TY - JOUR
T1 - Option pricing with illiquidity during a high volatile period
AU - El-Khatib, Youssef
AU - Hatemi Jarabad, Abdulnasser
N1 - Funding Information:
The first author would like to express his sincere appreciation to the United Arab Emirates University Research Office for the financial support of UPAR Grant No. 31S369. We also would like to thank the three anonymous reviewers for offering constructive comments, which have resulted in improving the paper. A previous version of this paper was presented at the conference ICNAAM 2018 (Rhodes, Greece). We thank the participants for their comments. The usual disclaimer applies however.
Publisher Copyright:
© 2021 John Wiley & Sons, Ltd.
PY - 2021
Y1 - 2021
N2 - This paper deals with the valuation of options in markets without liquidity and under stress. More precisely, a European option is considered when the dynamic of the underlying asset is governed by a Brownian motion. Following Liu and Young (2005), a term related to the number of invested stocks is embedded into the model. Moreover, the volatility of the asset is augmented by a separate function that models the abnormal increase of the volatility. Under these settings, we deal with the evaluation of European options. Dealing with illiquidity during a financial crisis is an important issue in terms of financial risk management, which has not been tackled with in the literature to the best of our knowledge. It is during these non-normal periods that volatility in the financial markets is very high and tools for reducing the underlying risk are urgently needed for hedging purposes. In this work, the PDE of the option price within this context is derived, which is a generalization of the PDE of Liu and Young (2005). Moreover, the hedging strategy to replicate the price of the option is obtained. Numerical simulations for the underlying asset price are conducted. The illustrations support several stylized facts of the model that seem to reflect what is operational in the real financial markets.
AB - This paper deals with the valuation of options in markets without liquidity and under stress. More precisely, a European option is considered when the dynamic of the underlying asset is governed by a Brownian motion. Following Liu and Young (2005), a term related to the number of invested stocks is embedded into the model. Moreover, the volatility of the asset is augmented by a separate function that models the abnormal increase of the volatility. Under these settings, we deal with the evaluation of European options. Dealing with illiquidity during a financial crisis is an important issue in terms of financial risk management, which has not been tackled with in the literature to the best of our knowledge. It is during these non-normal periods that volatility in the financial markets is very high and tools for reducing the underlying risk are urgently needed for hedging purposes. In this work, the PDE of the option price within this context is derived, which is a generalization of the PDE of Liu and Young (2005). Moreover, the hedging strategy to replicate the price of the option is obtained. Numerical simulations for the underlying asset price are conducted. The illustrations support several stylized facts of the model that seem to reflect what is operational in the real financial markets.
KW - derivatives securities
KW - financial crisis
KW - illiquid markets
KW - numerical methods
KW - PDEs
KW - stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=85108706217&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85108706217&partnerID=8YFLogxK
U2 - 10.1002/mma.7612
DO - 10.1002/mma.7612
M3 - Article
AN - SCOPUS:85108706217
SN - 0170-4214
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
ER -