This study designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the Value-at-Risk (VaR) constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Additionally, this study also calculates the optimal insurance levels for these models when we restrict the indemnity to be one of three common forms: a deductible policy, an upper-limit policy, or a policy with proportional coinsurance.

We are indebted to Robert I. Webb (the editor) and an anonymous referee for valuable comments and suggestions. We are responsible for any remaining errors.This study extends the long-term temperature model proposed by Alaton et al. (2002) by taking into account ARCH/GARCH effects to reflect the clustering of volatility in temperature. The fixed variance model and the ARCH model are estimated using Taiwan weather data from 1974 through 2003. The results show that for HDD/CDD the call price is higher under ARCH-effects variance than under fixed variance, while the put price is lower. Although different pricing methods are employed in pricing weather options, the effects of mean and standard deviation on option prices are mathematically proved to be the same as those in pricing traditional financial derivatives using the Black-Scholes formula.

This study develops an optimal insurance contract endogenously under a value-at-risk (VaR) constraint. Although Wang et al. [2005] had examined this problem, their assumption implied that the insured is risk neutral. Consequently, this study extends Wang et al. [2005] and further considers a more realistic situation where the insured is risk averse. The study derives the optimal insurance contract as a single deductible insurance when the VaR constraint is redundant or as a double deductible insurance when the VaR constraint is binding. Finally, this study discusses the optimal coverage level from common forms of insurances, including deductible insurance, upper-limit insurance, and proportional coinsurance.

No abstract

This study designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the Value-at-Risk (VaR) constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Additionally, this study also calculates the optimal insurance levels for these models when we restrict the indemnity to be one of three common forms: a deductible policy, an upper-limit policy, or a policy with proportional coinsurance. Copyright Springer Science + Business Media, Inc. 2005value at risk, optimal insurance, deductible, policy limit, coinsurance,