Pricing and hedging equity-indexed annuities via local risk-minimization

ABSTRACT

Lin et al. (2009) employed the Esscher transform method to price equity-indexed annuities (EIAs) when the dynamic of the market value of a reference asset was driven by a generalized geometric Brownian motion model with regime-switching. Some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in asset prices, and hence we sometimes need to consider jump models. This paper extends the model and analysis in Lin et al. (2009). Specifically, we assume that the financial market has a regime-switching jump-diffusion model, under which we price the point-to-point, the Asian-end, the high water mark and the annual reset EIAs by exploiting the local risk-minimization approach. The effects of the model parameters on the EIAs pricing are illustrated through numerical experiments. Meanwhile, we present the locally risk-minimizing hedging strategies for EIAs.

KEYWORDS:

• Equity-indexed annuity
• Jump diffusion process
• Locally risk-minimizing strategy
• Minimal martingale measure
• Regime-switching.

MATHEMATICS SUBJECT CLASSIFICATION:

• 91B25
• 91G20

Acknowledgments

We would like to thank the referees for many helpful comments which significantly improve our paper.

Additional information

Funding

This work was supported in part by National Natural Science Foundation of China (11571113, 11771147), Zhejiang Provincial Natural Science Foundation of China (LY17G010003), Ningbo City Natural Science Foundation (2016A610076) and the 111 Project (B14019).