The Role of Contagion in Financial Markets--论文代写范文精选

这种解释被称为股票溢价,发生在1930年至1932年的经济危机,美国经济每年萎缩10%以上。经济活动是难以调和的。大萧条的经验表明,这些事件并不是独立的,一旦经历了经济衰退,它可能会重复,导致经济危机展开了一段时间。下面的essay代写范文进行讲述。

Abstract 
Severe economic downturns like the great depression of the 1930s take place over extended periods of time. I model an economy where rare economic disasters increase the likelihood of subsequent near term disasters. The mechanism generates more clustering of disasters than existing models. Serial correlation in disasters has important implications for asset prices. For example, it generates a larger equity premium and a lower risk free rate than similarly calibrated models without this feature. The calibrated model developed here replicates the temporal structure of severe economic downturns in OECD countries. It quantitatively explains the equity premium, the risk-free rate, excess volatility and return predictability. It also generates the implied volatility smile observed in equity index options.

Introduction 
To explain what has come to be known as the equity premium puzzle1 , financial economists have pointed to the risk of rare economic disasters. An example of such a disaster occurred from 1930 to 1932, when the U.S. economy contracted by more than 10% each year. A sequence of large annual declines in economic activity like this is difficult to reconcile with existing disaster models developed in Rietz (1988), Barro (2006), Gabaix (2010), and Wachter (2010), which view each disaster as an isolated rare event. The great depression experience suggests that these events are not independent: Once an economic decline is experienced, it is likely to repeat, causing the economic crisis to unfold over an extended period of time. 

This paper models the general equilibrium dynamics of asset prices - including stocks, bonds, and options - when large scale declines in consumption tend to cluster. If economic agents rationally anticipate such clustering, their consumption and investment plans will dramatically differ from those generated in the extant literature on rare events. Moreover, they will revise their consumption and investment decisions in response to an initial adverse consumption shock which could mark the beginning of a crisis. The desire to form precautionary savings will then be more pronounced. This will increase demand for riskless investments, resulting in a lower risk-free rate. Furthermore, increased uncertainty about future economic health brought about by the arrival of a rare disaster makes agents reluctant to hold risky assets. Fear of further economic downturns will require these assets to increase their expected returns. 

Hence, valuation multiples like the price to dividend ratio will drop and price declines will exceed the decline in cash flows. In most instances the economy will prove resilient; economic downturns will be short-lived, and, in hindsight, economic participants will appear to have been overly prudent in their investment decisions. This mechanism results in an ex-post excessive reaction of economic quantities to realized risk, which can account for observed pricing phenomena. These include time-varying expected returns and risk-premia that can be predicted by the price-dividend ratio as well as excess stock market volatility. The recent financial crisis of 2007-2009 illustrates one such episode where an initial disaster occurred in one part of the financial sector that subsequently caused contagion with widespread consequences throughout the financial system. Fear of this downturn to develop into another great depression led households to slash consumption and investors to shy away from risky assets.2

During the fourth quarter of 2008, nondurable consumption expenditures declined by 7.66%, which translates into an annualized reduction of 27.29%. This represents the single largest drop in over half a century and constitutes an event more than six standard deviations from its historical mean.3 During this period, S&P 500 option implied volatility, measured by the Volatility Index (VIX) sharply increased from 18.81% on August 22nd to 80.86% on November 20th and then reverted to a lower level in the months following these events.4 Explaining such a drastic jump in implied volatility within the context of a consumption based asset pricing model requires a sudden change in one of the state variables characterizing economic uncertainty, like the conditional probability of further economic disasters. 

Existing models in the disaster risk literature assume the disaster intensity to be either constant over time as in Barro (2006), predicting option-implied volatility to be constant over time as well, or to be subject to time variation that is unrelated to disaster arrival e.g. Wachter (2010). Under either set of assumptions, option-implied volatility does not respond to the occurrence of a disaster itself. The implied volatility pattern experienced during the recent financial crisis can be explained in a model where the arrival of a disaster magnifies the probability of disasters in the near future. Moreover, during the fourth quarter of 2008, the S&P 500 index declined from 1282.83 on August 29th to 903.25 on December 31st, a 29.59% drop, which far exceeds the contemporaneous decline in personal consumption of 7.66%. 

