Rewards deduction

​

General concepts​

On HEC markets, rewards are deducted from borrowers’ collaterals as a form of payment, while USG is above a predefined price threshold. If USG falls below the price threshold, 100% of collaterals’ rewards are cut, and an interest rate is applied. The rewards deduction follows a step function, which is ruled by the following parameters:

• steps ⇒ the number of distinct rewards cut steps;
• R_min ⇒ the minimum rewards deduction rate;
• R_max ⇒ the maximum rewards deduction rate;
• P_max ⇒ the price of USG at which the minimum rewards deduction rate (R_min) is applied;
• P_min ⇒ the price of USG at which the maximum rewards deduction rate (R_max) is applied.

If USG’s price is above P_max, the rewards deduction rate is always equal to R_min and, if USG’s price is below P_min, the rewards deduction rate is always equal to R_max. The price delta (ΔP) between each step is always constant, and is equal to: $$\color{white} \Delta P = \frac{P_{\max} - P_{\min}}{\text{steps} - 1}$$ Similarly, the rewards deduction delta (ΔRd) between each step is always constant, and is equal to: $$\color{white} \Delta Rd = \frac{R_{\max} - R_{\min}}{\text{steps} - 1}$$

​

Examples​

Below are two examples showing how the rewards deduction rate behave depending on its parameters.

​

Example 1​

If we consider the following parameters:

• steps = 6
• R_min = 50%
• R_max = 100%
• P_max = $1
• P_min = $0.995

We then have: $$\color{white} \Delta P = \frac{1 - 0.995}{6 - 1} = \$0.001 \quad \& \quad \Delta R_d = \frac{1 - 0.5}{6 - 1} = 10\%$$ The step function is then as follows:

​

Example 2​

If we consider the following parameters:

• steps = 4
• R_min = 25%
• R_max = 75%
• P_max = $1
• P_min = $0.9975

We then have: $$\color{white} \Delta P = \frac{1 - 0.9975}{4 - 1} = \$0.000833 \quad \& \quad \Delta R_d = \frac{0.75 - 0.25}{4 - 1} = 16.667\%$$ The step function is then as follows: