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January
2022, 9(1): 97-115.
doi: 10.3934/jdg.2021027
Crisis risk prediction with concavity from Polymodel
| 1. | State University of New York at Stony Brook, Stony Brook, NY, USA |
| 2. | Sorbonne Economics Center, University Paris 1-Sorbonne, CNRS, France |
Financial crises are an important research topic because of their impact on the economy, businesses, and populations. However, prior research tends to generate reactive systemic risk measures, in the sense that the measure surges after the crisis starts. Few of them succeed in warning of financial crises in advance. In this paper, we first sketch a toy model that produces normal mixture distributions based on a dynamic regime switching model. We derive that the relative concavity among various indices tends to increase before a crisis. Using Polymodel theory, we introduce a measure of concavity as a crisis risk indicator, and test it against known crises observed in the past. We validate this indicator by a trading strategy holding long or short positions on the S & P 500 Index, depending on the indicator value.
Mathematics Subject Classification:
62P05, 62P20, 91G10, 91G15, 91G70.
Citation:
Yao Kuang, Raphael Douady. Crisis risk prediction with concavity from Polymodel. Journal of Dynamics and Games,
2022, 9
(1)
: 97-115.
doi: 10.3934/jdg.2021027
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References:
| [1] |
B. K. Adhikari and J. E. Hilliard,
The VIX, VXO and realised volatility: A test of lagged and contemporaneous relationships, Internat. J. Financial Markets Derivatives, 3 (2014), 222-240.
doi: 10.1504/IJFMD.2014.059637. |
| [2] |
A. Ang and J. Chen,
Asymmetric correlations of equity portfolios, J. Finance Econ., 63 (2002), 443-494.
doi: 10.1016/S0304-405X(02)00068-5. |
| [3] |
A. Ang and A. Timmermann,
Regime changes and financial markets, Ann. Rev. Finance Econ., 4 (2011), 313-337.
doi: 10.3386/w17182. |
| [4] |
C. Aschwanden, Not even scientists can easily explain p-values, FiveThirtyEight, (2015). Available from: https://web.archive.org/web/20190925221600/https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/. |
| [5] |
L. E. Baum and T. Petrie,
Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist., 37 (1966), 1554-1563.
doi: 10.1214/aoms/1177699147. |
| [6] |
C. Brownlees and R. F. Engle,
SRISK: A conditional capital shortfall measure of systemic risk, Rev. Financial Stud., 30 (2017), 48-79.
doi: 10.1093/rfs/hhw060. |
| [7] |
A. S. Cherny, R. Douady and S. A. Molchanov, On measuring hedge fund risk, SSRN Electric J., (2008).
doi: 10.2139/ssrn.1113620. |
| [8] |
R. Cumby, S. Figlewski and J. Hasbrouck,
Forecasting volatility and correlations with EGARCH models, J. Derivatives, 1 (1993), 51-63.
doi: 10.3905/jod.1993.407877. |
| [9] |
A. Gil, J. Segura and N. M. Temme, Numerical Methods for Special Functions, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.
doi: 10.1137/1.9780898717822. |
| [10] |
E. Helleiner,
Understanding the 2007–2008 global financial crisis: Lessons for scholars of international political economy, Ann. Rev. Polit. Sci., 14 (2011), 67-87.
doi: 10.1146/annurev-polisci-050409-112539. |
| [11] |
F. Longin and B. Solnik,
Extreme correlation of international equity markets, J. Finance, 56 (2002), 649-676.
doi: 10.1111/0022-1082.00340. |
| [12] |
D. K. Patro, M. Qi and X. Sun,
A simple indicator of systemic risk, J. Financial Stabil., 9 (2013), 105-116.
doi: 10.2139/ssrn.1569805. |
| [13] |
D. Sornette and J. V. Andersen,
A nonlinear super-exponential rational model of speculative financial bubbles, Internat. J. Modern Phys. C, 13 (2002), 171-187.
doi: 10.1142/S0129183102003085. |
| [14] |
R. Tibshirani,
Regression shrinkage and selection via the lasso, J. Roy. Statist. Soc. Ser. B., 58 (1996), 267-288.
