Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations
The recombining binomial tree approach, which has been initiated by Cox et al. (J Financ Econ 7: 229–263, 1979 ) and extended to arbitrary diffusion models by Nelson and Ramaswamy (Rev Financ Stud 3(3): 393–430, 1990 ) and Hull and White (J Financ Quant Anal 25: 87–100, 1990a ), is applied to the simultaneous evaluation of price and Greeks for the amortized fixed and variable rate mortgage prepayment option. We consider the simplified binomial tree approximation to arbitrary diffusion processes by Costabile and Massabo (J Deriv 17(3): 65–85, 2010 ) and analyze its numerical applicability to the mortgage valuation problem for some Vasicek and CIR-like interest rate models. For fixed rates and binomial trees with about thousand steps, we obtain very good results. For the Vasicek model, we also compare the closed-form analytical approximation of the callable fixed rate mortgage price by Xie (IAENG Int J Appl Math 39(1): 9, 2009 ) with its binomial tree counterpart. With respect to the binomial tree values one observes a systematic underestimation (overestimation) of the callable mortgage price (prepayment option price) analytical approximation. This numerical discrepancy increases at longer maturities and becomes impractical for a valuable estimation of the prepayment option price. Copyright Springer-Verlag 2012
Volume (Year): 35 (2012)
Issue (Month): 2 (November)
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- Denis Belomestny & Grigori Milstein & John Schoenmakers, 2007.
"Sensitivities for Bermudan Options by Regression Methods,"
SFB 649 Discussion Papers
SFB649DP2007-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Denis Belomestny & G. Milstein & John Schoenmakers, 2010. "Sensitivities for Bermudan options by regression methods," Decisions in Economics and Finance, Springer, vol. 33(2), pages 117-138, November.
- Chen, Ren-Raw & Scott, Louis, 2003. "Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model," The Journal of Real Estate Finance and Economics, Springer, vol. 27(2), pages 143-72, September.
- Sumit Agarwal & John C. Driscoll & David I. Laibson, 2013.
"Optimal Mortgage Refinancing: A Closed‐Form Solution,"
Journal of Money, Credit and Banking,
Blackwell Publishing, vol. 45(4), pages 591-622, 06.
- Sumit Agarwal & John C Driscoll & David Laibson, 2008. "Optimal Mortgage Refinancing: A Closed Form Solution," Levine's Working Paper Archive 122247000000002021, David K. Levine.
- Sumit Agarwal & John C. Driscoll & David Laibson, 2007. "Optimal Mortgage Refinancing: A Closed Form Solution," NBER Working Papers 13487, National Bureau of Economic Research, Inc.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994.
"Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Discussion Paper Serie B
308, University of Bonn, Germany.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Richard Stanton & Nancy Wallace, 1995. "ARM Wrestling: Valuing Adjustable Rate Mortgages Indexed to the Eleventh District Cost of Funds," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 23(3), pages 311-345.
- Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-99, August.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Hans-Jürg Büttler & Jorg Waldvogel, 1996. "Pricing Callable Bonds By Means Of Green'S Function," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 53-88.
- Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
- 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.
- Nicholas Sharp & Paul Johnson & David Newton & Peter Duck, 2009. "A New Prepayment Model (with Default): An Occupation-time Derivative Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 39(2), pages 118-145, August.
- Schwartz, Eduardo S & Torous, Walter N, 1992. "Prepayment, Default, and the Valuation of Mortgage Pass-through Securities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 221-39, April.
- Nicholas Sharp & David Newton & Peter Duck, 2008. "An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options," The Journal of Real Estate Finance and Economics, Springer, vol. 36(3), pages 307-342, April.
- Kau, James B, et al, 1993. "Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages," The Journal of Business, University of Chicago Press, vol. 66(4), pages 595-618, October.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Arden R. Hall, 1985. "Valuing the Mortgage Borrower's Prepayment Option," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(3), pages 229-247.
- 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.
- Giulia De Rossi & Tiziano Vargiolu, 2010. "Optimal prepayment and default rules for mortgage-backed securities," Decisions in Economics and Finance, Springer, vol. 33(1), pages 23-47, May.
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