Optimal Timing to Exercise Options in a Regime-Switching Market

The standard no-arbitrage pricing model assumes that all option positions can be hedged perfectly by continuously trading the underlying asset.

However, in many financial applications, the underlying is not liquidly traded; instead, the investor (option holder or writer) trades a correlated asset as a proxy to minimize risk exposure. Examples include employee stock options, weather derivatives, and commodity options.

Moreover, asset prices are often seen as dependent on market conditions. Asset price dynamics can be considered as modulated by a continuous-time Markov chain representing the stochastic market regime.

In these so-called regime-switching market models, it is common that the risks associated with regime changes are unhedgeable. More importantly, the hedging strategies and timing to exercise the options should vary across different market regimes.

In this example, the holder exercises the first call option at the lowest exercise boundary in each regime, and subsequent ones at higher boundaries. The exercise boundaries in regime 1 (bad state) are higher than the corresponding ones in regime 2 (good state).

In this paper, we consider the problem of dynamically hedging a long position in American (early exercisable) options written on a non-traded asset in a regime-switching market. In the model, the investor (option holder) faces the…