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Securities Markets, Diffusion State Processes, and Arbitrage-Free Shadow Prices

Published online by Cambridge University Press:  06 April 2009

John Heaney  and
Geoffrey Poitras
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Abstract

This paper develops the parametric restrictions imposed on diffusion state processes by the requirement of arbitrage-free asset pricing. Using the equivalent martingale measure as a starting point, the diffusion property is exploited to specify the shadow pricing function, which takes conditional state variable probabilities under the reference measure into arbitrage-free contingent claim prices. The main results of the paper provide differential equations associated with the shadow price function that are used to identify restrictions on the parameters of assumed diffusion processes. The paper concludes with an application to the CIR model where the state variable, the instantaneous interest rate, is assumed to follow a square root process. Calculations are also provided for the parametric restrictions imposed on the Brownian bridge and OU state variable processes.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 29 , Issue 2 , June 1994 , pp. 223 - 239
Copyright
Copyright © School of Business Administration, University of Washington 1994

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References

Arnold, L.Stochastic Differential Equations. New York, NY: John Wiley (1974).Google Scholar
Back, K., and Pliska, S.. “On the Fundamental Theorem of Asset Pricing with an Infinite State Space.” Journal of Mathematical Economics, 20 (1991), 1–18.CrossRefGoogle Scholar
Bick, A. “On the Consistency of the Black-Scholes Model with a General Equilibrium Framework.” Journal of Financial and Quantitative Analysis, 22 (1987), 259–275.CrossRefGoogle Scholar
Bick, A. “On Viable Diffusion Price Processes of the Market Portfolio.” Journal of Finance, 45 (1990), 673–689.CrossRefGoogle Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–659.CrossRefGoogle Scholar
Breeden, D., and Litzenberger, R.. “Prices of State-Contingent Claims Implicit in Option Prices.” Journal of Business, 51 (1978), 621–651.CrossRefGoogle Scholar
Brennan, M. “The Pricing of Contingent Claims in Discrete Time Models.” Journal of Finance, 34 (1979), 53–68.CrossRefGoogle Scholar
Brennan, M., and Schwartz, E.. “Conditional Predictions of Bond Prices and Returns.” Journal of Finance, 35 (1980), 405–417.CrossRefGoogle Scholar
Cheng, S. “On the Feasibility of Arbitrage-Based Option Pricing when Stochastic Bond Price Processes are Involved.” Journal of Economic Theory, 53 (1991), 185–198.CrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “An Intertemporal General Equilibrium Model of Asset Prices.” Econometrica, 53 (03 1985a), 363–384.CrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (03 1985b), 385–407.CrossRefGoogle Scholar
Duffie, D. “Stochastic Equilibria: Existence, Spanning Number and the ‘No Expected Financial Gains from Trade’ Hypothesis.” Econometrica, 54 (1986), 1161–1184.CrossRefGoogle Scholar
Duffie, D.Dynamic Asset Pricing Theory. Princeton, NJ, Princeton Univ. Press (1992).Google Scholar
Feigen, P. “Maximum Likelihood Estimation for Continuous-Time Stochastic Processes.” Advances in Applied Probability, 8 (1976), 712–736.CrossRefGoogle Scholar
Flesaker, B. “Arbitrage Free Pricing of Interest Rate Futures and Forward Contracts.” Journal of Futures Markets, 13 (1993), 77–92.CrossRefGoogle Scholar
Garman, M. “A General Theory of Asset Valuation under Diffusion State Processes.” Center for Research in Management Science Working Paper 50, Univ. of California at Berkeley (1977).Google Scholar
Grenander, U.Abstract Inference. New York, NY: Wiley (1981).Google Scholar
Harrison, J., and Kreps, D.. “Martingales and Arbitrage in Multiperiod Securities Markets.” Journal of Economic Theory, 20 (1979), 381–408.CrossRefGoogle Scholar
Harrison, J., and Pliska, S.. “Martingales and Stochastic Integrals in the Theory of Continuous Trading.” Stochastic Processes and Applications, 11 (1981), 215–260.CrossRefGoogle Scholar
Harrison, J., and Pliska, S.. “A Stochastic Calculus Model of Continuous Trading.” Stochastic Processes and Applications, 15 (1983), 313–316.CrossRefGoogle Scholar
He, H., and Leland, H.. “On Equilibrium Asset Price Processes.” Review of Financial Studies, 6 (1993), 593–617.CrossRefGoogle Scholar
Huang, C. “Information Structures and Viable Price Systems.” Journal of Mathematical Economics, 14 (1985), 215–240.CrossRefGoogle Scholar
Huang, C. “An Intertemporal General Equilibrium Asset Pricing Model.” Econometrica, 55 (1987), 117–142.CrossRefGoogle Scholar
Ingersoll, J.Theory of Financial Decision Making. Totawa, NJ: Rowan Littlefield (1989).Google Scholar
R., Jarrow, and Madan, D.. “A Characterization of Complete Securities Markets on a Brownian Filtration.” Mathematical Finance, 1 (1991), 31–43.Google Scholar
Kreps, D. “Arbitrage and Equilibrium in Economies with Infinitely Many Commodities.” Journal of Mathematical Economics, 8 (1981), 15–35.CrossRefGoogle Scholar
Rabinovitch, R. “Pricing Stock and Bond Options when the Default-Free Rate is Stochastic.” Journal of Financial and Quantitative Analysis, 24 (1989), 447–457.CrossRefGoogle Scholar
Ritchken, P., and Boenawan, K.. “On Arbitrage-Free Pricing of Interest Rate Contingent Claims.” Journal of Finance, 45 (1990), 259–264.Google Scholar
Rogers, L., and Williams, D.. Diffusions, Markov Processes and Martingales. V.2 Ito Calculus. New York, NY: Wiley (1987).Google Scholar
Taqqu, M., and Willinger, W.. “The Analysis of Finite Security Markets Using Martingales.” Advances in Applied Probability, 19 (1987), 1–25.CrossRefGoogle Scholar
Vasicek, O. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5 (1977), 177–188.CrossRefGoogle Scholar