[1] |
Merton R C. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 1971, 3: 373–413. doi: 10.1016/0022-0531(71)90038-X
|
[2] |
Ye W, Wu B, Chen P. Pricing VIX derivatives using a stochastic volatility model with a flexible jump structure. Probability in the Engineering and Informational Sciences, 2023, 37 (1): 245–274. doi: 10.1017/S0269964821000577
|
[3] |
Cui Z, Lee C, Liu M. Valuation of VIX derivatives through combined Ito-Taylor expansion and Markov chain approximation. Hoboken, NJ: Stevens Institute of Technology, 2021.
|
[4] |
Chen T, Zhuo H. Pricing VIX options with realized volatility. Journal of Futures Markets, 2021, 41 (8): 1180–1200. doi: 10.1002/fut.22201
|
[5] |
Yin F, Bian Y, Wang T. A short cut: Directly pricing VIX futures with discrete-time long memory model and asymmetric jumps. Journal of Futures Markets, 2021, 41 (4): 458–477. doi: 10.1002/fut.22183
|
[6] |
Yuan P. Time-varying skew in VIX derivatives pricing. Management Science, 2021, 68 (10): 7065–7791. doi: 10.1287/mnsc.2021.4168
|
[7] |
Mencía J, Sentana E. Valuation of VIX derivatives. Journal of Financial Economics, 2013, 108 (2): 367–391. doi: 10.1016/j.jfineco.2012.12.003
|
[8] |
Simon D P. Trading the VIX futures roll and volatility premiums with VIX options. Journal of Futures Markets, 2017, 37 (2): 184–208. doi: 10.1002/fut.21788
|
[9] |
Simon D P, Campasano J. The VIX futures basis: Evidence and trading strategies. The Journal of Derivatives, 2014, 21 (3): 54–69. doi: 10.3905/jod.2014.21.3.054
|
[10] |
Chen H C, Chung S L, Ho K Y. The diversification effects of volatility-related assets. Journal of Banking & Finance, 2011, 35 (5): 1179–1189. doi: 10.1016/j.jbankfin.2010.09.024
|
[11] |
Black K H. Improving hedge fund risk exposures by hedging equity market volatility, or how the VIX ate my kurtosis. The Journal of Trading, 2006, 1 (2): 6–15. doi: 10.3905/jot.2006.628190
|
[12] |
Daigler R T, Rossi L. A portfolio of stocks and volatility. The Journal of Investing, 2006, 15 (2): 99–106. doi: 10.3905/joi.2006.635636
|
[13] |
Carr P, Jin X, Madan D P. Optimal investment in derivative securities. Finance and Stochastics, 2001, 5 (1): 33–59. doi: 10.1007/s007800000023
|
[14] |
Liu J, Pan J. Dynamic derivative strategies. Journal of Financial Economics, 2003, 69 (3): 401–430. doi: 10.1016/S0304-405X(03)00118-1
|
[15] |
Bates D S. Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. The Review of Financial Studies, 1996, 9 (1): 69–107. doi: 10.1093/rfs/9.1.69
|
[16] |
Lian G H, Zhu S P. Pricing VIX options with stochastic volatility and random jumps. Decisions in Economics and Finance, 2013, 36: 71–88. doi: 10.1007/s10203-011-0124-0
|
[17] |
Escobar M, Ferrando S, Rubtsov A. Robust portfolio choice with derivative trading under stochastic volatility. Journal of Banking & Finance, 2015, 61: 142–157. doi: 10.1016/j.jbankfin.2015.08.033
|
[18] |
Moreira A, Muir T. Volatility-managed portfolios. The Journal of Finance, 2017, 72 (4): 1611–1644. doi: 10.1111/jofi.12513
|
[19] |
Gatheral J, Jaisson T, Rosenbaum M. Volatility is rough. Quantitative Finance, 2018, 18 (6): 933–949. doi: 10.2139/ssrn.2509457
|
Figure
1.
Sensitivity of portfolio weights for the complete market case. The lines are in the same style of Fig. 1 in Ref. [14] to make comparison, i.e., the
Figure
4.
