One typically models the log returns of a portfolio of equities by some unimodal, symmetric (or nearly symmetric) distribution with parameters like the mean and standard deviation estimated by empirical estimators. For example, the most basic model would be to assume the returns are normal (yes, I know the tails are not fat enough), then fit the mean and volatility. To get fancier, one might try to fit returns to a fat-tailed distribution like a Tukey g-and-h, or a J-transformation, Lambert W x Gaussian, whatever.
What are the commonly used approaches, I am wondering, for modeling the returns of portfolios of one-sided instruments. For example, a portfolio consisting entirely of long vanilla put and call options. When considered from purchase to expiration, the maximum loss is bounded, but the upside is theoretically unbounded (if you have call options). Fitting to an unbounded and symmetric distribution like a normal seems unsatisfactory. What are the most commonly used models for this? I like simple models as much as fancy ones.