Instant Borrowing IRM

The interest rate model related to the Instant Borrowing model.

Formulas

Liquidity risk materializes when utilization is high, its becomes more problematic as
UU
gets closer to 100%. In order to mitigate against this constraint, the interest rate curve is split in two linear rate curves around an optimal utilization rate
UoptimalU_{optimal}
. Before
UoptimalU_{optimal}
the slope is small but afterward it starts rising sharply.
The interest rate
RaR_a
follows the model:
​
ifU<Uoptimal:Ra=R0+UtUoptimalRslope1if \hspace{1mm} U < U_{optimal}: \hspace{1cm} R_a = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}
​
ifUβ‰₯Uoptimal:Ra=R0+Rslope1+Utβˆ’Uoptimal1βˆ’UoptimalRslope2if \hspace{1mm} U \geq U_{optimal}: \hspace{1cm} R_a = R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}}R_{slope2}
​
The following protocol parameters will be adjusted according to market conditions:
  • ​
    UOptimalU_{Optimal}
    ​
  • ​
    R0R_0
    ​
  • ​
    Rslope1R_{slope1}
    ​
  • ​
    Rslope2R_{slope2}
    ​
  • ​
    InsuranceFundRatioInsurance Fund Ratio
    ​
In addition to the above parameters, the reserve factors discussed in Supply APY will also be adjusted according to market conditions.

