Sato processes and the valuation of structured products

We report on the adequacy of using Sato processes to value equity structured products. In models used to price options on realized variance, the latter must be a random variable with a positive variance. An analysis of this variance of realized variance for Sato processes shows that these processes may be suited to option contracts on realized volatility. Nonlinear pricing principles based on hedging to acceptability are outlined for the purpose of pricing structured transactions. It is shown that, typically, different products should be priced using different models. Pricing comparisons of Sato process prices with other standard models like Heston stochastic volatility, with and without jumps, VGSA, local volatility and local CGMY are also provided. Sato processes tend to overprice cliquets relative to other models. They also maintain the value of long dated out-of-the-money realized variance options.