Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?

We extend and generalize some results on bounding security prices under two stochastic volatility models that provide closed‐form expressions for option prices. In detail, we compute analytical expressions for benchmark and standard good‐deal bounds. For both models, our findings show that our benchmark results generate much tighter bounds. A deep analysis of the properties of option prices and bounds involving a sensitivity analysis and analytical derivation of Greeks for both option prices and bounds is also presented. These results provide strong practical applications taking into account the relevance of pricing and hedging strategies for traders, financial institutions, and risk managers.