ArticleOriginal scientific text

Title

Security price modelling by a binomial tree

Authors 1, 2

Affiliations

  1. Department of Mathematics, Vilnius University, Naugarduko 24, Vilnius 2600, Lithuania
  2. Institute of Mathematics and Informatics, Akademijos 4, Vilnius 2600, Lithuania

Abstract

We consider multidimensional tree-based models of arbitrage-free and path-independent security markets. We assume that no riskless investment exists. Contingent claims pricing and hedging problems in such a market are studied.

Keywords

numeraire portfolio, binomial market model, arbitrage-free market

Bibliography

  1. J. C. Cox, S. A. Ross and M. Rubinstein (1979), Option pricing: a simplified approach, J. Financial Econom. 7, 229-263.
  2. J. M. Harrison and S. Pliska (1981), Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl. 11, 215-260.
  3. J. Jacod and A. N. Shiryaev (1998), Local martingales and the fundamental asset pricing theorems in the discrete-time case, Finance Stochastics 2, 259-273.
  4. B. A. Jensen and J. A. Nielsen (1996), Pricing by 'No arbitrage', in: Time Series Models in Econometrics, Finance and Other Fields, D. R. Cox et al. (eds.), Chapman & Hall, London, 177-223.
  5. Yu. M. Kabanov and D. O. Kramkov (1994), No-arbitrage and equivalent martingale measures: an elementary proof of the Harrison-Pliska theorem, Theory Probab. Appl. 39, 635-640.
  6. D. Lamberton and B. Lapeyre (1996), Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, London.
  7. J. B. Long Jr. (1990), The numeraire portfolio, J. Financial Econom. 26, 29-69.
  8. M. Motoczyński and Ł. Stettner (1998), On option pricing in the multidimensional Cox-Ross-Rubinstein model, Appl. Math. (Warsaw) 25, 55-72.
Pages:
253-266
Main language of publication
English
Received
1998-06-25
Accepted
1999-02-08
Published
1999
Exact and natural sciences