Abstract
The authors employ the recent stochastic-control-based approach to financial mathematics to solve a problem of determination of the risk premium for a stochastic interest rate model, and the corresponding problem of equity valuation. The risk premium is determined explicitly, by means of solving a corresponding partial differential equation (PDE), in two forms: one, time-dependent, corresponding to a finite time contract expiration, and the simpler version corresponding to perpetual contracts. As stocks are perpetual contracts, when solving the problem of equity valuation, the latter form of the risk premium is used. By means of solving the general pricing PDE, an efficient equity valuation method was developed that is a combination of some sophisticated explicit formulas, and a numerical procedure.
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References
S. D. Stojanovic, Pricing and hedging of multi type contracts under multidimensional risks in incomplete markets modeled by general Itô SDE systems, Asia Pacific Financial Markets, 2006, 13: 345–372.
S. D. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution, C. R. Acad. Sci. Paris Ser. I, 2005, 340: 551–556.
S. D. Stojanovic, The dividend puzzle unpuzzled (working paper series), Available at SSRN: http://ssrn.com/abstract=879514.
J. F. Harper, Reducing parabolic partial differential equations to canonical form, European Journal of Applied Mathematics, 1994, 5: 159–164.
S. D. Stojanovic, Higher dimensional fair option pricing and hedging under HARA and CARA utilities (submitted, preprint August 2005, revised 2006, June, 28), available at SSRN: http://ssrn.com/abstract=912763.
S. D. Stojanovic, Advanced Financial Engineering for Interest Rates, Equity, and FX, garp, New York 2007.
D. Brigo and F. Mercurio, Interest Rate Models: Theory and Practice, Springer, Berlin, 2001.
J. James and N. Webber, Interest Rate Modelling, Wiley, 2000.
O. Vasicek, An Equilibrium Characterisation of the Term Structure, Journal of Financial Economics, 1977, 5: 177–188.
M. Abramowitz and I. A. Stegun, Error Function and Fresnel Integrals, in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, 1972, 83–86.
J. Kallsen, Utility-based derivative pricing in incomplete markets, Mathematical Finance-Bachelier Congress 2000, H. Geman, D. Madan, S. R. Pliska, Vorst, T. (Eds.), Springer, Berlin, 2002.
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This research was supported in part by the Center for Financial Engineering at the Suzhou University, China, and the Taft Research Center at the University of Cincinnati, USA.
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Kang, Z., Stojanovic, S.D. Interest rate risk premium and equity valuation. J Syst Sci Complex 23, 484–498 (2010). https://doi.org/10.1007/s11424-010-0142-y
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DOI: https://doi.org/10.1007/s11424-010-0142-y