基于最小二乘蒙特卡洛简化算法的保险公司经济资本度量研究

The research on the simplified algorithm of economic capital measurement of insurance companies based on least square monte carlo method

对最小二乘蒙特卡洛方法(LSMC)在保险公司经济资本度量中的简化进行了研究,探讨了该方法在实施过程中的模型处理以及对于嵌套随机模拟的简化效果与效率提升。在此基础上,针对变额年金产品,在不同预测期限下,借助最小二乘蒙特卡洛方法对经济资本进行了度量,并与完整嵌套随机模拟进行了效果比较。研究结果表明,最小二乘蒙特卡洛方法在经济资本度量中起到了良好的简化作用,对于风险损失的尾部拟合具有良好效果。同时相比于经济资本度量中常用的嵌套随机模拟,大大提高了运算效率。

With the introduction of the Chinese Risk-Oriented Solvency System(C-ROSS),management for insurance solvency capital focuses more on the actual risk exposure rather than before.An insurer can project the value of their assets and liabilities to some future time using Monte Carlo simulation to reserve adequate capital to cover the risk with a high level of confidence.However,the huge amount of computation seriously hinders its application in practice.This paper applies the LSMC method as a simplified algorithm to measure Economic Capital as well as discusses the practical application and simplification effects of this method.Taking a GMDB product with an embedded option as an example,this paper tests the fitting effect of the simplified algorithm with crude nested stochastic simulation.The results show that the LSMC method could make a good performance in the simplification,especially for the tail distribution for risk.The main content includes the following:Firstly,based on the computational inefficiency of nested-simulation and the path-dependent character of many insurance investment accounts,this paper builds up a regulation based approximation model known as Least Square Monte Carlo(LSMC).This method can efficiently simplify the inner simulation that occupies most of the computational resources of nested-simulation.With the use of LSMC,a large amount of risk-neutral scenarios can be represented by the combination of the finite orthogonal base.As such,the scenario generation for several risk factors in the proxy function is sufficed.Secondly,this paper adopts low-discrepancy sampling,risk-neutral calibration,and stepwise regression techniques.Sobol sampling at the end of each outer scenario could effectively avoid the excessive concentration around the mean value,which could guarantee the sample adequacy of the tail risk.And then,at the stage of inner scenario generation,the risk-neutral calibration eliminates the effect of risk premium in the parameters estimated by the historical data.At last,the stepwise regression with Legendre polynomials makes sure the proxy function completely unaffected by the multicollinearity of risk factors.At last,we use a Guaranteed Minimum Death Benefits(GMDB)insurance product with embedded options and Chinese economic data as an example to testify the simplification effect of the LSMC method.It shows that the LSMC model can well match the crude nested-stochastic simulation,especially for tail loss,which is the critical focus of both insurance companies and regulators.It also dramatically shortens the running time.The use of the LSMC method for Economic Capital improves the level of insurance companies’risk management with practical significance.