Evaluation of equity-linked products in the presence of policyholder surrender option using risk-control strategies

Throughout the past couple of decades, the surge in the sale of equity-linked products has led to many discussions on the evaluation and risk management of surrender options embedded in these products. However, most studies treat such options as American/Bermudian style options. In this article, a different approach is presented where only a portion of the policyholders react optimally due to the belief that not all policyholders are rational. Through this method, a probability of surrender is obtained based on the option moneyness and the product is partially hedged using local risk-control strategies. This partial hedging approach is versatile since few assumptions are required for the financial framework. To compare the different surrender assumptions, the initial capital requirement for an equity-linked product is obtained under a regime-switching equity model. Numerical examples illustrate the dynamics and efficiency of this hedging approach.

CVaR-hedging and its applications to equity-linked life insurance contracts with transaction costs

<p style='text-indent:20px;'>This paper analyzes Conditional Value-at-Risk (CVaR) based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs. A nonlinear partial differential equation (PDE) that an option value process inclusive of transaction costs should satisfy is provided. In particular, the closed-form expression of a European call option price is given. Meanwhile, the CVaR-based partial hedging strategy for a call option is derived explicitly. Both the CVaR hedging price and the weights of the hedging portfolio are based on an adjusted volatility. We obtain estimated values of expected total hedging errors and total transaction costs by a simulation method. Furthermore,our results are implemented to derive target clients’ survival probabilities and age of equity-linked life insurance contracts.</p>

Risk minimization for game options in markets imposing minimal transaction costs

We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction cost. We prove that in the continuous-time Black‒Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model.