Forward start options under Heston affine jump-diffusions and stochastic interest rate

Rehez Ahlip, Laurence A. F. Park, Ante Prodan and Stephen Weissenhofer
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Rehez Ahlip: School of Computer, Data and Mathematical Sciences, Western Sydney University, Australia
Laurence A. F. Park: School of Computer, Data and Mathematical Sciences, Western Sydney University, Australia
Ante Prodan: School of Computer, Data and Mathematical Sciences, Western Sydney University, Australia
Stephen Weissenhofer: School of Computer, Data and Mathematical Sciences, Western Sydney University, Australia

International Journal of Financial Engineering (IJFE), 2021, vol. 08, issue 01, 1-24

Abstract: This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the Forward Start European call option. It is derived using probabilistic approach combined with the Fourier inversion technique, as developed in Ahlip and Rutkowski [Ahlip, R and M Rutkowski (2014). Forward start foreign exchange options under Heston’s volatility and CIR interest rates, Inspired By Finance Springer, pp. 1–27], Carr and Madan [Carr, P and D Madan (1999). Option valuation using the fast Fourier transform, Journal of Computational Finance 2, 61–73, Carr, P and D Madan (2009). Saddle point methods for option pricing, Journal of Computational Finance 13, 49–61] as well as Levendorskiĩ [Levendorskiĩ, S (2012). Efficient pricing and reliable calibration in the Heston model, International Journal of Applied Finance 15, 1250050].

Keywords: Forward start options; Heston’s model; CIR model; affine models (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S2424786321500055

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