Discrete-time option pricing with stochastic liquidity |
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| Affiliation: | 1. Department of Banking and Finance, University of Zurich, Switzerland;2. Swiss Finance Institute (SFI), Switzerland;1. Universidad Pública de Navarra, Spain;2. Universidad CEU Cardenal Herrera, Spain;1. College of Business Administration, Chonnam National University, Gwangju, South Korea;2. College of Business, Korea Advanced Institute of Science and Technology, Seoul, South Korea;3. Korea Exchange, Busan, South Korea;1. Universität zu Köln and Technische Universität Dortmund, Meister-Ekkehart-Str. 9, 50923 Köln, Germany;2. Universität Leipzig and Technische Universität Dortmund, Grimmaische Str. 12, 04109 Leipzig, Germany;3. FOM Hochschule für Oekonomie & Management, Feldstraße 88, 46535 Dinslaken, Germany |
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| Abstract: | Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant liquidity model of Madan (2010). With this extension, we can replicate the term and skew structures of bid-ask spreads typically observed in option markets. We show how to implement such a stochastic liquidity model within our framework using multidimensional binomial trees and we calibrate it to call and put options on the S&P 500. |
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