In this paper we discuss foreign-exchange option pricing in conditionally Gaussian models, namely in the variance-gamma and in the normal-inverse Gaussian models. It happens that in the both models closed-form pricing is attainable. The used method developes the one of the work by Madan et al. (Eur Finance Rev 2:79–105, 1998) where the price of the European call is primarily derived. The obtained formulas are based on values of the Gauss and the Appell hypergeometric functions.
- Foreign-exchange option
- Hypergeometric function
- Normal-inverse Gaussian process
- Time-changed Lévy process
- Variance-gamma process
ASJC Scopus subject areas
- Economics, Econometrics and Finance (miscellaneous)