Sequential real rainbow options

Abstract

We develop two models to value European sequential rainbow options. The first model is a sequential option on the better of two stochastic assets, where these assets follow correlated geometric Brownian motion processes. The second model is a sequential option on the mean-reverting spread between two assets, which is applicable if the assets are co-integrated. We provide numerical solutions in the form of finite difference frameworks and compare these with Monte Carlo simulations. For the sequential option on a mean-reverting spread, we also provide a closed-form solution. Sensitivity analysis provides the interesting results that in particular circumstances, the sequential rainbow option value is negatively correlated with the volatility of one of the two assets, and that the sequential option on the spread does not necessarily increase in value with a longer time to maturity. With given maturity dates, it is preferable to have less time until expiry of the sequential option if the current spread level is way above the long-run mean.

Keywords:

• uncertainty
• flexibility
• sequential rainbow option
• mean-reversion
• co-integration

JEL Classification:

• D81
• G31
• L72

Acknowledgements

We thank Roger Adkins, Nelson Areal, Paul Johnson, Stewart Myers, Peter Oliver, Mark Shackleton, two anonymous referees, and participants at the PFN Conference 2010 for helpful comments.