Pricing catastrophe options in discrete operational time

Carolyn W. Chang, Jack S.K. Chang and WeiLi Lu

Insurance: Mathematics and Economics, 2008, vol. 43, issue 3, 422-430

Abstract: We employ a doubly-binomial process as in Gerber [Gerber, H.U., 1988. Mathematical fun with the compound binomial process. ASTIN Bull. 18, 161-168] to discretize and generalize the continuous "randomized operational time" model of Chang et al. ([Chang, C.W., Chang, J.S.K., Yu, M.T., 1996. Pricing catastrophe insurance futures call spreads: A randomized operational time approach. J. Risk Insurance 63, 599-616] and CCY hereafter) from a complete-market continuous-time setting to an incomplete-market discrete-time setting, so as to price a richer set of catastrophe (CAT) options. For futures options, we derive the equivalent martingale probability measures by benchmarking to the shadow price of a bond to span arrival uncertainty, and the underlying futures price to span price uncertainty. With a time change from calendar time to the operational transaction-time dimension, we derive CCY as a limiting case under risk-neutrality when both calendar-time and transaction-time intervals shrink to zero. For a cash option with non-traded underlying loss index, we benchmark to the market reinsurance premiums to span claim uncertainty, and with a time change to claim time, we derive the cash option price as a binomial sum of claim-time binomial Asian option prices under the martingale measures.

Keywords: Catastrophe; insurance; derivatives; Randomized; operational; time; Trinomial; tree; Stochastic; time; change; Binomial; Tree; with; random; time; steps; Option; pricing (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:43:y:2008:i:3:p:422-430

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