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Pricing growth-rate risk

机译：定价增长率风险

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We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S. We also consider a reference growth process G that may represent the growth in the payoff of a single asset or of the macroeconomy. Both S and G are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. We consider the pricing implications of parametrized family of growth processes G~ε, with G~0=G, as ε is made small. This parametrization defines a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon, we trace a term structure of risk prices that shows how the valuation of risky cash flows depends on the investment horizon. Using methods of Hansen and Scheinkman (Econometrica 77:177-234, 2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily long.
机译：我们刻画了均衡增长中投资者对增长风险承担的补偿要求。给定控制经济状态变量的潜在马尔可夫扩散，经济模型暗示了随机贴现因子过程S。我们还考虑了参考增长过程G，该增长过程G可以代表单个资产或宏观经济的收益增长。 S和G都可以方便地建模为多维布朗运动的乘法函数。我们考虑参数化的增长过程G〜ε族的价格含义，因为ε变小，G〜0 = G。此参数化定义了使用随机折现因子S定价的增长率风险敞口的方向。通过更改投资范围，我们可以追踪风险价格的期限结构，以显示风险现金流的估值如何取决于投资范围。使用Hansen和Scheinkman的方法（Econometrica 77：177-234，2009），我们将风险价格的限制行为刻画为随投资期限的任意延长而定。

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