基于杠杆和流动性冲击的股指期货保证金定价

Pricing model of margin of stock index futures based on leverage and liquidity shock

现有研究对股指期货保证金定价多仅围绕波动率因素来考虑,而忽视了流动性冲击、杠杆和交叉持股所导致的现货价格极端变化对期货保证金的影响,即在保证金定价中未能考虑现货市场的流动性风险和组合再平衡风险.鉴于此,本文首先分析了流动性冲击下杠杆对投资组合价值的影响机理,以及交叉持股对现货标的的正反馈效应;然后通过持有成本模型将这些因素引入到股指期货价格变化中,最终构建保证金定价模型.模拟分析发现：现货市场中的杠杆水平、流动性冲击水平均与股指期货保证金显著正相关;且与传统模型相比,本文提出的定价模型所计算的股指期货保证金要显著高于前者,这也意味着本模型的确能够有效解决流动性冲击严重或者杠杆过高情况下,股指期货保证金的合理调整问题.

The margin of stock index futures is often calculated simply based on the volatility of futures at present, while ignoring that margin of stock index futures is affected by the extreme changes of spot price resulting from leverage and cross-shareholding under the situation of liquidity shock. In other words, it ignores the liquidity risk and portfolio rebalancing risk when pricing the margin of stock index futures. Given that, the paper firstly analyzes how positive feedback effect of leverage and cross-shareholding affects the value of portfolio under the situation of liquidity shock. And then introduces these factors into the futures price changes through the cost of carry model. Finally determine margin of stock index futures. The significantly positive correlation between margin of stock index futures and the level of leverage or liquidity shock in stock spot market is found through Monte Carlo simulation. And the margin of stock index futures should be further raised when considering the negative impact in the financial market.