# Risk Mutualization in Central Clearing: An Answer to the Cross-Guarantee Phenomenon from the Financial Stability Viewpoint

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## Abstract

**:**

## 1. Introduction

## 2. Related Literature of Stress Tests

## 3. Model

^{−1}(99%) is the inverse of the normal distribution’s cumulative distribution function at the 99% probability, D* is the modified duration of the bond, $Va{R}_{t}^{y}$ is the value-at-risk at day t for the logreturn (y) in case of the stock and the currency, while $Va{R}_{t,bond}^{y}$ is the value-at-risk for the bond’s logreturn. The value-at-risk expressed for the price instead of the logreturn is based on Equations (12) and (13), where S is coming from the ABM (Equations (1) and (2)), while P is coming from the Vasicek model (Equations (3)–(6)), and T is the liquidaton period, which is set to 2 days, based on the regulation (EMIR 2012; RTS 2013),

_{CMt}in Equation (22)) of a particular CM portfolio. One unit of change in the spot price is the value of the asset’s actual margin calculated in Equations (10)–(21), while one unit of change in the standard deviation is 90% of the actual daily standard deviation.

- Historical 1—Min stock: lowest stock return during the 7500 days and taking the currency returns and the bond yield change on the same day.
- Historical 2—Max stock: highest stock return during the 7500 days and taking the currency returns and the bond yield change on the same day.
- Historical 3—Min bond: lowest yield change during the 7500 days and taking the stock and currency returns the same day.
- Historical 4—Max bond: highest yield change during the 7500 days and taking the stock and currency returns the same day.
- Historical 5—Min currency: lowest currency return during the 7500 days and taking the stock returns and bond yield change the same day.
- Historical 6—Max currency: highest currency return during the 7500 days and taking the stock returns and bond yield change the same day.

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Parameter | Stock | Currency |
---|---|---|

α | 7.71% | 0.09% |

σ | 22.37% | 11.85% |

S_{0} | 1345.26 | 1.1965 |

dt | 1 day | 1 day |

Parameters for the Price Simulation | |
---|---|

Vasicek | Bond |

a | 5 |

σ | 2.49% |

b | 12.20% |

y_{0} | 2.69% |

T | 5 |

dt | 1 day |

Face value | 100 |

Shock Parameter Affecting the Value of the Shock | |||

Stock | Currency | Bond | |

μ | −10.00 | −10.00 | −10.00 |

σ | 2.25 | 2.25 | 2.25 |

decrease of shock | 0.97 | 0.97 | 0.97 |

Shock Parameters Affecting the Date of the Shock | |||

λ | 0.005 | 0.0045 | 0.004 |

Position of Clearing Members | Clearing Member 1 | Clearing Member 2 | Clearing Member 3 | Clearing Member 4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Stock | Bond | Currency | Stock | Bond | Currency | Stock | Bond | Currency | Stock | Bond | Currency | |

Long Put | 3 | 5 | 2 | |||||||||

Short Put | 5 | 5 | ||||||||||

Long Call | 3 | 5 | ||||||||||

Short Call | 3 | 5 | ||||||||||

Long Futures | 5 | 5 | 5 | |||||||||

Short Futures | 5 | 10 | ||||||||||

Long Underlying | 2 | 3 | 6 | 5 | ||||||||

Short Underlying | 8 | 5 | 3 | |||||||||

Name of position | Long straddle + spot | Futures | Long straddle + futures | Protective put | Futures + spot | Futures | Covered call + short straddle + spot | Futures | Short straddle | Spot | Spot | --- |

Scenario | The Change in Spot Price Will Be Multiplied by This Amount | The Change in Standard Deviation Will Be Multiplied by This Amount |
---|---|---|

1 | 0.00 | 1 |

2 | 0.00 | −1 |

3 | 0.33 | 1 |

4 | 0.33 | −1 |

5 | −0.33 | 1 |

6 | −0.33 | −1 |

7 | 0.67 | 1 |

8 | 0.67 | −1 |

9 | −0.67 | 1 |

10 | −0.67 | −1 |

11 | 1.00 | 1 |

12 | 1.00 | −1 |

13 | −1.00 | 1 |

14 | −1.00 | −1 |

15 | 2.00 | 0 |

16 | −2.00 | 0 |

Historical Scenarios | Hypothetical Scenarios | |||||||
---|---|---|---|---|---|---|---|---|

Parameters | Min Stock | Max Stock | Min Currency | Max Currency | Min Bond | Max Bond | First | Second |

Stock | −5.28% | 4.71% | −0.48% | −1.59% | −1.59% | 0.08% | −2.80% | 2.80% |

Bond | 0.00% | 0.00% | 0.00% | 0.00% | 0.03% | −0.02% | −0.07% | 0.07% |

Currency | −1.26% | 0.13% | −2.69% | 2.90% | 0.92% | −0.29% | 1.23% | −1.23% |

Number of day in the simulation | 6839 | 179 | 3380 | 915 | 5897 | 5576 |

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**MDPI and ACS Style**

Friesz, M.; Muratov-Szabó, K.; Prepuk, A.; Váradi, K.
Risk Mutualization in Central Clearing: An Answer to the Cross-Guarantee Phenomenon from the Financial Stability Viewpoint. *Risks* **2021**, *9*, 148.
https://doi.org/10.3390/risks9080148

**AMA Style**

Friesz M, Muratov-Szabó K, Prepuk A, Váradi K.
Risk Mutualization in Central Clearing: An Answer to the Cross-Guarantee Phenomenon from the Financial Stability Viewpoint. *Risks*. 2021; 9(8):148.
https://doi.org/10.3390/risks9080148

**Chicago/Turabian Style**

Friesz, Melinda, Kira Muratov-Szabó, Andrea Prepuk, and Kata Váradi.
2021. "Risk Mutualization in Central Clearing: An Answer to the Cross-Guarantee Phenomenon from the Financial Stability Viewpoint" *Risks* 9, no. 8: 148.
https://doi.org/10.3390/risks9080148