Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model

- The instantaneous forward interest rates follow Markov-modulated Heath-Jarrow-Morton model.
- The foreign price dynamics is driven by a regime switching jump-diffusion model.
- We adopt the regime-switching Esscher transform to construct the risk-neutral measure.
- Our findings include explicit closed-form solutions for four different types of European quanto call options.

We consider the valuation of European quanto call options in an incomplete market where the domestic and foreign forward interest rates are allowed to exhibit regime shifts under the Heath-Jarrow-Morton (HJM) framework, and the foreign price dynamics is exogenously driven by a regime switching jump-diffusion model with Markov-modulated Poisson processes. We derive closed-form solutions for four different types of quanto call options, which include: options struck in a foreign currency, a foreign equity call struck in domestic currency, a foreign equity call option with a guaranteed exchange rate, and an equity-linked foreign exchange-rate call.