# Pricing a guaranteed annuity option under correlated and regime-switching risk factors

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## Abstract

A Markov-modulated affine framework for dependent risk factors is proposed to value a guaranteed annuity option (GAO). Concentrating on the important effect of volatilities, both diffusion components of the interest and mortality rates are driven by a finite-state continuous time Markov chain. We derive an explicit solution to the price of a pure endowment by solving a system of linear ordinary differential equations with the aid of the forward measure. Utilising the endowment-risk-adjusted measure with pure endowment as the corresponding numéraire, we provide an efficient and accurate formula in obtaining the GAO price. Such valuation efficiency and accuracy were demonstrated through numerical experiments. We benchmark our results with those of the Monte-Carlo simulation method and show significant differences in standard errors and computing times.

## Keywords

Markov chain Change of numéraire Exponential affine Mortality Interest rate## Notes

### Acknowledgments

The authors would like to express their appreciation to the anonymous referee and co-editor for their encouragement and helpful comments.

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