Implied volatility surface construction for commodity futures options traded in China

Abstract

European futures options are not traded on the Chinese exchanges and that generates difficulties to calibrate fundamental market parameters, such as the implied volatilities. We propose an efficient willow tree method to resolve the problem of calibrating the implied volatility from American-style options. The proposed willow tree construction is independent of the volatility itself so as to minimize the cost of the calibration. We also apply the proposed method to calibrate the implied volatilities of most frequently traded options in the Chinese market, sugar and soybean meal, based on the daily closing prices, and construct the corresponding implied volatility surfaces. The results indicate the seasonality in the volatility of commodity spot prices and futures prices in China. Moreover, based on the implied volatility distortion close to the option maturity observed in our empirical results, we suggest a minimum tick price scheme to avoid the distortion and decrease of hedging costs.