Asset Pricing Base On The Extrapolation Of Stock Price Jump

Asset pricing is one of the cores of modern financial economics,and the construction of a reasonable asset pricing model is one of the important foundations for the effective asset pricing study.In asset pricing model,the price jumps are one of the important research objects.The existing empirical results show that there is a clustering phenomenon in the jumps of stock prices.However,the existing asset pricing models cannot provide a reasonable explanation for the occurrence of jump clustering in stock price.Therefore,based on the extrapolation theory of behavioral finance,this paper tries to explain the internal mechanism of jump clustering in stock price from the perspective of investors’ extrapolation bias for stock price jump.Then,under the continuous-time consumption asset pricing framework,this paper constructs an asset pricing model based on the extrapolation of stock price jump to capture the characteristics of jump clustering in stock prices and provide a new explanation for some financial anomalies in the securities market.Besides,this paper also applies the proposed model to portfolio theory study,option pricing,and empirical research on stock prices.The main research works of this paper are briefly summarized as follows:First,based on the proposed model,this paper derives the optimal consumption and investment proportion of investors,and further derives the expressions of risk-free interest rate,stock price and some statistical characteristics of stock price under the market equilibrium condition,and analyzes the impact of the extrapolation bias of stock price jump on the above variables.This paper finds that the extrapolation bias of stock price jump can lead to the short-term momentum effect and long-term reversal effect in stock price,and the cum-dividend excess return and instantaneous conditional variance of stock price will be larger than those under the traditional consumption asset pricing model.Besides,this paper also analyzes the impact of some parameters on the statistical characteristics of stock prices by using numerical simulation method.Second,based on the proposed model,this paper expands the single asset pricing to the multi-assets pricing,and derives the expression of the price and some statistical characteristics of some stock price for each security,and analyzes the impact of the extrapolation bias of stock price jump on the above variables.Then,this paper aims at the investors’ risk aversion optimization,derives the optimal portfolio and takes it as the market portfolio,and further derives the conditional beta coefficient and the conditional capital asset pricing model based on the extrapolation of stock price jump.The analysis results for the above capital asset pricing model show that:(1)the sentiment-adjusted cum-dividend excess return of stock is equal to its conditional beta coefficient times the sentiment-adjusted cum-dividend excess return of market portfolio;(2)Compared with the traditional capital asset pricing model,the proposed model can generate a flat security market line when the long-term investor sentiment is positive,which can explain the beta anomaly found in the empirical study to some extent;(3)The securities market line becomes more flat or even has a negative slope when investors’ sentiment is high,and becomes steeper when investors’ sentiment is low.Thirdly,based on the proposed model,this paper derives the familiar conditional characteristic function of stock log price under the risk-neutral measure,and further derives the expressions of European call and put option prices by combining the riskneutral pricing theory and the generalized Fourier transform,and analyzes the impact of the extrapolation bias of stock price jump on option price.Then,base on the option price expression,this paper derives and analyses some Greeks of the option price.This paper also derives the dynamic optimal hedging position of European option by using the mean-variance hedging strategy,and finds that the dynamic optimal hedging position is proportional to the option price,and inversely proportional to the stock price,and the relationship with the extrapolation bias of stock price jump depends on the values of the model parameters.Fourthly,this paper uses the data of Chinese consumption,risk-free interest rate,dividend and price of stock index to calibrate the proposed model based on the extrapolation of stock price jump,and takes the model with lower extrapolation of stock price jump as the benchmark model.This paper simulates the monthly risk-free interest rate,dividend and stock price of the proposed model and benchmark model by using Monte Carlo simulation method,and contrastively analyzes the abilities of the two models to match the statistical characteristics of financial assets.The results show that:(1)The means and standard deviations of the log dividend growth rate,the firstorder autoregressive coefficients of log price-dividend ratio and the Sharpe ratios matched by the two models are all close to the realistic results,and the means of the risk-free rate matched by the two models are also similar.(2)Compared with the benchmark model,the proposed model can generate larger equity risk premium,log price-dividend ratio,risk-free interest rate,stock price volatility,and stronger negative correlation between log price-dividend ratio and interest-bearing excess return,which can better match the realistic results.Fifth,this paper explores the predictive abilities of the log price-dividend ratio and the variance risk premium on the stock excess return by using the monthly samples simulated by the proposed model and benchmark model.For the log price-dividend ratio,this paper finds that:(1)the log-price-dividend ratio can significantly predict the stock excess return with negative coefficient under both two models,which is consistent with the existing empirical conclusions;(2)The proposed model can better describe the real ability of the log-price-dividend ratio to predict the stock excess return,while the log-price-dividend ratio simulated by the benchmark model will overestimate the stock excess return.For the variance risk premium,this paper finds that:(1)compared with the benchmark model,the mean and standard deviation of conditional variance and variance risk premium simulated by the proposed model are both larger;(2)The variance risk premium simulated by the proposed model can significantly predict the stock excess return,which is consistent with the existing empirical conclusions,while the variance risk premium simulated by the benchmark model has no significant predictive effect on the stock excess return.Sixth,based on the monthly stock returns simulated by the two models,this paper fits the left-tail and right-tail distributions of stock returns respectively,and explores the abilities of the two models to describe the fat-tail characteristic of stock returns.The results show that,compared with the benchmark model,the distribution of stock return simulated by the proposed model has fatter left tail and fatter right tail,which can better describe the tail of distribution of the real stock return.Seventh,this paper explores the abilities of the two models to describe the jump clustering characteristics of stock returns by using the daily stock returns simulated by the two models.The results show that the current jump in stock return simulated by the proposed model significantly increases the probability of future jump in stock return,while the current jump in stock return simulated by the benchmark model has no significant effect on the probability of future jump in stock return.After changing the jump thresholds of stock return,the above results are still robust.Therefore,the proposed model can accurately and reasonably describe the jump clustering characteristics of real stock returns.