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A SEMI-ANALYTICAL PRICING FORMULA FOR EUROPEAN OPTIONS UNDER THE ROUGH HESTON-CIR MODEL

Part of: Stochastic processes Mathematical finance

Published online by Cambridge University Press:  06 March 2020

XIN-JIANG HE Open the ORCID record for XIN-JIANG HE [Opens in a new window]  and
SHA LIN Open the ORCID record for SHA LIN [Opens in a new window]
XIN-JIANG HE
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email [email protected]
SHA LIN*
Affiliation:
School of Finance, Zhejiang Gongshang University, Hangzhou, Zhejiang Province, China email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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We combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation of which involves solving a fractional Riccati equation. The rough Heston-CIR model is more general, taking both the rough Heston model and the Heston-CIR model as special cases. The influence of rough volatility and stochastic interest rate is shown to be significant through numerical experiments.

Keywords

rough Heston-CIR modelsemi-analyticalfractional Riccati equationEuropean options

MSC classification

Primary: 91G20: Derivative securities
Secondary: 60G22: Fractional processes, including fractional Brownian motion
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 4 , October 2019 , pp. 431 - 445
Copyright
© 2020 Australian Mathematical Society

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