Abstract
Chapter 8 applies the theory developed in Chap. 7 to some concrete examples with the aim of illustrating these techniques in detail so that readers can apply them to their fields of interest. In the first part of the chapter, we recall the Vasicek and the Cox-Ingersoll-Ross model and derive some well-known results pertaining to these models. These formulas have all appeared under the classical risk neutral paradigm. In the second part of the chapter, we focus on the benchmark approach introduced in Chap. 1 and we recall the Minimal Market Model which we had already discussed in Chap. 3. We demonstrate explicitly how the benchmarked Laplace transforms introduced in Chap. 7 can be used to price financial derivatives on the realized variance of an equity index. The chapter concludes by employing forward measures under the benchmark approach as discussed in Chap. 7 to derive an explicit formula for a particular financial derivatives contract, namely a spread option.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)
Baldeaux, J., Chan, L., Platen, E.: Derivatives on realized variance and volatility of an index under the benchmark approach. Working paper, University of Technology, Sydney (2011a)
Carr, P., Geman, H., Madan, D., Yor, M.: Pricing options on realized variance. Finance Stoch. 9(4), 453–475 (2005)
Chan, L., Platen, E.: Exact pricing and hedging formulas of long dated variance swaps under a 3/2 volatility model. Working paper, University of Technology, Sydney (2011)
Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of the term structure of interest rates. Econometrica 53(2), 385–407 (1985)
Filipović, D.: Term-Structure Models. Springer, Berlin (2009)
Filipović, D., Mayerhofer, E.: Affine diffusion processes: theory and applications. In: Albrecher, H., Runggaldier, W., Schachermayer, W. (eds.) Advanced Financial Modelling, pp. 125–165. de Gruyter, Berlin (2009)
Gatheral, J.: The Volatility Surface. A Practitioner’s Guide. Wiley, Chichester (2006)
Hurst, T.R., Zhou, Z.: A Fourier transform method for spread option pricing. SIAM J. Financ. Math. 1(1), 142–157 (2010)
Lennox, K.: Lie symmetry methods for multi-dimensional linear parabolic PDEs and diffusions. PhD thesis, UTS, Sydney (2011)
Mamon, R.S.: Three ways to solve for bond prices in the Vasicek model. J. Appl. Math. Decis. Sci. 8(1), 1–14 (2004)
Vasiček, O.A.: An equilibrium characterization of the term structure. J. Financ. Econ. 5(2), 177–188 (1977)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Baldeaux, J., Platen, E. (2013). Pricing Using Affine Diffusions. In: Functionals of Multidimensional Diffusions with Applications to Finance. Bocconi & Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-00747-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-00747-2_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00746-5
Online ISBN: 978-3-319-00747-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)