The valuation of nature-linked bonds with exchange rate risk

Abstract

This paper develops an arbitrage approach to pricing insurance bonds that bear currency risk. Bondholders are shown to have a short position on path-dependent digital options written on risk-tracking indices. It implements the technique of forward-neutral change of numeraire and comes down to computing first-passage-time distributions of drifted Brownian motions. We derive closed-form formulas or perform simulations depending on whether interest rates are deterministic or stochastic. Along the way, we evaluate outside-barrier currency call options. Then this research studies the effects of both nature risk and exchange rate uncertainty and shows that the former is more significant than the latter.