Asia-Pacific Financial Markets

, Volume 11, Issue 4, pp 431–444 | Cite as

A Complete-Market Generalization of the Black-Scholes Model

  • Koichiro TakaokaEmail author


The author proposes a new single-stock generalization of the Black-Scholes model. The stock price process is Markovian, the volatility is time-varying, and the market is complete. We also consider the option pricing based on our model and a connection with the equilibrium theory.

Key words

Black-Scholes model complete market models equilibrium price option pricing volatility 


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  1. Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities, J. Political Economy 81(3), 637–659.CrossRefGoogle Scholar
  2. Cox, J. C. and Ross, S. A. (1976) The valuation of options for alternative stochastic processes, Journal of Financial Economics 3, 145–166.CrossRefGoogle Scholar
  3. Heston, S. L. (1993) A closed form solution for options with stoshastic volatility with applications to bond currency options, Review of Financial Studies 6, 327–342.CrossRefGoogle Scholar
  4. Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton University Press, 1974.Google Scholar
  5. Hull, J. C. Options, Futures, and Other Derivatives, Fifth Edition, Prentice-Hall, 2002.Google Scholar
  6. Hull, J. C. and White, A. (1987) The pricing of options on asset with stochastic volatilities, Journal of Finance 42, 281–300.CrossRefGoogle Scholar
  7. Ishimura, N. and Sakaguchi, T. Exact solutions of a model for asset prices by K. Takaoka, To appear in Asia-Pacific Financial Markets.Google Scholar
  8. Jamshidian, F. (1989) An exact bond option formula, Journal of Finance 44(1), 205–209.CrossRefGoogle Scholar
  9. Karatzas, I. and Shreve, S. E. Methods of Mathematical Finance, Springer, 1998.Google Scholar
  10. Merton, R. C. (1976) Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics 3, 125–144.CrossRefGoogle Scholar
  11. Musiela, M. and Rutkowski, M. Martingale Methods in Financial Modelling, Springer, 1997.Google Scholar
  12. Protter, P. Stochastic Integration and Differential Equations, Springer, 1992.Google Scholar
  13. Takaoka, K. An equilibrium model of the short-term stock price behavior, Working Paper 49, Faculty of Commerce, Hitotsubashi University (2000).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Graduate School of Commerce and ManagementHitotsubashi UniversityTokyoJapan

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