在隨機波動模型下風險溢酬的曲線

Abstract

波動風險溢酬在近些年是一個很重要的變量，因為它可以表達經濟市場狀態的變化，然而在不同文獻中對於波動風險溢酬的定義非常多樣。而今天我們要討論的是在隨機波動模型下，如何不需要引進損失函數或一些替代品計算出波動風險溢酬，在我們的方法中我們將利用Heston (1993)提出的模型和Niu(2013)提出隨機波動模型的概似函數的近似進行統計推論，我們可以找到波動風險溢酬和選擇權價錢之間的一對一關係，在此篇論文的最後介紹了波動風險溢酬在S&P 500下的曲線變化以及市場不同狀態如合影響波動風險溢酬的曲線。

The volatility risk premium is an important factor for recent study and in mathematical finance since it represents the variability of economic state. However, there are many literatures that define the risk premium with different methods. In this paper, we discussed how to compute the volatility risk premium without introducing any extra loss function and proxy. We used the Heston (1993) model and simulated likelihood method proposed by Niu (2013) to do statistic inference. We can find a one-to-one relation between option price and volatility risk premium. At last, we use S&P 500 to show the volatility risk premium curve and assess market risk for different curve.