SOME NOTES ABOUT THE MARTINGALE REPRESENTATION THEOREM AND THEIR APPLICATIONS

Reza Habibi     (Iran Banking Institute, Central Bank of Iran, Pasdaran Ave., 8-th Negarestan, Tehran, Iran, Islamic Republic of)

Abstract


An important theorem in stochastic finance field is the martingale representation theorem. It is useful in the stage of making hedging strategies (such as cross hedging and replicating hedge) in the presence of different assets with different stochastic dynamics models. In the current paper, some new theoretical results about this theorem including derivation of serial correlation function of a martingale process and its conditional expectations approximation are proposed. Applications in optimal hedge ratio and financial derivative pricing are presented and sensitivity analyses are studied. Throughout theoretical results, simulation-based results are also proposed. Two real data sets are analyzed and concluding remarks are given. Finally, a conclusion section is given.


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References


  1. Baxter M. Financial Calculus: an Introduction to Derivative Pricing. 1st ed. UK: Cambridge University Press, 1996. 233 p.
  2. Duffie D. Dynamic Asset Pricing Theory. 1st ed. USA: Princeton University Press, 1992. 472 p.
  3. Gann W.D. Method for Forecasting the Stock Market. USA: Create Space Independent Publishing Platform, 2012. 28 p.
  4. Hull J. Options, Futures and Other Derivatives. 1st ed. USA: Prentice-Hall, 1993. 496 p.
  5. Klebaner F. Introduction to Stochastic Calculus with Applications. 2nd ed. UK: Imperial College, 2005. 430 p.
  6. Ross S. A First Course in Probability. 8th Ed. USA: Prentice Hall, 2010. 552 p.
  7. Wilmott P. Option Pricing: Mathematical Models and Computation. UK: Oxford Financial, 1993. 457 p.



DOI: http://dx.doi.org/10.15826/umj.2020.2.008

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