Local Hedging of Variable Annuities in the Presence of Basis Risk

Abstract

A method to hedge variable annuities in the presence of basis risk is developed. A regime-switching model is considered for the dynamics of market assets. The approach is based on a local optimization of risk and is therefore very tractable and flexible. The local optimization criterion is itself optimized to minimize capital requirements associated with the variable annuity policy, the latter being quantified by the Conditional Value-at-Risk (CVaR) risk metric. In comparison to benchmarks, our method is successful in simultaneously reducing capital requirements and increasing profitability. Indeed the proposed local hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. A robust version of the hedging strategies addressing model risk and parameter uncertainty is also provided.

On Fund Mapping Regressions Applied to Segregated Funds Hedging Under Regime-Switching Dynamics

“…The number of long positions 2 within the hedging portfolio during the time interval (t, t + 1] are respectively denoted by θ The injection at time t is denoted by I t (negative amounts correspond to withdrawals). Such injections are characterized by Proposition 2.1 of Trottier et al (2018). As shown in the latter work, they can be approximated by…”

“…This model is used among others by Trottier et al (2018). Regime switching processes are very popular in the segregated funds literature to model equity return dynamics, see for instance Hardy (2001Hardy ( , 2003.…”

“…See Trottier et al (2018) for additional properties of this model. An implicit feature of this model is that conditional on being in a given regime, the dependence between the two assets is driven by the Gaussian copula.…”

“…We consider the variable annuities hedging framework developed in Trottier et al (2018), which is recalled in Appendix A. In the latter setup, an insurance company hedges the risk pertaining to a GMMB contract on the underlying mutual fund F. The latter scheme considers risk on a standalone basis for a single policy at a time.…”

“…Finally, in Section 4, this note illustrates that fund mapping procedures applied within are a particular case of the family of hedging strategies developed by Trottier et al (2018). The impact induced by fund mapping regressions on hedging errors is discussed.…”