Transaction Cost Under The Link To Guarantee Rights And Interests Of The Life Insurance Contract Pricing

In presence of proportional transaction costs, we discuss the pricing models and methods of the equity-linked life insurance with guarantee. Assuming that the insurance company is risk neutral towards mortality risk, the benefits of the contract can be decomposed into two parts:part of fixed guarantee asset and part of European standard call options. We apply the Leland method and the utility indifference method of hedging options on it, and derive pricing formulas separately in discrete and continuous time.Firstly, the paper reviews the Leland method to copy the call option in discrete time, the price formula given by it is essentially volatility modified Black-Scholes formula, and the modifying of volatility depends on the proportion of transaction costs and the revision period. Numerical analysis shows, the replication error decreases as the revision frequency and expiration date increase, and is slightly affected by the transaction costs. Appling the Leland method to the equity-linked life insurance contract with guarantee, the price formula is derived, which is closely related to the transaction costs and the revision period.Secondly, we introduce the utility indifference method of hedging options in continuous time, which is different from Delta hedging strategy, but provides an optimal trading interval for investors. Numerical analysis shows, the optimal interval will be narrower with the increase of the risk aversion coefficient, and will be wider with the increase of transaction costs. Appling the utility indifference method, we obtain the price of the equity-linked life insurance contract with guarantee, which can be solved numerically, then we use the discrete dynamic programming formula to compute it.The simulation results show that the prices calculated by these two methods both increase, as each of the proportion of transaction costs and the guarantee increases, and decrease with the extension of maturity. Leland method depends on the rebalance period of the hedging portfolio, which must be fixed, the shorter the period is, the higher the price of the contract we get. While utility indifference method relies on insurance company’s risk aversion on financial markets, the greater the risk aversion coefficient is, the higher the price of the contract we get. From comparative analysis of calculation results of the two methods, we can see, the latter price is higher than the former price, which indicates that risk attitude is a very important factor to affect investors’decisions.