasticinterest rate, and In this paper, the call option price is evaluated based on linear investment strategy in order to hedge the risk actively in stock market with stochastic interest rate. The Vasicek model is used to describe the structure of interest rates.

## The interest rate for the fixed interest rate model is set to be the interest rate from the stochastic interest rate model for the bond that matures when the option expires. we analyze the pricing of three-month call options and two-year call options. Except for ρ and T shown, other parameter values are the same as the ones in Table 1.

Follow. About IEEE Xplore | Contact Us | Help | Accessibility | First, while theory predicts that the short-term interest rates are strongly related Pricing stock options under stochastic volatility and interest rates with efficient Jun 10, 2015 There are two basic types of options: call options and put options. A call option allows the holder to buy the underlying asset at a predetermined ments, such as futures, options, and interest rate swaps, caps, and floors. equation for the price of the call option after establishing appropriate boundary the Black-Scholes price of a knock-out put option as a function of the volatility risk-free interest rate (assuming per-period compounding), q is the dividend yield and We will not focus on stochastic calculus or the various numerical pricing

### Keywords: Futures options; Stochastic interest rates; Delta hedging; Interest rate option, respectively, then the price of a European call futures option is the

The interest rate for the fixed interest rate model is set to be the interest rate from the stochastic interest rate model for the bond that matures when the option expires. we analyze the pricing of three-month call options and two-year call options. Except for ρ and T shown, other parameter values are the same as the ones in Table 1. Theorem 1 generalizes the BS call option pricing model to the case of stochastic interest rates. 14 In the BS model the price, C t T(, ), of the option is a function of the time to maturity, τ= −T t , the price of the underlying asset, S t(), at time t, its volatility, σ , and a constant risk-free rate. price of a European call option when the spot asset is correlated with volatility, and it adapts the model to incorporate stochastic interest rates. Thus, the model can be applied to bond options and currency options. 1. Stochastic Volatility Model We begin by assuming that the spot asset at time tfollows the diffusion dS(t) = tS dt + VSv _tiSdzl (t), (1)