Marginal Expected Shortfall Measurement Based On Sequential Monte Carlo Method

The outbreak of the financial crisis makes the financial regulators of many countries aware of the importance of systemic risk in the financial system,which also makes researchers interested in systemic risk.In order to effectively strengthen the regulation of systemic risk,we must be able to effectively identify and scientifically measure systemic risk as a prerequisite.Marginal Expected Shortfall is a new method to measure the financial systemic risk proposed by Acharya et al.(2011).After the financial crisis in 2008,this measure has been widely used.MES is the expected loss an equity investor in a financial firm would experience if the overall market declined substantially,which can be used to determine the capital loss that the company will face in a financial crisis.The corresponding long-term indicator is the Long Run Marginal Expected Shortfall(LRMES),the systemic risk contribution of a single financial institution when the market stock price index falls more than a certain threshold over a long period of time.Brownlees and Engle(2012)calculate LRMES through rejection method.However,when the threshold is large,the sampling efficiency of the method will be very low.Therefore,this paper adopted Sequential Importance Sampling method to calculate LRMES.To be specific,this paper uses Sequential Importance Sampling method to improve the acceptance probability of the sample and solve the problem that the effective sample ratio is too low.In the sequential importance sampling process,some partial samples are seriously skewed,resulting in minimal contribution to the sample estimation(LRMES),the number of practical effective samples decreases.Therefore,this paper considers the Sequential Importance Sampling with Resampling method to improve the number of practical effective samples.At the same time,since the calculation of the weight involves high dimensional integral,this paper calculates the weight by generating pilots.The simulation results show that the Sequential Importance Sampling method can effectively improve the probability of sample acceptance.Resampling method guided by pilots can increase the number of practical effective samples and improve the accuracy of sample estimation.