An Optimal Lower Bound for a Guaranteed Annuity Option

We consider the valuation of a guaranteed annuity option (GAO) where the interest and mortality rates are correlated. We employ a change of measure in a more direct and accessible way in order to decompose the value of the option into a product of a survival bond and an easier option value expression and derive formulae that can be implemented easily. We then derive a lower bound of the option in terms of a free parameter. We then obtain an optimal value of the free parameter which results in the a sharper lower bound. To demonstrate the effectiveness of this approach, we compare the lower bounds with comonotonicity bounds. Experimental results show that our approach is an effective alternative way to comonotonicity bounds