The Black Scholes Barenblatt (BSB) equation for the envelope of option prices with uncertain volatility and interest rate is derived from the Black Scholes equation with the maximum principle for diffusion equations and shown to be equivalent to a readily solvable standard Black Scholes equation...

The paper presents a pricing rule for market models with stochastic volatility and with an uncertainty in its evolution law. It is shown that the most common stochastic volatility models allow a possibility that the option price calculated for random volatility with an error in volatility...

We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV)...

In this paper we present two methods for the pricing of Target Volatility Options (TVOs), a recent market innovation in the field of volatility derivative. TVOs allow investors to take a joint view on the future price of a given underlying (e.g. stocks, commodities, etc) and its realized...

We analyze the performance of robust hedging strategies of digital double barrier options of Cox and Obłój (2011) against that of traditional hedging methods such as delta and delta/vega hedging. Digital double barrier options are financial derivative contracts which pay out a fixed amount on...

We formulate the portfolio choice problem as a robust control problem under uncertainty or ambiguity aversion. By considering a stochastic investment opportunity set, we derive optimal robust portfolio rules in the cases of one and two risky assets. With two risky assets and ambiguity structure...