Communications in Mathematical Sciences

Volume 14 (2016)

Number 7

Option replication in discrete time with the cost of illiquidity

Pages: 1947 – 1962

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n7.a8

Authors

Yegor Sorokin (Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada; and Market Risk Measurement, Scotiabank, Toronto, Ontario, Canada)

Hyejin Ku (Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada)

Abstract

We introduce a model of liquidity risk through a stochastic supply curve for price taking traders. The supply curve gives the actual execution cost investors face in trading assets. We use the solutions to the modified Black–Scholes type PDE and obtain the delta-hedging strategies. We then show the replicating portfolio including liquidity costs converges to the payoff of the option. We demonstrate the replication error of discrete-time trading strategy decreases with inhomogeneous rebalancing times, and investigate an optimal positioning of them.

Keywords

option replication, inhomogeneous rebalancing, liquidity risk, illiquidity

2010 Mathematics Subject Classification

91B24, 91G20, 91G80

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