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

Jimmy E. Hilliard and Jitka Hilliard

Journal of Banking & Finance, 2019, vol. 98, issue C, 137-155

Abstract: 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.

Date: 2019
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