A jump-diffusion model for pricing and hedging with margined options: An application to Brent crude oil contracts

• Published in: Journal of banking & finance 2019-01, Vol.98, p.137-155
• Main Authors: Hilliard, Jimmy E., Hilliard, Jitka
• Format: Article
• Language: English
• ISSN: 0378-4266; 1872-6372
• DOI: 10.1016/j.jbankfin.2018.10.013

•Generalized proof of put-call parity for margined options.•Generalized proof of no-early exercise premium for margined options.•Pricing a margined option under a jump-diffusion.•Methodology for hedging options with underlying jump-diffusion.•Application to Brent Crude margined options on futures. We develop a jump-diffusion model for pricing and hedging with margined options on futures. Unlike a standard equity option, margined options require no up-front payment. An attractive feature of margined options is that there is no early exercise premiums under general assumptions. Model parameter estimates and out-of-sample pricing errors are calculated using data on Brent crude contracts. Using the same pricing technology, we also hedge equity style options with margined options. Hedging coefficients are derived by matching an extended set of Greeks. We find that a target equity option can be effectively hedged using a portfolio of two margined options and the underlying. As has been reported elsewhere, a delta hedge is inappropriate when the underlying is a jump-diffusion.