沪铜期货及其期权的量化定价实证研究

Quantitative Research on Futures and Options in Shanghai Copper Market

作为最大的铜消费市场,铜在我国占据着最重要地位。随着2018年9月沪铜期货期权正式登陆上海期货交易所,我国铜交易产品进一步与国际接轨。虽然拥有世界领先的铜交易市场,但我国学术领域尚缺乏采用量化方法对沪铜期货及其期权的深入实证研究。在大宗商品量化领域,Schwartz二因子模型[1]被看作是量化期货定价的基准模型,本文通过实证分析发现经典二因子模型在中国市场应用时会产生“水土不服”,因此本文采用波动参数的思想,修正了Schwartz二因子模型在中国沪铜市场的“水土不服”。另外,根据早期文献对认购期货期权的量化定价模型[2,3],本文明确了认沽期货期权的量化定价公式,并通过对沪铜期货期权定价模型的实证分析,发现目前沪铜期货期权存在套利空间。

As the largest copper consumer market in the world,Shanghai Copper Futures holds the most important position in China’s commodity market.Especially with the official listing of the options on copper futures on the Shanghai Futures Exchange in September 2018,the way of participating in Shanghai copper market has been expanded.Although China has the world’s leading copper trading market,the research on pricing futures and options on the underlying futures in the field of quantitative finance is seriously inadequate in China.In the field of quantitative finance,Schwartz Two-Factor model(1997)is considered as a benchmark model for pricing a futures contract.This paper finds that through Schwartz Two-Factor model(1997)generally works in the China’s Copper Futures Market,it is still shown that flaws needed to be fixed to get better results.Therefore,this paper proposes a way to run the Schwartz Two-Factor model with stochastic parameters,so that the prediction accuracy is greatly improved.In addition to these,according to the early literature on pricing call options on futures(Hilliard and Reis(2018)&Ewald et al(2018)),this paper proposes the formula for pricing put options on futures and finds that the methods proposed and tested in this paper are useful for pricing options of Copper Futures with different features and different maturities.Last,this paper argues that there is arbitrage possibility in the Shanghai Copper market.