IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/30859.html
   My bibliography  Save this paper

One numerical procedure for two risk factors modeling

Author

Listed:
  • Cocozza, Rosa
  • De Simone, Antonio

Abstract

We propose a numerical procedure for the pricing of financial contracts whose contingent claims are exposed to two sources of risk: the stock price and the short interest rate. More precisely, in our pricing framework we assume that the stock price dynamics is described by the Cox, Ross Rubinstein (CRR, 1979) binomial model under a stochastic risk free rate, whose dynamics evolves over time accordingly to the Black, Derman and Toy (BDT, 1990) one-factor model. To this aim, we set the hypothesis that the instantaneous correlation between the trajectories of the future stock price (conditional on the current value of the short rate) and of the future short rate is zero. We then apply the resulting stock price dynamics to evaluate the price of a simple contract, i.e. of a stock option. Finally, we compare the derived price to the price of the same option under different pricing models, as the traditional Black and Scholes (1973) model. We expect that, the difference in the two prices is not sensibly large. We conclude showing in which cases it should be helpful to adopt the described model for pricing purposes.

Suggested Citation

  • Cocozza, Rosa & De Simone, Antonio, 2011. "One numerical procedure for two risk factors modeling," MPRA Paper 30859, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:30859
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/30859/1/MPRA_paper_30859.pdf
    File Function: original 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. 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..
    3. Kosowski, Robert & Neftci, Salih N., 2014. "Principles of Financial Engineering," Elsevier Monographs, Elsevier, edition 3, number 9780123869685.
    4. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    5. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Rabinovitch, Ramon, 1989. "Pricing Stock and Bond Options when the Default-Free Rate is Stochastic," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(4), pages 447-457, December.
    8. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(4), pages 907-929, November.
    9. Yong-Jin Kim & Naoto Kunitomo, 1999. "Pricing Options under Stochastic Interest Rates: A New Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 49-70, January.
    10. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    11. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    12. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Bacinello, Anna Rita & Ortu, Fulvio, 1996. "Fixed income linked life insurance policies with minimum guarantees: Pricing models and numerical results," European Journal of Operational Research, Elsevier, vol. 91(2), pages 235-249, June.
    15. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    16. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    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. 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.
    2. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    3. 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.
    4. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, July-Dece.
    5. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    6. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    7. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175.
    8. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    9. Sebastián A. Rey, 2016. "Theory of long-term interest rates," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-18, September.
    10. 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.
    11. Sorwar, Ghulam & Barone-Adesi, Giovanni & Allegretto, Walter, 2007. "Valuation of derivatives based on single-factor interest rate models," Global Finance Journal, Elsevier, vol. 18(2), pages 251-269.
    12. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    13. repec:uts:finphd:40 is not listed on IDEAS
    14. Jimmy E. Hilliard & Adam L. Schwartz & Alan L. Tucker, 1996. "Bivariate Binomial Options Pricing With Generalized Interest Rate Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(4), pages 585-602, December.
    15. Dimson, Elroy & Mussavian, Massoud, 1999. "Three centuries of asset pricing," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1745-1769, December.
    16. David Babbel & Craig Merrill, 1998. "Economic Valuation Models for Insurers," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 1-15.
    17. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    18. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    19. Coutant, Sophie & Jondeau, Eric & Rockinger, Michael, 2001. "Reading PIBOR futures options smiles: The 1997 snap election," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1957-1987, November.
    20. Jonathan A. Batten & Karren Lee-Hwei Khaw & Martin R. Young, 2014. "Convertible Bond Pricing Models," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 775-803, December.
    21. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).

    More about this item

    Keywords

    option pricing; stochastic short rate model; binomial tree;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:pra:mprapa:30859. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.