Indifference valuation in incomplete binomial models

M. Musiela[1]; E. Sokolova[2]; T. Zariphopoulou[3]

  • [1] BNP Paribas London
  • [2] Barclays Capital
  • [3] The Oxford-Man Institute and Mathematical Institute, University of Oxford; and Departments of Mathematics and IROM, The University of Texas in Austin

MathematicS In Action (2010)

  • Volume: 3, Issue: 2, page 1-36
  • ISSN: 2102-5754

Abstract

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The indifference valuation problem in incomplete binomial models is analyzed. The model is more general than the ones studied so far, because the stochastic factor, which generates the market incompleteness, may affect the transition propabilities and/or the values of the traded asset as well as the claim’s payoff. Two pricing algorithms are constructed which use, respectively, the minimal martingale and the minimal entropy measures. We study in detail the interplay among the different kinds of market incompleteness, the pricing measures and the price functionals. The dependence of the prices on the choice of the trading horizon is discussed. The family of “almost complete” (reduced) binomial models is also studied. It is shown that the two measures and the associated price functionals coincide, and that the effects of the horizon choice dissipate.

How to cite

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Musiela, M., Sokolova, E., and Zariphopoulou, T.. "Indifference valuation in incomplete binomial models." MathematicS In Action 3.2 (2010): 1-36. <http://eudml.org/doc/116436>.

@article{Musiela2010,
abstract = {The indifference valuation problem in incomplete binomial models is analyzed. The model is more general than the ones studied so far, because the stochastic factor, which generates the market incompleteness, may affect the transition propabilities and/or the values of the traded asset as well as the claim’s payoff. Two pricing algorithms are constructed which use, respectively, the minimal martingale and the minimal entropy measures. We study in detail the interplay among the different kinds of market incompleteness, the pricing measures and the price functionals. The dependence of the prices on the choice of the trading horizon is discussed. The family of “almost complete” (reduced) binomial models is also studied. It is shown that the two measures and the associated price functionals coincide, and that the effects of the horizon choice dissipate.},
affiliation = {BNP Paribas London; Barclays Capital; The Oxford-Man Institute and Mathematical Institute, University of Oxford; and Departments of Mathematics and IROM, The University of Texas in Austin},
author = {Musiela, M., Sokolova, E., Zariphopoulou, T.},
journal = {MathematicS In Action},
keywords = {indifference pricing; incomplete markets; utility function; minimal martingale measure; minimal entropy measure; binomial model},
language = {eng},
number = {2},
pages = {1-36},
publisher = {Société de Mathématiques Appliquées et Industrielles},
title = {Indifference valuation in incomplete binomial models},
url = {http://eudml.org/doc/116436},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Musiela, M.
AU - Sokolova, E.
AU - Zariphopoulou, T.
TI - Indifference valuation in incomplete binomial models
JO - MathematicS In Action
PY - 2010
PB - Société de Mathématiques Appliquées et Industrielles
VL - 3
IS - 2
SP - 1
EP - 36
AB - The indifference valuation problem in incomplete binomial models is analyzed. The model is more general than the ones studied so far, because the stochastic factor, which generates the market incompleteness, may affect the transition propabilities and/or the values of the traded asset as well as the claim’s payoff. Two pricing algorithms are constructed which use, respectively, the minimal martingale and the minimal entropy measures. We study in detail the interplay among the different kinds of market incompleteness, the pricing measures and the price functionals. The dependence of the prices on the choice of the trading horizon is discussed. The family of “almost complete” (reduced) binomial models is also studied. It is shown that the two measures and the associated price functionals coincide, and that the effects of the horizon choice dissipate.
LA - eng
KW - indifference pricing; incomplete markets; utility function; minimal martingale measure; minimal entropy measure; binomial model
UR - http://eudml.org/doc/116436
ER -

References

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