Constants Table

Asset
UOptimal
Base (R0)
RSlope 1
RSlope 2
USDC
50%
5%
65%
150%
SOL
50%
5%
65%
150%
Other Constants
Rate
Reserveplatform
20%
ReservePixelPanther
75%
Insurance Fund Ratio
5%
In our unique interest rate model, the amount of Borrow APR and Supply APY is based on
UaU_a
at any time.
​
UU
(Utilization Rate)
Borrow APR if U<Uoptimal​
Borrow APR if U>Uoptimal
Borrow APRActual
Supply APYUSDC
NIIplatform
Insurance Fund
NIIAIF
NIIpp
0%
5.0%
-80.00%
5.00%
0.00%
5.00%
0.25%
4.75%
1.19%
1%
6.3%
-77.00%
6.30%
0.05%
6.25%
0.31%
5.94%
1.48%
2%
7.6%
-74.00%
7.60%
0.12%
7.48%
0.37%
7.10%
1.78%
3%
8.9%
-71.00%
8.90%
0.21%
8.69%
0.43%
8.25%
2.06%
4%
10.2%
-68.00%
10.20%
0.33%
9.87%
0.49%
9.38%
2.34%
5%
11.5%
-65.00%
11.50%
0.46%
11.04%
0.55%
10.49%
2.62%
6%
12.8%
-62.00%
12.80%
0.61%
12.19%
0.61%
11.58%
2.89%
7%
14.1%
-59.00%
14.10%
0.79%
13.31%
0.67%
12.64%
3.16%
8%
15.4%
-56.00%
15.40%
0.99%
14.41%
0.72%
13.69%
3.42%
9%
16.7%
-53.00%
16.70%
1.20%
15.50%
0.77%
14.72%
3.68%
10%
18.0%
-50.00%
18.00%
1.44%
16.56%
0.83%
15.73%
3.93%
11%
19.3%
-47.00%
19.30%
1.70%
17.60%
0.88%
16.72%
4.18%
12%
20.6%
-44.00%
20.60%
1.98%
18.62%
0.93%
17.69%
4.42%
13%
21.9%
-41.00%
21.90%
2.28%
19.62%
0.98%
18.64%
4.66%
14%
23.2%
-38.00%
23.20%
2.60%
20.60%
1.03%
19.57%
4.89%
15%
24.5%
-35.00%
24.50%
2.94%
21.56%
1.08%
20.48%
5.12%
16%
25.8%
-32.00%
25.80%
3.30%
22.50%
1.12%
21.37%
5.34%
17%
27.1%
-29.00%
27.10%
3.69%
23.41%
1.17%
22.24%
5.56%
18%
28.4%
-26.00%
28.40%
4.09%
24.31%
1.22%
23.09%
5.77%
19%
29.7%
-23.00%
29.70%
4.51%
25.19%
1.26%
23.93%
5.98%
20%
31.0%
-20.00%
31.00%
4.96%
26.04%
1.30%
24.74%
6.18%
21%
32.3%
-17.00%
32.30%
5.43%
26.87%
1.34%
25.53%
6.38%
22%
33.6%
-14.00%
33.60%
5.91%
27.69%
1.38%
26.30%
6.58%
23%
34.9%
-11.00%
34.90%
6.42%
28.48%
1.42%
27.05%
6.76%
24%
36.2%
-8.00%
36.20%
6.95%
29.25%
1.46%
27.79%
6.95%
25%
37.5%
-5.00%
37.50%
7.50%
30.00%
1.50%
28.50%
7.13%
26%
38.8%
-2.00%
38.80%
8.07%
30.73%
1.54%
29.19%
7.30%
27%
40.1%
1.00%
40.10%
8.66%
31.44%
1.57%
29.87%
7.47%
28%
41.4%
4.00%
41.40%
9.27%
32.13%
1.61%
30.52%
7.63%
29%
42.7%
7.00%
42.70%
9.91%
32.79%
1.64%
31.15%
7.79%
30%
44.0%
10.00%
44.00%
10.56%
33.44%
1.67%
31.77%
7.94%
31%
45.3%
13.00%
45.30%
11.23%
34.07%
1.70%
32.36%
8.09%
32%
46.6%
16.00%
46.60%
11.93%
34.67%
1.73%
32.94%
8.23%
33%
47.9%
19.00%
47.90%
12.65%
35.25%
1.76%
33.49%
8.37%
34%
49.2%
22.00%
49.20%
13.38%
35.82%
1.79%
34.03%
8.51%
35%
50.5%
25.00%
50.50%
14.14%
36.36%
1.82%
34.54%
8.64%
36%
51.8%
28.00%
51.80%
14.92%
36.88%
1.84%
35.04%
8.76%
37%
53.1%
31.00%
53.10%
15.72%
37.38%
1.87%
35.51%
8.88%
38%
54.4%
34.00%
54.40%
16.54%
37.86%
1.89%
35.97%
8.99%
39%
55.7%
37.00%
55.70%
17.38%
38.32%
1.92%
36.41%
9.10%
40%
57.0%
40.00%
57.00%
18.24%
38.76%
1.94%
36.82%
9.21%
41%
58.3%
43.00%
58.30%
19.12%
39.18%
1.96%
37.22%
9.30%
42%
59.6%
46.00%
59.60%
20.03%
39.57%
1.98%
37.60%
9.40%
43%
60.9%
49.00%
60.90%
20.95%
39.95%
2.00%
37.95%
9.49%
44%
62.2%
52.00%
62.20%
21.89%
40.31%
2.02%
38.29%
9.57%
45%
63.5%
55.00%
63.50%
22.86%
40.64%
2.03%
38.61%
9.65%
46%
64.8%
58.00%
64.80%
23.85%
40.95%
2.05%
38.91%
9.73%
47%
66.1%
61.00%
66.10%
24.85%
41.25%
2.06%
39.18%
9.80%
48%
67.4%
64.00%
67.40%
25.88%
41.52%
2.08%
39.44%
9.86%
49%
68.7%
67.00%
68.70%
26.93%
41.77%
2.09%
39.68%
9.92%
50%
70.0%
70.00%
70.00%
28.00%
42.00%
2.10%
39.90%
9.98%
51%
71.3%
73.00%
73.00%
29.78%
43.22%
2.16%
41.06%
10.26%
52%
72.6%
76.00%
76.00%
31.62%
44.38%
2.22%
42.16%
10.54%
53%
73.9%
79.00%
79.00%
33.50%
45.50%
2.28%
43.23%
10.81%
54%
75.2%
82.00%
82.00%
35.42%
46.58%
2.33%
44.25%
11.06%
55%
76.5%
85.00%
85.00%
37.40%
47.60%
2.38%
45.22%
11.31%
56%
77.8%
88.00%
88.00%
39.42%
48.58%
2.43%
46.15%
11.54%
57%
79.1%
91.00%
91.00%
41.50%
49.50%
2.48%
47.03%
11.76%
58%
80.4%
94.00%
94.00%
43.62%
50.38%
2.52%
47.86%
11.97%
59%
81.7%
97.00%
97.00%
45.78%
51.22%
2.56%
48.66%
12.16%
60%
83.0%
100.00%
100.00%
48.00%
52.00%
2.60%
49.40%
12.35%
61%
84.3%
103.00%
103.00%
50.26%
52.74%
2.64%
50.10%
12.52%
62%
85.6%
106.00%
106.00%
52.58%
53.42%
2.67%
50.75%
12.69%
63%
86.9%
109.00%
109.00%
54.94%
54.06%
2.70%
51.36%
12.84%
64%
88.2%
112.00%
112.00%
57.34%
54.66%
2.73%
51.92%
12.98%
65%
89.5%
115.00%
115.00%
59.80%
55.20%
2.76%
52.44%
13.11%
66%
90.8%
118.00%
118.00%
62.30%
55.70%
2.78%
52.91%
13.23%
67%
92.1%
121.00%
121.00%
64.86%
56.14%
2.81%
53.34%
13.33%
68%
93.4%
124.00%
124.00%
67.46%
56.54%
2.83%
53.72%
13.43%
69%
94.7%
127.00%
127.00%
70.10%
56.90%
2.84%
54.05%
13.51%
70%
96.0%
130.00%
130.00%
72.80%
57.20%
2.86%
54.34%
13.59%
71%
97.3%
133.00%
133.00%
75.54%
57.46%
2.87%
54.58%
13.65%
72%
98.6%
136.00%
136.00%
78.34%
57.66%
2.88%
54.78%
13.70%
73%
99.9%
139.00%
139.00%
81.18%
57.82%
2.89%
54.93%
13.73%
74%
101.2%
142.00%
142.00%
84.06%
57.94%
2.90%
55.04%
13.76%
75%
102.5%
145.00%
145.00%
87.00%
58.00%
2.90%
55.10%
13.78%
76%
103.8%
148.00%
148.00%
89.98%
58.02%
2.90%
55.12%
13.78%
77%
105.1%
151.00%
151.00%
93.02%
57.98%
2.90%
55.08%
13.77%
78%
106.4%
154.00%
154.00%
96.10%
57.90%
2.90%
55.01%
13.75%
79%
107.7%
157.00%
157.00%
99.22%
57.78%
2.89%
54.89%
13.72%
80%
109.0%
160.00%
160.00%
102.40%
57.60%
2.88%
54.72%
13.68%
81%
110.3%
163.00%
163.00%
105.62%
57.38%
2.87%
54.51%
13.63%
82%
111.6%
166.00%
166.00%
108.90%
57.10%
2.86%
54.25%
13.56%
83%
112.9%
169.00%
169.00%
112.22%
56.78%
2.84%
53.94%