Risk Price Model Of Stochastic Discount Factor And Its Frequency Domain Analysis

Asset pricing has always been a hot topic in the field of financial research.With the increasing number of financial products and derivatives,the situation of financial market has become very complicated.Investors need to price financial products reasonably if they want to get profits from market.This is the reason why asset pricing has become the core of modern financial theory research.Asset pricing theory studies the relationship between risk and return of assets.Since the portfolio selection theory was put forward,asset pricing theory has undergone many developments,such as capital asset pricing theory,arbitrage pricing theory,option pricing theory and so on.Among them,the theory of stochastic discount factor is the most widely used one.This paper studies the risk price in the stochastic discount factor model in frequency domain.The purpose of this study is to observe how risk prices are priced from the perspective of frequency domain.In this paper,Dewbecker and Giglio's method is improved.The integral transformation is carried out in the basis of complete orthogonal basis,and the frequency domain model of risk price is given.The model divides the risk price into two parts: the consumption dynamics in frequency domain and the risk price in frequency domain.Because the risk price in frequency domain is determined by the utility function of investors,and is not affected by the change of consumption,they can be analyzed independently.Based on a set of complete orthogonal bases,this paper analyses the consumption dynamics in frequency domain and the risk price in frequency domain,and draws the following conclusions:First,if shocks have a long-term impact on consumption level,the consumption dynamics in the frequency domain are mainly in the low frequency band;if shocks have a short-term impact,the consumption dynamics in the frequency domain are mainly in the high frequency band.Second,risk price in frequency domain can reflect investors' frequency risk preference.For example,investors with internal habits formation are averse to highfrequency risk,while most investors with Epstein-Zin preference are averse to lowfrequency risk.Finally,we compare the pricing results of different investors on the risk price of shocks,and verify the validity of the risk price frequency domain model.