Discrete-Time Option Pricing with Stochastic Liquidity

46 Pages Posted: 8 Mar 2016 Last revised: 7 Sep 2016

See all articles by Markus Leippold

Markus Leippold

University of Zurich; Swiss Finance Institute

Steven Schaerer

University of Zurich - Department Finance

Date Written: September 6, 2016

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.

Keywords: Market Liquidity; Bid-Ask Spreads; Option Pricing; Stochastic Liquidity; Conic Finance

JEL Classification: C51; D52; G12; G13

Suggested Citation

Leippold, Markus and Schaerer, Steven, Discrete-Time Option Pricing with Stochastic Liquidity (September 6, 2016). Swiss Finance Institute Research Paper No. 16-15, Available at SSRN: https://ssrn.com/abstract=2744493 or http://dx.doi.org/10.2139/ssrn.2744493

Markus Leippold (Contact Author)

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Steven Schaerer

University of Zurich - Department Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland

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