Pricing Rainbow Options Using PINNs

In this study, we consider the valuation of rainbow options using unsupervised machine learning methods. In particular, we consider the pricing of multi-asset (rainbow) European and American options, using Physics Informed Neural Net- works (PINNS). After developing the PINNS architecture, we benchmark the method by using it to price vanilla and exotic options with one and two un- derlying assets. We then use the methodology to price a multi-asset European option, followed by the pricing of the multi-asset American option by solving the linear complementarity problem. We compare our results to those obtained using preexisting numerical methods and note excellent agreement. Unlike con- ventional numerical methods, we note that this methodology does not suffer from the ’curse of dimensionality’. The time complexity of our method is con- siderably less than that of the conventional techniques. Thus PINNS may offer a faster more efficient solution to the pricing of rainbow options.