Discounted-likelihood valuation of variance and volatility swaps

The valuation of financial derivatives often assumes risk neutrality with respect to the risk-neutral martingale measure, which prevents arbitrage opportunities. However, casual traders may still incur substantial losses when trading at this risk-neutral price, especially when the price has to be paid now and the payoff is only realized in the future. This study proposes a new valuation framework that provides risk-sensitive investors with an additional safeguard. The proposed framework embraces a worst-case perspective while exploiting the underlier’s stochastic process, representing a combination of robust optimization and stochastic programming. Notably, it aims to mitigate losses in the likelier scenarios of the underlying asset’s prices. When the underlier’s returns are independent and lognormally but not necessarily identically distributed, our approach for pricing variance and volatility swaps could be greatly simplified, benefit from parallel computing, and be solved by a two-dimensional grid search. We further derive a closed-form solution in some special stationary cases and provide experimental results to highlight the effect of risk aversion on fending off sizable trading losses.