# The option pricing under double Heston model with jumps

Authors

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

In this paper, by introducing of the double Heston's stochastic volatility model, since the prices of underlying asset in the financial markets are subject to the abrupt changes caused by different factors, by adding  jump term to the double Heston model, we propose a new financial model, called the double Heston's stochastic volatility model with jumps. Then, by determining the characteristic function of the underlying stock price process, we obtain a formula for the European call option pricing under the proposed model by using the Fast Fourier transform method. Due to existence the jump term in the stock price process, the proposed model can be widely used in the financial markets, such as oil, gold and stock financial markets. Therefore, the model is more flexible than the Heston model and covers the abrupt changes of underlying asset price. The main goal of this paper is to present the model and derive a numerical scheme for the European option pricing.

Keywords

#### References

[1] Black, F. and Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 637-659. [2] Duffie, D., Pan, J. and Singleton, K. (2000), Transform analysis and asset pricing for affine jump-diffusion, Econometrica, 68,
1343–1376. [3] Hull, J. C. and White, A. (1987), The pricing of options on sssets with stochastic volatilities, Journal of Finance,
42, 281–300. [4] Scott, L. (1987), Option pricing when the variance changes randomly: Theory, estimation and An Application.
Journal of Financial and Quantitative Analysis, 22, 419–438. [5] Stein, E.M. and Stein, J.C. (1991), Stock price distribution with stochastic volatility: An analytic approach. Review of Financial Studies, 4, 727–752. [6] Heston, S.L. (1993), A closed-form
solution for options with stochastic volatility with applications to bonds and currency options, The Review of Financial Studies, 6(2), 327–343.

### History

• Receive Date: 08 July 2014
• Accept Date: 08 July 2014
• First Publish Date: 23 August 2014