Liquidity in a binomial market

Selim Gökay, Halil Mete Soner

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study the binomial version of the illiquid market model introduced by Çetin, Jarrow, and Protter for continuous time and develop efficient numerical methods for its analysis. In particular, we characterize the liquidity premium that results from the model. In Çetin, Jarrow, and Protter, the arbitrage free price of a European option traded in this illiquid market is equal to the classical value. However, the corresponding hedge does not exist and the price is obtained only inL 2-approximating sense. Çetin, Soner, and Touzi investigated the super-replication problem using the same supply curve model but under some restrictions on the trading strategies. They showed that the super-replicating cost differs from the Black-Scholes value of the claim, thus proving the existence of liquidity premium. In this paper, we study the super-replication problem in discrete time but with no assumptions on the portfolio process. We recover the same liquidity premium as in the continuous-time limit. This is an independent justification of the restrictions introduced in Çetin, Soner, and Touzi. Moreover, we also propose an algorithm to calculate the option's price for a binomial market.

Original languageEnglish (US)
Pages (from-to)250-276
Number of pages27
JournalMathematical Finance
Volume22
Issue number2
DOIs
StatePublished - Apr 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

Keywords

  • Binomial model
  • Dynamic programming
  • Liquidity
  • Super-replication

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