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Valuation of forward start options under affine jump-diffusion models

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  • João Pedro Vidal Nunes
  • Tiago Ramalho Viegas Alcaria

Abstract

Under the general affine jump-diffusion framework of Duffie et al. [ Econometrica , 2000, 68 , 1343--1376], this paper proposes an alternative pricing methodology for European-style forward start options that does not require any parallel optimization routine to ensure square integrability. Therefore, the proposed methodology is shown to possess a better accuracy--efficiency trade-off than the usual and more general approach initiated by Hong [Forward Smile and Derivative Pricing. Working paper, UBS, 2004] that is based on the knowledge of the forward characteristic function . Explicit pricing solutions are also offered under the nested jump-diffusion setting proposed by Bakshi et al. [ J. Finance , 1997, 52 , 2003--2049], which accommodates stochastic volatility and stochastic interest rates, and different integration schemes are numerically tested.

Suggested Citation

  • João Pedro Vidal Nunes & Tiago Ramalho Viegas Alcaria, 2016. "Valuation of forward start options under affine jump-diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 727-747, May.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:5:p:727-747
    DOI: 10.1080/14697688.2015.1049200
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    3. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    6. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    7. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    8. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    9. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. Louis O. Scott, 1997. "Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 413-426, October.
    12. Susanne Kruse & Ulrich Nögel, 2005. "On the pricing of forward starting options in Heston’s model on stochastic volatility," Finance and Stochastics, Springer, vol. 9(2), pages 233-250, April.
    13. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    14. Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
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