doi: 10.1111/j.2517-6161.1996.tb02080.x. |
| [15] |
X. Ye and R. Douady, Systemic risk indicators based on nonlinear PolyModel, J. Risk Financial Manag., 12 (2018).
doi: 10.3390/jrfm12010002. |
| [16] |
H. Zou and T. Hastie,
Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B Stat. Methodol., 67 (2005), 301-320.
doi: 10.1111/j.1467-9868.2005.00503.x. |
show all references
References:
| [1] |
B. K. Adhikari and J. E. Hilliard,
The VIX, VXO and realised volatility: A test of lagged and contemporaneous relationships, Internat. J. Financial Markets Derivatives, 3 (2014), 222-240.
doi: 10.1504/IJFMD.2014.059637. |
| [2] |
A. Ang and J. Chen,
Asymmetric correlations of equity portfolios, J. Finance Econ., 63 (2002), 443-494.
doi: 10.1016/S0304-405X(02)00068-5. |
| [3] |
A. Ang and A. Timmermann,
Regime changes and financial markets, Ann. Rev. Finance Econ., 4 (2011), 313-337.
doi: 10.3386/w17182. |
| [4] |
C. Aschwanden, Not even scientists can easily explain p-values, FiveThirtyEight, (2015). Available from: https://web.archive.org/web/20190925221600/https://fivethirtyeight.com/features/not-even-scientists-can-easily-explain-p-values/. |
| [5] |
L. E. Baum and T. Petrie,
Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist., 37 (1966), 1554-1563.
doi: 10.1214/aoms/1177699147. |
| [6] |
C. Brownlees and R. F. Engle,
SRISK: A conditional capital shortfall measure of systemic risk, Rev. Financial Stud., 30 (2017), 48-79.
doi: 10.1093/rfs/hhw060. |
| [7] |
A. S. Cherny, R. Douady and S. A. Molchanov, On measuring hedge fund risk, SSRN Electric J., (2008).
doi: 10.2139/ssrn.1113620. |
| [8] |
R. Cumby, S. Figlewski and J. Hasbrouck,
Forecasting volatility and correlations with EGARCH models, J. Derivatives, 1 (1993), 51-63.
doi: 10.3905/jod.1993.407877. |
| [9] |
A. Gil, J. Segura and N. M. Temme, Numerical Methods for Special Functions, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.
doi: 10.1137/1.9780898717822. |
| [10] |
E. Helleiner,
Understanding the 2007–2008 global financial crisis: Lessons for scholars of international political economy, Ann. Rev. Polit. Sci., 14 (2011), 67-87.
doi: 10.1146/annurev-polisci-050409-112539. |
| [11] |
F. Longin and B. Solnik,
Extreme correlation of international equity markets, J. Finance, 56 (2002), 649-676.
doi: 10.1111/0022-1082.00340. |
| [12] |
D. K. Patro, M. Qi and X. Sun,
A simple indicator of systemic risk, J. Financial Stabil., 9 (2013), 105-116.
doi: 10.2139/ssrn.1569805. |
| [13] |
D. Sornette and J. V. Andersen,
A nonlinear super-exponential rational model of speculative financial bubbles, Internat. J. Modern Phys. C, 13 (2002), 171-187.
doi: 10.1142/S0129183102003085. |
| [14] |
R. Tibshirani,
Regression shrinkage and selection via the lasso, J. Roy. Statist. Soc. Ser. B., 58 (1996), 267-288.
doi: 10.1111/j.2517-6161.1996.tb02080.x. |
| [15] |
X. Ye and R. Douady, Systemic risk indicators based on nonlinear PolyModel, J. Risk Financial Manag., 12 (2018).
doi: 10.3390/jrfm12010002. |
| [16] |
H. Zou and T. Hastie,
Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B Stat. Methodol., 67 (2005), 301-320.
doi: 10.1111/j.1467-9868.2005.00503.x. |
Figure 2.
Financial Crises
Figure 3.
Concavity in Polymodel v.s. S & P 500 Index (monthly)
Figure 4.
Comparing concavity with its $ 90^{th} $ percentile (monthly)
Figure 5.
