American Option Pricing under Markov-Modulated Pure Jump Processes

Document Type : applied

Authors

1 Assistant Prof., Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

2 MSc. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

Abstract

In this paper, we present an approximate solution method based on finite-differences to the American option pricing problem under a Markov modulated. It could be shown by Ito calculus that the option price under this process satisfies a system ofpartial integro-differential equations (PIDEs) in which each equation is linked to an unknown early exercise (optimal) boundary. After extending the system to the entire domain by employing the dividend process, we arrive at a new numerical scheme. The results obtained support the claim that this scheme is stable and convergent. In conclusion, some further possible applications of this method specially in credit risk will be highlighted.
JEL: G00, G13
How to cite this paper: Foroush Bastani, A., & Safy, Kh. (2017). American Option Pricing under Markov-Modulated Pure Jump Processes. Quarterly Journal of Risk Modeling and Financial Engineering, 2(2), 133– 157. (In Persian)

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References

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