Abstract
An advanced financial market model should be analytically tractable and must reflect with a minimal number of factors essential stylised empirical facts. It must work equally well for derivative pricing and hedging as well as for risk measurement and portfolio management. All factors in such a market model should represent directly interpretable or observable quantities.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chan, K. C., G. A. Karolyi, F. A. Longstaff, & A. B. Sanders (1992). An empirical comparison of alternative models of the short-term interest rate.J. Finance 47, 1209–1227.
Clark, P. K. (1973). A subordinated stochastic process model with finite variance for speculative prices.Econometrica 41, 135–159.
Cox, J. C. & S. A. Ross (1976). The valuation of options for alternative stochastic processes.J. Financial Economics 3, 145–166.
Delbaen, F.&H. Shirakawa (1997). Squared Bessel processes and their applications to the square root interest rate model. Preprint. Department of Industrial Engineering and Management, Tokio Institute of Technology.
Derman, E. & I. Kani (1994). Riding on a smileRisk 7, 32–39.
Duffle, D. (1996).Dynamic Asset Pricing Theory(2nd ed.). Princeton, University Press.
Dupire, B. (1994). Pricing with a smile.Risk 7, 18–20.
Fouque, J. P., G. Papanicolau&K. R. Sircar (1999). Financial modelling in a fast mean-reverting stochastic volatility environment. Asian-Pacific Financial Markets 6, 37–48.
Frey, R. (1997). Derivative asset analysis in models with level-dependent and stochastic volatility. Mathematics of Finance, Part II.CWI Quarterly 10(1), 1–34.
Geman, H., D. Madan, & M. Yor (1998). Asset prices are Brownian motion: only in business time. University Paris IX Dauphine, (working paper).
Ghysels, E., A. Harvey, & E. Renault (1996). Stochastic volatility. InStatistical Methods in FinanceVolume 14 ofHandbook of Statist.pp. 119–191. North-Holland.
Heath, D.&E. Platen (2000). Pricing and hedging of derivatives under an alternative asset price model with stochastic volatility. University of Technology Sydney, (working paper).
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options.Rev. Financial Studies 6(2), 327–343.
Heyde, C. C. (1999). A risky asset model with strong dependence through fractal activity time. Columbia University, New York, (working paper).
Hurst, S. R. & E. Platen (1997). The marginal distributions of returns and volatility. In Y. Dodge (Ed.)Li-Statistical Procedures and Related TopicsVolume 31 of IMS Lecture Notes - Monograph Seriespp. 301–314. Institute of Mathematical Statistics Hayward, California.
Hurst, S. R., E. Platen, & S. T. Rachev (1997). Subordinated market index models: A comparison.Financial Engineering and the Japanese Markets 4, 97–124.
Karatzas, I. & S. E. Shreve (1988).Brownian Motion and Stochastic Calculus.Springer.
Karatzas, I.&S. E. Shreve (1998).Methods of Mathematical Finance, Volume 39 ofAppl. Math.Springer.
Platen, E. (1999a). On the log-return distribution of index benchmarked share prices. Technical report, University of Technology, Sydney. QFRG Research Paper 22.
Platen, E. (1999b). A short term interest rate model.Finance and Stochastics 3(2), 215–225.
Platen, E. (2000). Financial modelling with benchmark portfolio. University of Technology Sydney, (working paper).
Protter, P. (1990).Stochastic Integration and Differential Equations.Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Platen, E. (2001). A Minimal Financial Market Model. In: Kohlmann, M., Tang, S. (eds) Mathematical Finance. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8291-0_27
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8291-0_27
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9506-4
Online ISBN: 978-3-0348-8291-0
eBook Packages: Springer Book Archive