IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1512.03292.html
   My bibliography  Save this paper

Time-inhomogeneous affine processes and affine market models

Author

Listed:
  • Stefan Waldenberger

Abstract

This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for time-inhomogeneous Markov processes. For stochastically continuous affine processes we show that there always exists a c\`adl\`ag modification. Afterwards we consider the regularity and the semimartingale property of affine processes. Contrary to the time-homogeneous case, time-inhomogeneous affine processes are in general neither regular nor semimartingales and the time-inhomogeneous case raises many new and interesting questions. Assuming that an affine process is a semimartingale, we show that even without regularity the parameter functions satisfy generalized Riccati integral equations. This generalizes an important result for time-homogeneous affine processes. We also show that stochastically continuous affine semimartingales are essentially generated by deterministic time-changes of what we call absolutely continuously affine semimartingales. These processes generalize time-homogeneous regular affine processes. In the second part we consider the class of affine LIBOR market models. We contribute to this class of models in two ways. First, we modify the original setup of the affine LIBOR market models in such a way that next to nonnegative affine processes real-valued affine processes can also be used. Numerical examples show that this allows for more flexible implied volatility surfaces. Second, we introduce the class of affine inflation market models, an extension of the affine LIBOR market models. A calibration example shows that these models perform very well in fitting market-observed prices of inflation derivatives.

Suggested Citation

  • Stefan Waldenberger, 2015. "Time-inhomogeneous affine processes and affine market models," Papers 1512.03292, arXiv.org.
    • Handle: RePEc:arx:papers:1512.03292
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1512.03292
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03331510, HAL.
    3. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Post-Print halshs-03331510, HAL.
    4. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Cahiers de la Maison des Sciences Economiques b04050, Université Panthéon-Sorbonne (Paris 1).
    5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Flavia Antonacci & Cristina Costantini & Marco Papi, 2021. "Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates," Mathematics, MDPI, vol. 9(10), pages 1-20, May.
    2. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    3. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
    4. Emmanuel Gobet & Julien Hok, 2014. "Expansion Formulas For Bivariate Payoffs With Application To Best-Of Options On Equity And Inflation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-32.
    5. Nabyl Belgrade, 2004. "Market inflation seasonality management," Cahiers de la Maison des Sciences Economiques b04051, Université Panthéon-Sorbonne (Paris 1).
    6. Gabriele Sarais & Damiano Brigo, 2014. "Inflation securities valuation with macroeconomic-based no-arbitrage dynamics," Papers 1403.7799, arXiv.org, revised Jul 2014.
    7. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, September.
    8. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    9. Ivanova, Vesela & Puigvert Gutiérrez, Josep Maria, 2014. "Interest rate forecasts, state price densities and risk premium from Euribor options," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 210-223.
    10. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    11. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    12. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    13. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007.
    14. Francis A. Longstaff, 2004. "Optimal Recursive Refinancing and the Valuation of Mortgage-Backed Securities," NBER Working Papers 10422, National Bureau of Economic Research, Inc.
    15. R.C. Stapleton & Marti G. Subrahmanyam, 1999. "The Term Structure of Interest Rate-Futures Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-045, New York University, Leonard N. Stern School of Business-.
    16. Joshua Rosenberg, 1999. "Empirical Tests of Interest Rate Model Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-015, New York University, Leonard N. Stern School of Business-.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    18. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    19. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    20. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2015. "Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates," Research Paper Series 366, Quantitative Finance Research Centre, University of Technology, Sydney.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1512.03292. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.