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Pricing Stock and Bond Options when the Default-Free Rate is Stochastic

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  • Rabinovitch, Ramon

Abstract

We derive formulas for the valuation of call options on stocks and bonds when the defaultfree rate is stochastic. The formulas highlight the role of the correlation between the unanticipated returns on the underlying security and the changes in the short-term rate in determining the options value. Our numerical analysis indicates that option prices predicted by the proposed formula differ from those predicted by the Black and Scholes formula when this correlation is relatively large and the short-term rate's instantaneous variance is relatively large as well. Moreover, the proposed formula predicts higher (lower) stock option prices than those predicted by the Black and Scholes formula for correlation values that are lower (higher) than some positive critical value.

Suggested Citation

  • 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(04), pages 447-457, December.
  • Handle: RePEc:cup:jfinqa:v:24:y:1989:i:04:p:447-457_01
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    Cited by:

    1. San-Lin Chung, 2000. "American option valuation under stochastic interest rates," Review of Derivatives Research, Springer, vol. 3(3), pages 283-307, October.
    2. Griselda Deelstra & Jacques Janssen, 1998. "Interaction between asset liability management and risk theory," ULB Institutional Repository 2013/7586, ULB -- Universite Libre de Bruxelles.
    3. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    4. Kim, In Joon & Park, Gun Youb & Hyun, Jung-Soon, 2007. "What is the correct meaning of implied volatility?," Finance Research Letters, Elsevier, vol. 4(3), pages 179-185, September.
    5. Rose Neng Lai & Robert Order, 2014. "Securitization, Risk-Taking and the Option to Change Strategy," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 42(2), pages 343-362, June.
    6. Ben-Ameur, Hatem & Breton, Michele & Karoui, Lotfi & L'Ecuyer, Pierre, 2007. "A dynamic programming approach for pricing options embedded in bonds," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2212-2233, July.
    7. Sinha, Pankaj & Sharma, Sakshi & Sondhi, Kriti, 2013. "Market Valuation and Risk Assessment of Indian Banks using Black -Scholes -Merton Model," MPRA Paper 47442, University Library of Munich, Germany.
    8. Liu, Ying & Papakirykos, Eli & Yuan, Mingwei, 2006. "Market Valuation and Risk Assessment of Canadian Banks," Review of Applied Economics, Review of Applied Economics, vol. 2(1).
    9. Poon, Winnie P. H. & Duett, Edwin H., 1998. "An empirical examination of currency futures options under stochastic interest rates," Global Finance Journal, Elsevier, vol. 9(1), pages 29-50.
    10. Cocozza, Rosa & De Simone, Antonio, 2011. "One numerical procedure for two risk factors modeling," MPRA Paper 30859, University Library of Munich, Germany.
    11. Jaewon Choi & Matthew P. Richardson & Robert F. Whitelaw, 2014. "On the Fundamental Relation Between Equity Returns and Interest Rates," NBER Working Papers 20187, National Bureau of Economic Research, Inc.
    12. K. Nawalkha, Sanjay, 1995. "Face value convergence for stochastic bond price processes: a note on Merton's partial equilibrium option pricing model," Journal of Banking & Finance, Elsevier, vol. 19(1), pages 153-164, April.
    13. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Hedging Futures Options with Stochastic Interest Rates," Research Paper Series 375, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Dynamic Asset Allocation in a Mean-Variance Framework," Management Science, INFORMS, vol. 44(11-Part-2), pages 79-95, November.
    15. Ken Hung & Chang-Wen Duan & Chin W. Yang, 2006. "Rating, Credit Spread, and Pricing Risky Debt: Empirical Study on Taiwan's Security Market," Annals of Economics and Finance, Society for AEF, vol. 7(2), pages 405-424, November.
    16. Jin-Chuan, Duan & Moreau, Arthur F. & Sealey, C. W., 1995. "Deposit insurance and bank interest rate risk: Pricing and regulatory implications," Journal of Banking & Finance, Elsevier, vol. 19(6), pages 1091-1108, September.
    17. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    18. Nawalkha, Sanjay K., 1996. "A contingent claims analysis of the interest rate risk characteristics of corporate liabilities," Journal of Banking & Finance, Elsevier, vol. 20(2), pages 227-245, March.
    19. Ivanov, Ivan & Kabaivanov, Stanimir & Bogdanova, Boryana, 2016. "Stock market recovery from the 2008 financial crisis: The differences across Europe," Research in International Business and Finance, Elsevier, vol. 37(C), pages 360-374.
    20. repec:spt:fininv:v:6:y:2017:i:3:f:6_3_1 is not listed on IDEAS
    21. Driessen, Joost & Van Hemert, Otto, 2012. "Pricing of commercial real estate securities during the 2007–2009 financial crisis," Journal of Financial Economics, Elsevier, vol. 105(1), pages 37-61.
    22. 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.
    23. Duan, J. & Sealey, C. W. & Yan, Y., 1999. "Managing banks' duration gaps when interest rates are stochastic and equity has limited liability," International Review of Economics & Finance, Elsevier, vol. 8(3), pages 253-265, September.

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