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Pricing via anticipative stochastic calculus

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Eckhard Platen  and
Rolando Rebolledo
Eckhard Platen*
Affiliation:
The Australian National University
Rolando Rebolledo*
Affiliation:
Universidad Católica de Chile
*
* Postal address: IAS, SMS, The Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
** Postal address: Universidad Católica de Chile, Faculdad de Matemática, Casilla 306, Santiago 22, Chile.
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Abstract

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

Keywords

DERIVATIVE SECURITIESBONDSANTICIPATIVE LINEAR STOCHASTIC EQUATIONS

MSC classification

Secondary: 60G35: Signal detection and filtering 60H10: Stochastic ordinary differential equations

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 26 , Issue 4 , December 1994 , pp. 1006 - 1021
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This research was completed while R. R. was visiting the Australian National University. He acknowledges support received from ANU and FONDECYT grant 0807–91 for this program.

References

[1] Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. J. Political Economy 81, 637–659.Google Scholar
[2] Black, F., Derman, E. and Toy, W. (1990) A one-factor model of interest rates and its application to treasury bond options. Financial Analysis J. Jan./Feb. issue, 33–39.Google Scholar
[3] Brennan, M. J. and Schwartz, E. S. (1979). A continuous-time approach to the pricing of bonds. J. Banking and Finance 3, 133–155.CrossRefGoogle Scholar
[4] Buckdahn, R. (1988) Quasilinear partial stochastic difference equations without nonanticipation requirement. Preprint.Google Scholar
[5] Buckdahn, R. (1990) Linear Skorokhod stochastic differential equations. Prob. Theory. Rel. Fields 90, 223–240.CrossRefGoogle Scholar
[6] Cox, J. C., Ingersoll, J. E. and Ross, S. A. (1985) A theory of the term structure of interest rates. Econometrica 53, 385–407.Google Scholar
[7] Dellacherie, C. and Meyer, P. A. (1975) Probabilités et potentiel, Vol. 1. Hermann, Paris.Google Scholar
[8] Harrison, J. M. and Pliska, S. R. (1983) A stochastic calculus model of continuous trading: Complete markets. Stoch. Proc. Appl. 15, 313–316.CrossRefGoogle Scholar
[9] Heath, D., Jarrow, R. and Morton, A. (1987) Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Rev. Financial Studies. Google Scholar
[10] Ho, T. S. Y. and Lee, S. B. (1986). Term structure movements and pricing of interest rate claims. J. Finance 41, 1011–1029.Google Scholar
[11] Hull, J. and White, A. (1990) Pricing interest rate derivative securities. Rev. Financial Studies 3, 573–592.Google Scholar
[12] El Karoui, N., Myneni, R. and Viswanathan, R. (1992) Arbitrage pricing and hedging of interest claims with state variables. Working Paper, Stanford University.Google Scholar
[13] Nualart, D. (1990) Stochastic calculus for anticipating processes. Cuadernos de la Escuela de Invierno de Probabilidad y Estadística de Santiago.Google Scholar
[14] Nualart, D. and Pardoux, E. (1988) Stochastic calculus with anticipating integrand. Prob. Theory Rel. Fields 78, 80–129.Google Scholar
[15] Platen, E. (1993) An approach to bond pricing. Miniconference on Stochastics and Finance, pp. 57–70. ANU Statistics Reports CSTR-002-1993.Google Scholar
[16] Protter, P. (1990) Stochastic integrals and Stochastic Differential Equations. A New Approach. Springer-Verlag, Berlin.Google Scholar
[17] Vasicek, O. A. (1977) An equilibrium characterization of the term structure. J. Financial Econom. 5, 177–188.Google Scholar