UPST - Detail Report

Quick Overview

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)	Binomial IV (Period)	Yahoo IV (Period)	1σ Lower (68.27%)	1σ Upper	2σ Lower (95.45%)	2σ Upper
Daily	7.27%	5.07%	5.69%	8.68%	5.57%	5.53%	25.69	28.72	24.30	30.36
Weekly	18.33%	18.21%	15.38%	21.59%	12.27%	12.18%	24.02	30.71	21.25	34.71
Monthly	34.78%	48.87%	31.81%	46.59%	25.54%	25.36%	21.04	35.06	16.30	45.26
Quarterly	103.00%	112.24%	79.96%	102.77%	44.23%	43.92%	17.45	42.27	11.21	65.79
Annual	—	—	—	—	88.47%	87.84%	11.21	65.79	4.63	159.35
Option Time Horizon	—	—	—	—	33.39%	33.16%	19.45	37.93	13.93	52.96

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $27.16 | Strike (K): $27.50 (first OTM call ≥ spot) | Observed Mid-Price: $3.5000 (Bid $3.2500 / Ask $3.7500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 88.47% (CRR binomial tree, American, n=20 steps) | BS IV: 88.02% (European Black-Scholes) | Yahoo IV (Annual): 87.84% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.77. Further, an Excess Kurtosis of 23.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.56%	4	0.30%	0.30%
-21.56% to -16.11%	6	0.45%	0.76%
-16.11% to -10.65%	26	1.97%	2.73%
-10.65% to -5.20%	186	14.09%	16.82%
-5.20% to 0.25%	481	36.44%	53.26%
0.25% to 5.70%	417	31.59%	84.85%
5.70% to 11.15%	140	10.61%	95.45%
11.15% to 16.60%	34	2.58%	98.03%
16.60% to 22.06%	12	0.91%	98.94%
Greater than 22.06%	14	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.02%	7.52%	80.00%	68.27%
±2σ	-14.29%	14.79%	96.36%	95.45%
±3σ	-21.56%	22.06%	98.64%	99.73%

Descriptive Statistics

Mean	0.249%
Standard Error	0.200%
Median	-0.230%
Mode	-0.998%
Standard Deviation	7.269%
Sample Variance	52.842%
Kurtosis	23.15
Skewness	1.77
Range	145.748%
Minimum	-56.424%
Maximum	89.324%
Count	1320

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.295%	633	47.95%	2.539%
Negative	-4.420%	684	51.82%	-2.290%
Zero	0.000%	3	0.23%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.05%
20	1 Month	6.64%
60	1 Quarter	6.17%
250	1 Year	6.64%
750	3 Years	7.64%
1,250	5 Years	8.68%
2,500	10 Years	9.08%
5,000	20 Years	9.08%
12,500	50 Years	9.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.37. Further, an Excess Kurtosis of 9.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.40%	0	0.00%	0.00%
-6.40% to -2.60%	0	0.00%	0.00%
-2.60% to 1.21%	0	0.00%	0.00%
1.21% to 5.01%	262	19.83%	19.83%
5.01% to 8.82%	555	42.01%	61.85%
8.82% to 12.62%	305	23.09%	84.94%
12.62% to 16.43%	111	8.40%	93.34%
16.43% to 20.23%	33	2.50%	95.84%
20.23% to 24.04%	30	2.27%	98.11%
Greater than 24.04%	25	1.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.74%	13.89%	82.66%	68.27%
±2σ	-1.33%	18.96%	95.16%	95.45%
±3σ	-6.40%	24.04%	98.11%	99.73%

Descriptive Statistics

Mean	8.817%
Standard Error	0.140%
Median	7.568%
Mode	3.450%
Standard Deviation	5.073%
Sample Variance	25.733%
Kurtosis	9.53
Skewness	2.37
Range	50.053%
Minimum	2.155%
Maximum	52.208%
Count	1321

