This paper considers options pricing when the assumption of normality is replaced with that of the symmetry of the underlying distribution. Such a market affords many equivalent martingale measures (EMM). However we argue (as in the discrete-time setting of Klebaner and Landsman in Methodology and Computing in Applied Probability, 2007, doi:10.1007/s11009-007-9038-2) that an EMM that keeps distributions within the same family is a “natural” choice. We obtain Black–Scholes type option pricing formulae for symmetric Variance-Gamma and symmetric Normal Inverse Gaussian models.
- Equivalent martingale measure
- Lévy processes
- Normal Inverse Gaussian process
- Option pricing
- Risk-neutral pricing
- Symmetric distribution
- Variance Gamma process