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Noncausal affine processes with applications to derivative pricing

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  • Christian Gouriéroux
  • Yang Lu

Abstract

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi‐closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature nonaffine dynamics in calendar time, while still providing (quasi) closed form term structures and derivative pricing formulas. The framework is illustrated with term structure of interest rates and European call option pricing examples.

Suggested Citation

  • Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.
    • Handle: RePEc:bla:mathfi:v:33:y:2023:i:3:p:766-796
    DOI: 10.1111/mafi.12384
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282, April.
    3. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    4. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    5. B. Ramachandran, 1997. "On Geometric-Stable Laws, a Related Property of Stable Processes, and Stable Densities of Exponent One," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 299-313, June.
    6. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    7. Davis, Richard A. & Song, Li, 2020. "Noncausal vector AR processes with application to economic time series," Journal of Econometrics, Elsevier, vol. 216(1), pages 246-267.
    8. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    9. Karapanagiotidis, Paul, 2014. "Dynamic modeling of commodity futures prices," MPRA Paper 56805, University Library of Munich, Germany.
    10. Lee, Ji Hyung & Phillips, Peter C.B., 2016. "Asset pricing with financial bubble risk," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 590-622.
    11. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    12. Alain Monfort & Fulvio Pegoraro & Jean-Paul Renne & Guillaume Roussellet, 2017. "Staying at zero with affine processes : an application to term structure modelling," Rue de la Banque, Banque de France, issue 52, november.
    13. 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.
    14. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    15. Serge Darolles & Christian Gourieroux & Joann Jasiak, 2006. "Structural Laplace Transform and Compound Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 477-503, July.
    16. Alain Hecq & Joao Victor Issler & Sean Telg, 2020. "Mixed causal–noncausal autoregressions with exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(3), pages 328-343, April.
    17. 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.
    18. Madan, Dilip B. & Smith, Robert H. & Wang, King, 2017. "Laplacian risk management," Finance Research Letters, Elsevier, vol. 22(C), pages 202-210.
    19. C. Gourieroux & A. Monfort & V. Polimenis, 2006. "Affine Models for Credit Risk Analysis," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 494-530.
    20. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    21. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    22. Christian Gourieroux & Joann Jasiak, 2016. "Filtering, Prediction and Simulation Methods for Noncausal Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 405-430, May.
    23. Lof, Matthijs & Nyberg, Henri, 2017. "Noncausality and the commodity currency hypothesis," Energy Economics, Elsevier, vol. 65(C), pages 424-433.
    24. Andersen, Torben G, 1996. "Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
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