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.817%	1321	100.00%	8.817%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.02. Further, an Excess Kurtosis of 2.64 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.00%	8	0.61%	0.61%
-17.00% to -12.73%	18	1.36%	1.97%
-12.73% to -8.47%	54	4.09%	6.06%
-8.47% to -4.20%	177	13.40%	19.45%
-4.20% to 0.07%	385	29.14%	48.60%
0.07% to 4.34%	443	33.54%	82.13%
4.34% to 8.61%	161	12.19%	94.32%
8.61% to 12.88%	53	4.01%	98.33%
12.88% to 17.14%	16	1.21%	99.55%
Greater than 17.14%	6	0.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.62%	5.76%	73.96%	68.27%
±2σ	-11.31%	11.45%	94.70%	95.45%
±3σ	-17.00%	17.14%	98.94%	99.73%

Descriptive Statistics

Mean	0.070%
Standard Error	0.157%
Median	0.209%
Mode	0.000%
Standard Deviation	5.691%
Sample Variance	32.384%
Kurtosis	2.64
Skewness	0.02
Range	62.435%
Minimum	-27.413%
Maximum	35.022%
Count	1321

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.138%	681	51.55%	2.133%
Negative	-4.285%	636	48.15%	-2.063%
Zero	0.000%	4	0.30%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.76. Further, an Excess Kurtosis of 21.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.73%	0	0.00%	0.00%
-53.73% to -39.98%	1	0.36%	0.36%
-39.98% to -26.23%	6	2.19%	2.55%
-26.23% to -12.48%	43	15.69%	18.25%
-12.48% to 1.26%	96	35.04%	53.28%
1.26% to 15.01%	90	32.85%	86.13%
15.01% to 28.76%	24	8.76%	94.89%
28.76% to 42.51%	9	3.28%	98.18%
42.51% to 56.26%	3	1.09%	99.27%
Greater than 56.26%	2	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.07%	19.60%	76.64%	68.27%
±2σ	-35.40%	37.93%	97.08%	95.45%
±3σ	-53.73%	56.26%	99.27%	99.73%

Descriptive Statistics

Mean	1.264%
Standard Error	1.107%
Median	0.192%
Mode	-2.830%
Standard Deviation	18.332%
Sample Variance	336.067%
Kurtosis	21.35
Skewness	2.76
Range	212.995%
Minimum	-51.005%
Maximum	161.990%
Count	274

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.371%	138	50.37%	6.734%
Negative	-11.022%	136	49.63%	-5.471%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.81%
12	1 Quarter	15.35%
52	1 Year	15.60%
156	3 Years	19.16%
260	5 Years	21.59%
520	10 Years	22.57%
1,040	20 Years	22.57%
2,600	50 Years	22.57%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.39. Further, an Excess Kurtosis of 35.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.39%	0	0.00%	0.00%
-29.39% to -15.74%	0	0.00%	0.00%
-15.74% to -2.08%	0	0.00%	0.00%
-2.08% to 11.58%	32	11.64%	11.64%
11.58% to 25.24%	145	52.73%	64.36%
25.24% to 38.89%	55	20.00%	84.36%
38.89% to 52.55%	26	9.45%	93.82%
52.55% to 66.21%	13	4.73%	98.55%
66.21% to 79.87%	2	0.73%	99.27%
Greater than 79.87%	2	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.03%	43.45%	88.73%	68.27%
±2σ	-11.18%	61.66%	97.82%	95.45%
±3σ	-29.39%	79.87%	99.27%	99.73%

Descriptive Statistics

Mean	25.237%
Standard Error	1.098%
Median	19.464%
Mode	18.118%
Standard Deviation	18.210%
Sample Variance	331.615%
Kurtosis	35.13
Skewness	4.39
Range	197.491%
Minimum	6.472%
Maximum	203.963%
Count	275

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.237%	275	100.00%	25.237%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.04. Further, an Excess Kurtosis of 1.01 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.33%	1	0.36%	0.36%
-45.33% to -33.79%	3	1.09%	1.45%
-33.79% to -22.25%	11	4.00%	5.45%
-22.25% to -10.71%	37	13.45%	18.91%
-10.71% to 0.83%	96	34.91%	53.82%
0.83% to 12.37%	74	26.91%	80.73%
12.37% to 23.90%	32	11.64%	92.36%
23.90% to 35.44%	15	5.45%	97.82%
35.44% to 46.98%	6	2.18%	100.00%
Greater than 46.98%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.56%	16.21%	72.36%	68.27%
±2σ	-29.94%	31.60%	94.55%	95.45%
±3σ	-45.33%	46.98%	99.64%	99.73%

