We extend and generalize some results on bounding security prices under several stochastic volatility models that provide closed-form expressions for option prices. In detail, we have computed analytical expressions for benchmark and standard good-deal bounds. For all the models, our findings...

We apply the Malliavin calculus to the stochastic string framework and obtain a Clark-Ocone-like formula. This result allows us to rewrite the hedging portfolio explicitly in terms of the Malliavin derivative of the discounted payoff. We illustrate this new result with two applications. Firstly,...

This paper introduces a continuous-time model for commodity pricing under the assumption that logged prices converge to a mean level that experiences smooth, periodic fluctuations over long periods of time. Our model incorporates that assumption by modelling the mean reversion level through a...