Option pricing in a CEV model with liquidity costs

Krzysztof Turek

Applicationes Mathematicae (2016)

  • Volume: 43, Issue: 1, page 25-55
  • ISSN: 1233-7234

Abstract

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The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar to fixed point theorems and Feynman-Kac representation. Asymptotic behaviour of the option price for small values of the illiquidity parameter is also analysed and a numerical procedure along with some numerical results is included.

How to cite

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Krzysztof Turek. "Option pricing in a CEV model with liquidity costs." Applicationes Mathematicae 43.1 (2016): 25-55. <http://eudml.org/doc/286308>.

@article{KrzysztofTurek2016,
abstract = {The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar to fixed point theorems and Feynman-Kac representation. Asymptotic behaviour of the option price for small values of the illiquidity parameter is also analysed and a numerical procedure along with some numerical results is included.},
author = {Krzysztof Turek},
journal = {Applicationes Mathematicae},
keywords = {option pricing; CEV model; liquidity costs; hedging; price impact},
language = {eng},
number = {1},
pages = {25-55},
title = {Option pricing in a CEV model with liquidity costs},
url = {http://eudml.org/doc/286308},
volume = {43},
year = {2016},
}

TY - JOUR
AU - Krzysztof Turek
TI - Option pricing in a CEV model with liquidity costs
JO - Applicationes Mathematicae
PY - 2016
VL - 43
IS - 1
SP - 25
EP - 55
AB - The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar to fixed point theorems and Feynman-Kac representation. Asymptotic behaviour of the option price for small values of the illiquidity parameter is also analysed and a numerical procedure along with some numerical results is included.
LA - eng
KW - option pricing; CEV model; liquidity costs; hedging; price impact
UR - http://eudml.org/doc/286308
ER -

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