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Exact Solutions of a Model for Asset Prices by K. Takaoka

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Abstract

We are concerned with a model for asset prices introduced by Koichiro Takaoka, which extends the well known Black-Scholes model. For the pricing of contingent claims, partial differential equation (PDE) is derived in a special case under the typical delta hedging strategy. We present an exact pricing formula by way of solving the equation.

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References

  • Barucci, E., Polidoro, S. and Vespri, V. (2001) Some results on partial differential equations and Asian options, Math. Models Meth. Appl. Sci., 11, 475–497.

    Article  Google Scholar 

  • Baxter, M. and Rennie, A. (1996) Financial Calculus, Cambridge University Press, Cambridge.

  • Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities, J. Political Economy 81, 637–659.

    Article  Google Scholar 

  • Bouchouev, I. and Isakov, V. (1999) Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets, Inverse Problems, 15, R95–R116.

    Article  Google Scholar 

  • Dupire, B. (1994) Pricing with a smile, RISK J., 7, 18–20.

  • Fouque, J.-P., Papanicolaou, G. and Sircar, K.R. (2000) Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge.

  • Friedman, A. (1983) Partial Differential Equations of Parabolic Type, R.E. Krieger Publ. Inc., Florida.

  • Fujita, T. (2002) Introduction to the Stochastic Analysis for Financial Derivatives (Finance no Kakuritsu-kaiseki Nyumon), Kodan-shya, Tokyo (in Japanese).

  • Hull, J. (2000) Options, Futures, and Other Derivatives, 4th edition, Prentice-Hall, New Jersey.

  • Merton, R.C. (1973) Theory of rational option pricing, Bell J. Econ. Manag. Sci., 4, 141–183.

    Article  Google Scholar 

  • Protter, P. (2001) A partial introduction to financial asset pricing theory, Stoch. Processes Appl., 91, 169–203.

    Article  Google Scholar 

  • Sakaguchi, T. (2004) An extension of the Black-Scholes model (Black-Scholes model no Kakucho), Thesis for the Master-course degree, Graduate School of Economics, Hitotsubashi University (in Japanese).

  • Takaoka, K. (2002) An extension of the Black-Scholes model for asset prices (Black-Scholes Kabuka model-no Hitotsuno Kakucho), in ``Futures Markets in the New Era (Shin-seiki no Sakimono Shijyo),'' Edited by Graduate School of Commerce and Management, Hitotsubashi University, Toyo-Keizai Shinpo-shya, Tokyo pp. 47–54 (in Japanese). See also K. Takaoka; A complete-market generalization of the Black-Scholes model, Asia-Pacific Fin. Markets, this issue.

  • Wilmott, P., Howison, S. and Dewynne, J. (1995) J. The Mathematics of Financial Derivatives, Cambridge University Press, Cambridge.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Economics, Hitotsubashi University,Kunitachi,, Tokyo, 186-8601, Japan

    Naoyuki Ishimura

  2. Nippon Securities Technology Co. Ltd., Daiya-Building 5, Shin-kawa 1-28-23, Tokyo, 104-0033, Japan

    Toshi-hiko Sakaguchi

Authors
  1. Naoyuki Ishimura
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  2. Toshi-hiko Sakaguchi
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Correspondence to Naoyuki Ishimura.

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Mathematics Subject Classification(2000):91B28,35K15

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Ishimura, N., Sakaguchi, Th. Exact Solutions of a Model for Asset Prices by K. Takaoka. Asia-Pacific Finan Markets 11, 445–451 (2004). https://doi.org/10.1007/s10690-006-9022-9

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  • DOI: https://doi.org/10.1007/s10690-006-9022-9

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