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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.
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 -