在本篇研究中，我深入探討了有關波動度的風險溢酬與其成分的特性，藉由利用不同到期日劃分的資料子集,得出了波動度風險溢酬值會隨時間拉長而上升的期限結構，並且我藉由不同預測時間長度的預測檢驗回歸，證明波動度風險溢酬在預測股票超額報酬時，能有顯著的預測能力，且此結果在股票指數和個股上都能成立。

This article examines the properties of the related variance risk premia (VRP): the diffusive variance risk premium (DVRP) and the variance jump risk premium (VJRP) at both index and firm level. Using options data sorted by its maturity, we find a downward term structure of VRP, which is consistent at both levels. We show that VRP can be seen as a proxy for market fear since it is sensitive to extreme economic events. Our predictability test results show strong evidence that these related variance risk premia, along with slope defined as difference long-term component and short-term component, can help predict the excess stock return not only in the short-run horizon but also in long-term up to one year.

1. Introduction 4
2. Methodology 7
2.1 Stochastic volatility model of physical world 7
2.2 Estimation under physical measure 8
2.3 Estimation under risk-neutral approach 9
2.4 Risk premia estimation 11
2.5 Return predictability test 11
3. Data 12
Table 1 13
4. Empirical results 13
4.1 Physical and risk-neutral measure 14
4.1.1 Parameter estimates 14
Figure 1 15
Table 2. 16
Table 3. 16
4.1.2 MCMC states 18
Figure 2. 18
Figure 3. 19
4.2 The related risk premia 20
4.2.1 Static analysis and term structure 20
Table 4. 20
4.2.2 Dynamic analysis at index level 23
Figure 4. 23
Figure 5. 24

4.2.3 Correlation between risk premia 26
Table 5. 26
4.3 Stock return predictability test 27
4.3.1 Index level 28
4.3.2 Firm level 28
5. Conclusion 29
6. Reference 30
7. Appendix 31

Table 6. 32
Table 7. 34
Table 8. 36
Table 9. 38
Table 10. 40
Table 11. 42
Table 12. 44
Table 13. 46

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