Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model
Abstract
:1. Introduction
2. Literature Review
3. Stochastic Volatility and the Market Price of Risk
3.1. Volatility Risk Premium
3.2. NGARCH Stochastic Volatility Model
- (i)
- is lognormally distributed (under ),
- (ii)
- , almost surely with respect to ,
4. Model Estimation and Numerical Results
4.1. Parameter Estimates and Interpretation
4.2. Model Fit
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
References
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SPX | BTC | |||||
---|---|---|---|---|---|---|
Par. | Est. Value | Std. Error | Z-Stat. | Est. Value | Std. Error | Z-Stat. |
3.131 | 9.1783 | 35.2208 | ||||
0.1106 | 0.0122 | 9.0585 | 0.1657 | 0.0057 | 29.3083 | |
0.6768 | 0.0199 | 34.0946 | 0.7962 | 0.0037 | 217.9210 | |
1.3328 | 0.1243 | 10.7268 | 0.2504 | 0.0272 | 9.1968 | |
1.5521 | 0.0039 | 0.0011 | 3.6623 | |||
Persistence | 0.9838 | 0.9723 | ||||
Log-likelihood | −8697.73 | −7145.99 |
Min () | Max () | Med. () | Mean () | St.dev. () | Skew. () | Kurt. () | |
---|---|---|---|---|---|---|---|
SPX | −0.0441 | −0.0039 | −0.0230 | −0.0227 | 0.0079 | 0.0173 | 2.2497 |
BTC | −0.0428 | −0.0019 | −0.0294 | −0.0279 | 0.0100 | 0.4793 | 2.2233 |
Mean () | St.dev. () | Skewness () | Kurtosis () | |
---|---|---|---|---|
SPX | 0.0145 | 0.9994 | −0.5663 | 5.0493 |
BTC | 0.0121 | 1.0008 | 3.6860 | 93.2303 |
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Posedel Šimović, P.; Tafro, A. Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model. Mathematics 2021, 9, 2038. https://doi.org/10.3390/math9172038
Posedel Šimović P, Tafro A. Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model. Mathematics. 2021; 9(17):2038. https://doi.org/10.3390/math9172038
Chicago/Turabian StylePosedel Šimović, Petra, and Azra Tafro. 2021. "Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model" Mathematics 9, no. 17: 2038. https://doi.org/10.3390/math9172038
APA StylePosedel Šimović, P., & Tafro, A. (2021). Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model. Mathematics, 9(17), 2038. https://doi.org/10.3390/math9172038