相关噪声波动率对连续内部交易均衡的影响

The impact of correlated noise volatility on the equilibriumin continuous insider trading

研究了风险资产和流动交易量受到相关噪声影响的连续内部交易模型。应用滤波理论和动态规划方法,证明了由内部人的交易强度和市场流动性组成的线性均衡的存在性和唯一性。研究表明:若风险资产只随相关噪声变化,且只有当风险资产的波动率与流动交易量的波动率正线性相关时,内部人才不参与市场交易,否则,内部人总能赚钱。特别地,当风险资产的两个波动率和流动交易量的波动率均为常数时,市场流动性随相关噪声波动率的增大而增大,内部人的交易强度和期望总利润随之减小。此外,还发现内部人的期望总利润总等于流动交易者的期望总损失;在交易结束时,内部人的私有信息几乎全部释放完。

A model of continuous insider trading where the risky asset and liquidity trading volume are affected by a correlated noise is proposed.By applying filtering theory and dynamic programming principle,we establish the uniqueness and existence of a linear equilibrium consisting of insider trading strategy and market liquidity.It shows that if the risky asset only changes with the correlated noise,only when the volatility of the risky asset is positively linearly correlated to the volatility of the liquidity trading volume,the insider does not participate in market trading.Otherwise,the insider can always make money;In particular,when both the two volatility of the risky asset and the volatility of liquidity trading volume are constant,market liquidity increases as correlated noise volatility increases,while both the optimal trading intensity and expected total profit of the insider decrease accordingly.Moreover,we also find that the insider’s expected aggregate profit is always equal to the expected aggregate loss of liquidity traders;at the end of the transaction,the insider’s private information is almost completely released.