## Abstract

The implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a "bump and revalue" method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.

Original language | English |
---|---|

Pages (from-to) | 239-266 |

Number of pages | 28 |

Journal | ASTIN Bulletin |

Volume | 45 |

Issue number | 2 |

Early online date | 5 Jan 2015 |

DOIs | |

Publication status | Published - May 2015 |

Externally published | Yes |

## Keywords

- Greeks
- Heston stochastic volatility model
- likelihood-ratio method
- Monte Carlo estimation
- pathwise method
- sensitivities
- stochastic interest rates
- Stochastic simulation
- variable annuity