Sensitivity of certainty equivalent wealth
Figure
5.
Sensitivity of certainty equivalent wealth
[1] |
Merton R C. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 1971, 3: 373–413. doi: 10.1016/0022-0531(71)90038-X
|
[2] |
Ye W, Wu B, Chen P. Pricing VIX derivatives using a stochastic volatility model with a flexible jump structure. Probability in the Engineering and Informational Sciences, 2023, 37 (1): 245–274. doi: 10.1017/S0269964821000577
|
[3] |
Cui Z, Lee C, Liu M. Valuation of VIX derivatives through combined Ito-Taylor expansion and Markov chain approximation. Hoboken, NJ: Stevens Institute of Technology, 2021.
|
[4] |
Chen T, Zhuo H. Pricing VIX options with realized volatility. Journal of Futures Markets, 2021, 41 (8): 1180–1200. doi: 10.1002/fut.22201
|
[5] |
Yin F, Bian Y, Wang T. A short cut: Directly pricing VIX futures with discrete-time long memory model and asymmetric jumps. Journal of Futures Markets, 2021, 41 (4): 458–477. doi: 10.1002/fut.22183
|
[6] |
Yuan P. Time-varying skew in VIX derivatives pricing. Management Science, 2021, 68 (10): 7065–7791. doi: 10.1287/mnsc.2021.4168
|
[7] |
Mencía J, Sentana E. Valuation of VIX derivatives. Journal of Financial Economics, 2013, 108 (2): 367–391. doi: 10.1016/j.jfineco.2012.12.003
|
[8] |
Simon D P. Trading the VIX futures roll and volatility premiums with VIX options. Journal of Futures Markets, 2017, 37 (2): 184–208. doi: 10.1002/fut.21788
|
[9] |
Simon D P, Campasano J. The VIX futures basis: Evidence and trading strategies. The Journal of Derivatives, 2014, 21 (3): 54–69. doi: 10.3905/jod.2014.21.3.054
|
[10] |
Chen H C, Chung S L, Ho K Y. The diversification effects of volatility-related assets. Journal of Banking & Finance, 2011, 35 (5): 1179–1189. doi: 10.1016/j.jbankfin.2010.09.024
|
[11] |
Black K H. Improving hedge fund risk exposures by hedging equity market volatility, or how the VIX ate my kurtosis. The Journal of Trading, 2006, 1 (2): 6–15. doi: 10.3905/jot.2006.628190
|
[12] |
Daigler R T, Rossi L. A portfolio of stocks and volatility. The Journal of Investing, 2006, 15 (2): 99–106. doi: 10.3905/joi.2006.635636
|
[13] |
Carr P, Jin X, Madan D P. Optimal investment in derivative securities. Finance and Stochastics, 2001, 5 (1): 33–59. doi: 10.1007/s007800000023
|
[14] |
Liu J, Pan J. Dynamic derivative strategies. Journal of Financial Economics, 2003, 69 (3): 401–430. doi: 10.1016/S0304-405X(03)00118-1
|
[15] |
Bates D S. Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. The Review of Financial Studies, 1996, 9 (1): 69–107. doi: 10.1093/rfs/9.1.69
|
[16] |
Lian G H, Zhu S P. Pricing VIX options with stochastic volatility and random jumps. Decisions in Economics and Finance, 2013, 36: 71–88. doi: 10.1007/s10203-011-0124-0
|
[17] |
Escobar M, Ferrando S, Rubtsov A. Robust portfolio choice with derivative trading under stochastic volatility. Journal of Banking & Finance, 2015, 61: 142–157. doi: 10.1016/j.jbankfin.2015.08.033
|
[18] |
Moreira A, Muir T. Volatility-managed portfolios. The Journal of Finance, 2017, 72 (4): 1611–1644. doi: 10.1111/jofi.12513
|
[19] |
Gatheral J, Jaisson T, Rosenbaum M. Volatility is rough. Quantitative Finance, 2018, 18 (6): 933–949. doi: 10.2139/ssrn.2509457
|