Comparing concavity with its $ 80^{th} $ percentile (monthly)
Figure 6.
Concavity in Polymodel v.s. S & P 500 Index (bi-weekly)
Figure 7.
If Concavity Increases v.s. S & P 500 Index (bi-weekly)
Figure 8.
Concavity in Polymodel v.s. Russell 2000 Index (monthly)
Figure 9.
If Concavity Increases v.s. Russell 2000 Index (monthly)
Figure 10.
Crisis Indicator (monthly S & P 500 Index)
Figure 11.
Concavity Strategy (monthly S & P 500 Index)
Table 1.
Sample Indices Factors
| Category | Ticker | Description |
| Equity | SHCOMP Index | SSE Composite Index |
| Equity | STI Index | Singapore Stock Market Index |
| Equity | DAX Index | 30 Major German Stocks Index |
| Currency | DXY Index | US Dollar Index |
| Currency | USDCNY Curncy | USD to Chinese Yuan Exchange |
| Currency | USDJPY Curncy | USD to Japanese Yen Exchange |
| Bound & Yield | IRX | US 13 Week Treasury Bill Yield |
| Bound & Yield | USGG3M Index | US Government 3-Month Bond Yield |
| Bound & Yield | USGG5YR Index | US Government 5-year Bond Yield |
| Commodity | BCOMCN Index | Corn |
| Commodity | BCOMAG Index | Agriculture |
| Commodity | BCOMNG Index | Natural Gas |
| Volatility | VXO Index | CBOE S & P 100 Volatility Index |
| Note: Those factors are referred to in Ye and Douady [15]. | ||
| Category | Ticker | Description |
| Equity | SHCOMP Index | SSE Composite Index |
| Equity | STI Index | Singapore Stock Market Index |
| Equity | DAX Index | 30 Major German Stocks Index |
| Currency | DXY Index | US Dollar Index |
| Currency | USDCNY Curncy | USD to Chinese Yuan Exchange |
| Currency | USDJPY Curncy | USD to Japanese Yen Exchange |
| Bound & Yield | IRX | US 13 Week Treasury Bill Yield |
| Bound & Yield | USGG3M Index | US Government 3-Month Bond Yield |
| Bound & Yield | USGG5YR Index | US Government 5-year Bond Yield |
| Commodity | BCOMCN Index | Corn |
| Commodity | BCOMAG Index | Agriculture |
| Commodity | BCOMNG Index | Natural Gas |
| Volatility | VXO Index | CBOE S & P 100 Volatility Index |
| Note: Those factors are referred to in Ye and Douady [15]. | ||
Table 2.
Crises List
| Price peak month | Price bottom month | Drawdown from peak to trough |
| June, 1998 | August, 1998 | 15.57% |
| August, 2000 | September, 2002 | 46.28% |
| October, 2007 | February, 2009 | 52.56% |
| May, 2015 | September, 2015 | 8.89% |
| September, 2018 | December, 2018 | 13.97% |
| December, 2019 | March, 2020 | 20% |
| Price peak month | Price bottom month | Drawdown from peak to trough |
| June, 1998 | August, 1998 | 15.57% |
| August, 2000 | September, 2002 | 46.28% |
| October, 2007 | February, 2009 | 52.56% |
| May, 2015 | September, 2015 | 8.89% |
| September, 2018 | December, 2018 | 13.97% |
| December, 2019 | March, 2020 | 20% |
Table 3.
Strategies Annual Statistics (with monthly data)
| Annual | log-r (%) | std | Sharpe | r (%) | MDD (%) | Calmar |
| S & P 500 | 7.06 | 0.154 | 0.457 | 7.08 | 52.6 | 0.135 |
| Concavity | 10.57 | 0.146 | 0.725 | 10.62 | 24.0 | 0.443 |
| Annual | log-r (%) | std | Sharpe | r (%) | MDD (%) | Calmar |
| S & P 500 | 7.06 | 0.154 | 0.457 | 7.08 | 52.6 | 0.135 |
| Concavity | 10.57 | 0.146 | 0.725 | 10.62 | 24.0 | 0.443 |
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