# Timer option pricing of stochastic volatility model with changing coefficients under time-varying interest rate

Volume 11, Issue 12, pp 1294--1301 Publication Date: September 06, 2018       Article History
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### Authors

Jixia Wang - College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China. Dongyun Zhang - Business School, Henan Normal University, Henan Province, 453007, China.

### Abstract

Considering economic variables changing from time to time, the time-varying models can fit the financial data better. In this paper, we construct stochastic volatility models with time-varying coefficients. Furthermore, the interest rate risk is one of important factors for timer options pricing. Therefore, we study the timer options pricing for stochastic volatility models with changing coefficients under time-varying interest rate. Firstly, the partial differential equation boundary value problem is given by using $\Delta$-hedging approach and replicating a timer option. Secondly, we obtain the joint distribution of the variance process and the random maturity under the risk neutral probability measure. Thirdly, the explicit formula of timer option pricing is proposed which can be applied to the financial market directly. Finally, numerical analysis is conducted to show the performance of timer option pricing proposed.

### Keywords

• Timer option pricing
• stochastic volatility model
• risk neutral measure
• $\Delta$-hedging
• time-varying interest rate

•  60H10
•  60J60
•  60A10

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