Abstract
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 mathematical characterization is discussed for the unique no-arbitrage price associated with any attainable contingent claim. The appropriate numeraire (zero-coupon bond) and measures (T-forward measure) are chosen to simplify the calculations. Based on the designed linear investment strategy with stochastic interest rate, a novel option price approach is obtained under the T-forward measure.
Highlights
With the globalization of economy and the rapid development of financial derivatives market, the analysis of the option pricing is of great importance and has attracted considerable attention
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
Based on the designed linear investment strategy with stochastic interest rate, a novel option price approach is obtained under the T-forward measure
Summary
With the globalization of economy and the rapid development of financial derivatives market, the analysis of the option pricing is of great importance and has attracted considerable attention. In 1973, Black and Scholes [1] proposed the classical Black-Scholes model under the risk-neutral world with the assumption that the stock price follows geometric Brownian motion, and the expected return rate stock is a constant, while, the assumption of Black-Scholes model has a large difference with the real world. Merton [2] considered dividend and stochastic interest rate into the option pricing model. Cox and Rose [3] [4] used the alternative stochastic process to discuss the option pricing model and considered the expanded formula of stock price that does not include continuous sample path
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