Abstract
In the previous chapter we have introduced the general valuation framework and state price deflators as abstract concepts. In this and the next chapters we present explicit models for state price deflator modeling. In the present chapter we consider models that are based on spot rates. They include multivariate Gaussian distributions and affine term structure models such as the discrete time one-factor and multifactor Vasicek models, ARMA and conditionally heteroscedastic time-series models, gamma spot rate models and the discrete time Black–Karasinski model. These models are supported by explicit applications to Swiss market financial data, and we analyze their strengths and weaknesses.
Keywords
- Kalman Filter
- ARMA Model
- Multivariate Gaussian Distribution
- Spot Rate
- Maximum Likelihood Estimation Method
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- 1.
Both data sets are available on the website of the Swiss National Bank (SNB) www.snb.ch.
- 2.
The data are available on the website of the Swiss National Bank (SNB) www.snb.ch.
References
Audrino F, Filipova K (2009) Yield curve predictability, regimes, and macroeconomic information: a data driven approach. University of St Gallen. Discussion paper no 2009-10
Ball CA, Torous WN (1996) Unit roots and the estimation of interest rate dynamics. J Empir Finance 3(2):215–238
Bernadell C, Coche J, Nyholm K (2005) Yield curve prediction for the strategic investor. European central bank. Working paper series no 472, April 2005
Black F, Karasinski P (1991) Bond and option pricing when short rates are lognormal. Financ Anal J 47(4):52–59
Bolder DJ (2001) Affine term-structure models: theory and implementation. Bank of Canada. Working paper 2001-15
Brennan MJ, Schwartz ES (1979) A continuous time approach to the pricing of bonds. J Bank Finance 3(2):133–155
Brennan MJ, Schwartz ES (1982) An equilibrium model of bond pricing and a test of market efficiency. J Financ Quant Anal 17(3):301–329
Brigo D, Mercurio F (2006) Interest rate models—theory and practice, 2nd edn. Springer, Berlin
Brockwell PJ, Davis RA (1991) Time series: theory and methods, 2nd edn. Springer, Berlin
Brown SJ, Dybvig PH (1986) The empirical implications of the Cox, Ingersoll, Ross theory of the term structure of interest rates. J Finance 41(3):617–630
Bühlmann H, Gisler A (2005) A course in credibility theory and its applications. Springer, Berlin
Cairns AJG (2004) Interest rate models: an introduction. Princeton University Press, Princeton
Cairns AJG (2004) A family of term-structure models for long-term risk management and derivative pricing. Math Finance 14(3):415–444
Cairns AJG (2004) Interest-rate modeling. In: Teugels JL, Sundt B (eds) Encyclopedia of actuarial science. Wiley, New York, pp 911–921
Cowpertwait PSP, Metcalfe AV (2009) Introductory time series with R. Springer, Berlin
Cox JC, Ingersoll JE, Ross SA (1985) A theory of the term structure of interest rates. Econometrica 53(2):385–407
Dai Q, Singleton KJ (2000) Specification analysis of affine term structure models. J Finance 55(5):1943–1978
De Jong P, Zehnwirth B (1983) Claims reserving, state-space models and the Kalman filter. J Inst Actuar 110:157–181
Embrechts P, McNeil A, Straumann D (2002) Correlation and dependency in risk management: properties and pitfalls. In: Dempster MAH (ed) Risk management: value at risk and beyond. Cambridge University Press, Cambridge, pp 176–223
Filipović D (2009) Term-structure models. A graduate course. Springer, Berlin
Hull J, White A (1990) Pricing interest-rate-derivative securities. Rev Financ Stud 3(4):573–592
Hull J, White A (1994) Branching out. Risk 7:34–37
Jondeau E, Poon S, Rockinger M (2007) Financial modeling under non-Gaussian distributions. Springer, Berlin
Jordan TJ (2009) SARON—an innovation for the financial markets. Launch event for swiss reference rates, Zurich, 25 August 2009
Kraenzlin S, Nellen T (2011) Access to central bank operations and money market integration. Preprint, Swiss National Bank
Lemke W (2006) Term structure modeling and estimation in a state space framework. Springer, Berlin
Litterman RB, Scheinkman J (1991) Common factors affecting bond returns. J Fixed Income 1(1):54–61
McNeil AJ, Frey R, Embrechts P (2005) Quantitative risk management: concepts, techniques and tools. Princeton University Press, Princeton
Mercurio F (2009) Interest rates and the credit crunch: new formulas and market models. Bloomberg portfolio research paper no 2010-01-FRONTIERS
Mercurio F (2010) Modern LIBOR market models: using different curves for projecting rates and for discounting. Int J Theor Appl Finance 13(1):113–137
Mercurio F (2010) LIBOR market models with stochastic basis. Risk magazin, 01 Dec
Pfeiffer R, Bierbaum J, Kunze M, Quapp N, Bäuerle N (2010) Zinsmodelle für Versicherungen—Diskussion der Anforderungen und Vergleich der Modelle von Hull-White und Cairns. Blätter DGVFM 31:261–290
Rogers LCG (1995) Which model for term-structure of interest rates should one use? In: Mathematical finance. IMA, vol 65. Springer, Berlin, pp 93–116
Sahin S, Cairns A, Kleinow T, Wilkie AD (2008) Revisiting the Wilkie investment model. Conference paper AFIR 2008
Shiryaev AN (1999) Essentials of stochastic finance. World Scientific, Singapore
Shumway RH, Stoffer DS (2011) Time series analysis and its applications, with R examples, 3nd edn. Springer, Berlin
Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5(2):177–188
Wilkie AD (1986) A stochastic investment model for actuarial use. Trans Fac Actuar 39:341–402
Wilkie AD (1995) More on a stochastic investment model for actuarial use. Br Actuar J 1(5):777–964
Williams D (1991) Probability with martingales. Cambridge University Press, Cambridge
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Wüthrich, M.V., Merz, M. (2013). Spot Rate Models. In: Financial Modeling, Actuarial Valuation and Solvency in Insurance. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31392-9_3
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