Descriptive Statistics

Mean	0.827%
Standard Error	0.928%
Median	0.040%
Mode	-62.231%
Standard Deviation	15.385%
Sample Variance	236.709%
Kurtosis	1.01
Skewness	0.04
Range	105.628%
Minimum	-62.231%
Maximum	43.397%
Count	275

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.402%	138	50.18%	6.224%
Negative	-10.831%	137	49.82%	-5.396%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.09. Further, an Excess Kurtosis of 0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -99.96%	0	0.00%	0.00%
-99.96% to -73.87%	0	0.00%	0.00%
-73.87% to -47.78%	1	1.59%	1.59%
-47.78% to -21.69%	14	22.22%	23.81%
-21.69% to 4.39%	24	38.10%	61.90%
4.39% to 30.48%	10	15.87%	77.78%
30.48% to 56.57%	9	14.29%	92.06%
56.57% to 82.66%	1	1.59%	93.65%
82.66% to 108.75%	4	6.35%	100.00%
Greater than 108.75%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.39%	39.18%	68.25%	68.27%
±2σ	-65.17%	73.96%	93.65%	95.45%
±3σ	-99.96%	108.75%	100.00%	99.73%

Descriptive Statistics

Mean	4.395%
Standard Error	4.382%
Median	-3.315%
Mode	-53.166%
Standard Deviation	34.785%
Sample Variance	1209.967%
Kurtosis	0.77
Skewness	1.09
Range	149.479%
Minimum	-53.166%
Maximum	96.313%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.304%	27	42.86%	15.130%
Negative	-18.787%	36	57.14%	-10.735%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.62%
12	1 Year	30.87%
36	3 Years	43.50%
60	5 Years	46.59%
120	10 Years	49.79%
240	20 Years	49.79%
600	50 Years	49.79%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.80. Further, an Excess Kurtosis of 10.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -78.76%	0	0.00%	0.00%
-78.76% to -42.10%	0	0.00%	0.00%
-42.10% to -5.45%	0	0.00%	0.00%
-5.45% to 31.21%	10	15.62%	15.62%
31.21% to 67.86%	32	50.00%	65.62%
67.86% to 104.52%	14	21.88%	87.50%
104.52% to 141.17%	4	6.25%	93.75%
141.17% to 177.83%	2	3.12%	96.88%
177.83% to 214.48%	0	0.00%	96.88%
Greater than 214.48%	2	3.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.99%	116.74%	89.06%	68.27%
±2σ	-29.89%	165.61%	96.88%	95.45%
±3σ	-78.76%	214.48%	96.88%	99.73%

Descriptive Statistics

Mean	67.862%
Standard Error	6.109%
Median	57.432%
Mode	18.644%
Standard Deviation	48.874%
Sample Variance	2388.697%
Kurtosis	10.03
Skewness	2.80
Range	271.043%
Minimum	18.644%
Maximum	289.687%
Count	64

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	67.862%	64	100.00%	67.862%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.48. Further, an Excess Kurtosis of 0.50 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -90.60%	0	0.00%	0.00%
-90.60% to -66.74%	0	0.00%	0.00%
-66.74% to -42.89%	4	6.25%	6.25%
-42.89% to -19.03%	12	18.75%	25.00%
-19.03% to 4.83%	17	26.56%	51.56%
4.83% to 28.69%	18	28.12%	79.69%
28.69% to 52.54%	10	15.62%	95.31%
52.54% to 76.40%	2	3.12%	98.44%
76.40% to 100.26%	0	0.00%	98.44%
Greater than 100.26%	1	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.98%	36.64%	64.06%	68.27%
±2σ	-58.79%	68.45%	98.44%	95.45%
±3σ	-90.60%	100.26%	98.44%	99.73%

