Tail Risk Premium Analysis Based On Hawkes Process

From the perspective of tail risk premium,this paper finds that making use of Hawkes Process raised by Hawkes(1971)to describe the random process of return on assets can better estimate tail risk premium.On the basis of summing up the existing methods and its effectiveness,the expanding ICAPM model proposed by Xu(2014)is improved and applied to Taiwan market to estimate the shape parameters,jump intensity parameters and tail risk premium of Taiwan market under the risk neutral measure and the physical measure.In the process of estimating tail risk premium,this paper divides tail risk premium into positive-jumping tail risk premium which obtains the premium by burdening the risk of price rising,and negative-jumping tail risk premium which obtains the premium by burdening the risk of price dropping.When studying on the estimated shape parameter,jump intensity parameters and tail risk premium,this paper finds out that under the risk neutral measure or the physical measure,positive-jumping shape parameters are both greater than negative-jumping shape parameters.The value of jump intensity under the risk neutral measure is greater than that under the physical measure and the jump intensity under risk neutral measure and Taiwan weighed index turn out a converse tendency.Tail risk premium is influenced much more by negative-jumping tail risk premium,and there exist positive tail risk premium,positive negative-jumping tail risk premium and negative positive-jumping tail risk premium in Taiwan market.When studying on the forecast ability of tail risk premium on return,this paper finds that tail risk premium and negative-jumping risk premium can forecast return on Taiwan weighted index to some degree.When studying on the relationship among the jump intensity,tail risk premium and investor sentiment,it shows that jump intensity,positive-jumping tail risk premium and negative-jumping tail risk premium all contain the composition of investor sentiment,and they are all good proxy variables for investor sentiment.