Calculating Variable Annuity Liability 'Greeks' Using Monte Carlo Simulation

TL;DR

This paper explores advanced Monte Carlo simulation techniques to accurately estimate the sensitivities ('Greeks') of variable annuity liabilities, addressing limitations of traditional bump methods especially for higher-order Greeks.

Contribution

It introduces alternative estimators within a sophisticated economic scenario generator that includes stochastic interest rates and volatility, improving the reliability of Greek calculations.

Findings

New estimators improve accuracy of Greek calculations

Method handles stochastic interest rates and volatility

Can incorporate equity jumps easily

Abstract

Hedging methods to mitigate the exposure of variable annuity products to market risks require the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means these sensitivities typically must be estimated by Monte Carlo simulation. Standard market practice is to measure such sensitivities using a "bump and revalue" method. As well as requiring multiple valuations, such approaches can be unreliable for higher order Greeks, e.g., gamma. In this article we investigate alternative estimators implemented within an advanced economic scenario generator model, incorporating stochastic interest-rates and stochastic equity volatility. The estimators can also be easily generalized to work with the addition of equity jumps in this model.