Descriptive Statistics

Mean	4.829%
Standard Error	3.976%
Median	4.369%
Mode	-49.192%
Standard Deviation	31.810%
Sample Variance	1011.888%
Kurtosis	0.50
Skewness	0.48
Range	157.958%
Minimum	-49.192%
Maximum	108.766%
Count	64

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.429%	34	53.12%	15.103%
Negative	-21.917%	30	46.88%	-10.274%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.63. Further, an Excess Kurtosis of 8.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -287.23%	0	0.00%	0.00%
-287.23% to -209.98%	0	0.00%	0.00%
-209.98% to -132.73%	0	0.00%	0.00%
-132.73% to -55.48%	3	14.29%	14.29%
-55.48% to 21.77%	10	47.62%	61.90%
21.77% to 99.02%	6	28.57%	90.48%
99.02% to 176.27%	1	4.76%	95.24%
176.27% to 253.52%	0	0.00%	95.24%
253.52% to 330.77%	0	0.00%	95.24%
Greater than 330.77%	1	4.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-81.23%	124.77%	90.48%	68.27%
±2σ	-184.23%	227.77%	95.24%	95.45%
±3σ	-287.23%	330.77%	95.24%	99.73%

Descriptive Statistics

Mean	21.771%
Standard Error	22.476%
Median	-17.403%
Mode	-67.569%
Standard Deviation	102.999%
Sample Variance	10608.742%
Kurtosis	8.45
Skewness	2.63
Range	461.742%
Minimum	-67.569%
Maximum	394.173%
Count	21

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	98.177%	9	42.86%	42.076%
Negative	-35.534%	12	57.14%	-20.305%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	55.59%
12	3 Years	104.92%
20	5 Years	102.77%
40	10 Years	107.18%
80	20 Years	107.18%
200	50 Years	107.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.27. Further, an Excess Kurtosis of 1.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -164.81%	0	0.00%	0.00%
-164.81% to -80.64%	0	0.00%	0.00%
-80.64% to 3.54%	0	0.00%	0.00%
3.54% to 87.72%	5	22.73%	22.73%
87.72% to 171.89%	8	36.36%	59.09%
171.89% to 256.07%	5	22.73%	81.82%
256.07% to 340.25%	2	9.09%	90.91%
340.25% to 424.43%	1	4.55%	95.45%
424.43% to 508.60%	1	4.55%	100.00%
Greater than 508.60%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	59.66%	284.13%	72.73%	68.27%
±2σ	-52.58%	396.37%	95.45%	95.45%
±3σ	-164.81%	508.60%	100.00%	99.73%

Descriptive Statistics

Mean	171.894%
Standard Error	23.929%
Median	131.907%
Mode	52.206%
Standard Deviation	112.236%
Sample Variance	12596.991%
Kurtosis	1.26
Skewness	1.27
Range	425.506%
Minimum	52.206%
Maximum	477.712%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	171.894%	22	100.00%	171.894%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.19. Further, an Excess Kurtosis of 0.88 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -217.36%	0	0.00%	0.00%
-217.36% to -157.39%	0	0.00%	0.00%
-157.39% to -97.42%	0	0.00%	0.00%
-97.42% to -37.45%	6	27.27%	27.27%
-37.45% to 22.52%	6	27.27%	54.55%
22.52% to 82.49%	7	31.82%	86.36%
82.49% to 142.46%	0	0.00%	86.36%
142.46% to 202.43%	3	13.64%	100.00%
202.43% to 262.40%	0	0.00%	100.00%
Greater than 262.40%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-57.44%	102.48%	72.73%	68.27%
±2σ	-137.40%	182.44%	90.91%	95.45%
±3σ	-217.36%	262.40%	100.00%	99.73%

Descriptive Statistics

Mean	22.516%
Standard Error	17.048%
Median	12.331%
Mode	-79.852%
Standard Deviation	79.960%
Sample Variance	6393.584%
Kurtosis	0.88
Skewness	1.19
Range	280.469%
Minimum	-79.852%
Maximum	200.617%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	74.677%	12	54.55%	40.733%
Negative	-40.077%	10	45.45%	-18.217%
Zero	0.000%	0	0.00%	0.000%

UPST Deep Analytical Report