The 3/2 model as a stochastic volatility approximation for a large-basket price-weighted index - Hambly, B; Vaicenavicius, J (World Scientific Publishing, 2015)
We derive large-basket approximations of a price-weighted index whose component prices follow a single sector jump-diffusion model. As the basket size approaches infinity, a suitable average converges to a Black–Scholes model driven by the common factor process. We extend this by considering the behavior of the residual idiosyncratic noise and show that a version of the 3/2 model emerges as a natural stochastic volatility model approximation. This provides a theoretical justification for its use as a model for jointly pricing index and volatility derivatives.