We study the SABR stochastic volatility model with the volatility-of-volatility parameter ν . We provide a method to expand the price C_SABR(S, K, ν, σ, τ ) of a European call in this model as a Taylor series in ν , C_SABR(S, K, ν, σ, τ ) = C_BS(S,K, σ, τ ) ν C₁ ν²C₂ . . . ν^kC_k O(ν<sup>k...

We show that the call-put implied volatility spread (IVS) outperforms many well-known predictors of the U.S. equity premium at return horizons up to six months over the period from 1996:1 to 2017:12. The predictive ability of the IVS is unrelated to the dividend yield and is useful in explaining...

In March 2018, the US used an immense trade deficit as an excuse to provoke trade friction with China. This study uses the EGARCH model and event study methods to study the impact of the major risk event of Sino-US trade friction on soybean futures markets in China and the United States. Results...