Monotonicity of Liquidity sensitive Option Prices with respect to Market Liquidity Parameters

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2022-2-18

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Kuş, Selin Özlem

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Classical option pricing models assume that market prices of traded securities are given and independent of the actions of the traders. Recently, a number of option pricing models emerged where the impact of hedging transactions on prices of the traded securities is also taken into account in the pricing of the option. In this term project we study one of these models proposed by Gueant and Pu that is based on the optimal liquidation framework of Almgren and Chriss. The model includes the price impact of the hedging transactions and allows the option payoff to depend on the settlement of the option (physical or cash). We derive two results about this model in discrete time: the option price given by the model is monotone with respect to several parameters of appearing in the market impact function and with respect to the risk sensitivity parameter. Furthermore, when the increment of the underlying security has 0 expectation, the option price is always above the risk neutral price. We compute the liquidity based option price numerically for a call option with physical settlement and provide graphical examples to the derived results.

Subject Keywords

Optimal Liquidation, Option pricing and hedging, market impact, transaction costs

URI

https://hdl.handle.net/11511/96272

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Graduate School of Applied Mathematics, Term Project

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Citation Formats

S. Ö. Kuş, “Monotonicity of Liquidity sensitive Option Prices with respect to Market Liquidity Parameters,” M.S. - Master Of Science Without Thesis, Middle East Technical University, 2022.