On the convergence of He and Zhu's new series solution for pricing options with the Heston model
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Abstract
In this paper, a modified formula for European options and a set of complete convergence proofs for the solution that would cover the entire time horizon of a European option contact are presented under the Heston model with minimal entropy martingale measure. Although He and Zhu (2016) have worked on this model, they only provided a converged solution with a condition imposed on the time to expiry. The new solution presented here is only slightly modified in its form. But, it is accompanied with the proof of convergence of the solution for the entire span of the time horizon of an option.
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How to Cite
Zhu, S., & He, X.
(2017).
On the convergence of He and Zhu's new series solution for pricing options with the Heston model.
Acta Mathematica Universitatis Comenianae, 86(2), 321-327.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/490/475
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References
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[2] F. Black and M. Scholes. The pricing of options and corporate liabilities. The journal of political economy, pages 637-654, 1973.
[3] C. R. Gukhal. Analytical valuation of american options on jump-diffusion processes. Mathematical Finance, 11(1):97-115, 2001.
[4] X.-J. HE and S.-P. ZHU. Pricing european options with stochastic volatility under the minimal entropy martingale measure. European Journal of Applied Mathematics, 27(2):233-247, 2016.
[5] S. L. Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of financial studies, 6(2):327-343, 1993.
[6] J. Hull and A. White. The pricing of options on assets with stochastic volatilities. The journal of finance, 42(2):281-300, 1987.
[7] E. M. Stein and J. C. Stein. Stock price distributions with stochastic volatility: an analytic approach. Review of financial Studies, 4(4):727-752, 1991.