This excessive stock market reaction is a recurring phenomenon summarized in Paul Samuelson’s remark that ”Wall Street indexes [had] predicted nine out of the last five recessions”. Indeed, this stylized fact is not unique to U.S. capital markets. Barro and Urs´ua (2009) document that only 28% of all stock market declines exceeding 25% are accompanied by a macroeconomic contraction exceeding 10% in OECD countries. I contend that this apparent puzzle can be accounted for by the model developed in this paper. The consumption drop in the fall of 2008 was a rare event that caused a surge in the probability of further disasters. While no similar consumption shock has happened to this day, the fear of another such disaster remains above its normal level as evidenced by high dividend-yields, a low risk-free rate, and a VIX that is above average. The economic consequences of the possibility that a disaster can beget a crisis are analyzed in the context of a representative agent endowment economy. 

The model is set in continuous-time where the agent’s preferences are expressed using stochastic differential utility. The departure from standard time-separable expected utility separates risk aversion from the willingness to substitute consumption over time and has been proven successful in addressing the equity premium and risk-free rate puzzles in the long-run risk literature initiated by Bansal and Yaron (2004). Aggregate consumption is subject to both diffusive risk and infrequent jumps, which account for the possibility of rare but potentially disastrous events. In order to capture the idea of serial correlation in disasters, I introduce a self-exciting jump-diffusion into the consumption-based asset pricing framework. Self-exciting processes, developed in Hawkes (1971b), have recently been brought to bear in the field of credit risk modeling to explain the phenomenon of default clustering.5 

In the context of the model presented here, these processes allow the occurrence of a disaster to affect the intensity of future disaster arrival. The conditional likelihood of further significant economic downturns increases in response to a substantial adverse shock to consumption, leading to the possibility of self-perpetuating economic disasters. Self-exciting disaster risk in conjunction with a preference for early resolution of uncertainty gives rise to an additional channel by which disasters affect risk-premia, interests rates, and asset prices. Expected utility does not exhibit a preference for the timing of resolution of uncertainty, which stochastic differential utility does. With a preference for the timing of resolution of uncertainty, the pricing kernel involves continuation utility as well as instantaneous consumption growth. （essay代写)

This dependence of the stochastic discount factor on continuation utility makes makes it necessary to solve for the representative agent’s value function in order to obtain equilibrium asset prices. Since the partial differential equation characterizing indirect utility is nonlinear, standard PDE techniques such as Fourier and Laplace transforms, which are essentially linear operations, are of no avail in this situation. Instead, I resort to a log-linear approximation of the non-linear term in the PDE around the unconditional mean consumption-to-wealth ratio, which is endogenous to the model, in order to address this issue.6 This approximation is exact if the representative agent has unit elasticity of intertemporal substitution and yields closed form solutions for the pricing kernel, the risk-free rate, and risk-premia. Valuation ratios of claims to aggregate consumption and corporate dividends are then exponentially affine functions of the state variables. This affine structure gives rise to equity option prices in quasi closedform that can be efficiently determined by Fourier inversion techniques along the lines of Duffie, Pan, and Singleton (2000).（essay代写)

The paper is organized as follows. Section 2 introduces the model and derives general equilibrium results for claims to corporate dividends and aggregate consumption, government debt, as well as equity index options in this endowment economy. Section 3 presents a calibration to historical U.S. data and empirically investigates the asset pricing implications of the economic channel proposed in this paper. Section 4 concludes the analysis of this paper. The appendix presents a generalized version of the model that features long-run risk as well as stochastic volatility in consumption and accounts for the possibility that rare disasters are generated by a finite number of interrelated mutually-exciting jump processes. Technical proofs following in the appendix are provided for the general model.（essay代写)

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