EigenScore
EigenScore
Under the risk-neutral measure, the stock price at expiry T has some distribution with a smooth density on (0, infinity). The distribution is not disclosed. The continuously compounded rate is r.
You observe the prices C_1, ..., C_m of European calls with strikes K_1 < K_2 < ... < K_m (equally spaced), all expiring at T, priced under this distribution and then rounded to 8 decimal places.
Compute P(S_T > x_j) for each of the three query levels x_1, x_2, x_3. All query levels lie strictly inside the strike range.
The first line contains r, T and m. The next m lines each contain K_j and C_j. The last line contains x_1, x_2 and x_3.
Three real numbers on one line: P(S_T > x_1), P(S_T > x_2), P(S_T > x_3), each within 1e-4 of the true value.
40 <= m <= 80
-0.03 <= r <= 0.08, 0.05 <= T <= 5
Every answer lies in [0.02, 0.98]
The prices are exact up to the disclosed rounding (8 decimal places)
This is a standard problem: a submission scores full points if it produces the correct output for every test case, and zero otherwise.
Numeric answers are accepted if they are within an absolute tolerance of 0.0001 or a relative tolerance of 0.0001 of the expected value.
0.033487 4.84095 69 39.9713 29.79087459 41.546 28.47617808 43.1207 27.17178853 44.6955 25.88061261 46.2702 24.60616756 47.845 23.35191958 49.4197 22.12181528 50.9945 20.91951562 52.5692 19.74888562 54.144 18.61325661 55.7187 17.51590710 57.2934 16.45946152 58.8682 15.44605290 60.4429 14.47746629 62.0177 13.55468343 63.5924 12.67838620 65.1672 11.84851915 66.7419 11.06478083 68.3167 10.32625846 69.8914 9.63188855 71.4661 8.98018554 73.0409 8.36945747 74.6156 7.79796916 76.1904 7.26373046 77.7651 6.76483418 79.3399 6.29922415 80.9146 5.86498221 82.4894 5.46011739 84.0641 5.08280717 85.6388 4.73122743 87.2136 4.40364684 88.7883 4.09848788 90.3631 3.81418745 91.9378 3.54935263 93.5126 3.30261413 95.0873 3.07275806 96.662 2.85860933 98.2368 2.65907842 99.8115 2.47318985 101.3863 2.29999053 102.961 2.13863938 104.5358 1.98831412 106.1105 1.84828881 107.6853 1.71785287 109.26 1.59637829 110.8347 1.48325639 112.4095 1.37792155 113.9842 1.27986578 115.559 1.18859016 117.1337 1.10365220 118.7085 1.02461698 120.2832 0.95109828 121.858 0.88271634 123.4327 0.81913358 125.0074 0.76002171 126.5822 0.70507458 128.1569 0.65401599 129.7317 0.60657462 131.3064 0.56250886 132.8812 0.52158158 134.4559 0.48358159 136.0306 0.44830395 137.6054 0.41555772 139.1801 0.38517060 140.7549 0.35697392 142.3296 0.33081747 143.9044 0.30655438 145.4791 0.28405387 147.0539 0.26318826 111.2599 121.4327 125.653
0.0799459921 0.0502082481 0.0412945523
0.011816 1.914023 62 19.8726 15.57751003 20.8256 14.66575054 21.7785 13.77054117 22.7314 12.89967655 23.6843 12.06183524 24.6373 11.26538485 25.5902 10.51765023 26.5431 9.82355452 27.496 9.18547975 28.4489 8.60313314 29.4019 8.07382080 30.3548 7.59323909 31.3077 7.15581888 32.2606 6.75560468 33.2135 6.38673736 34.1665 6.04380883 35.1194 5.72223767 36.0723 5.41815438 37.0252 5.12854631 37.9782 4.85112384 38.9311 4.58433053 39.884 4.32704985 40.8369 4.07860574 41.7898 3.83862708 42.7428 3.60693367 43.6957 3.38355917 44.6486 3.16854767 45.6015 2.96200809 46.5544 2.76405758 47.5074 2.57477953 48.4603 2.39428708 49.4132 2.22259458 50.3661 2.05969289 51.319 1.90552735 52.272 1.75998343 53.2249 1.62294920 54.1778 1.49422705 55.1307 1.37359987 56.0837 1.26080841 57.0366 1.15560262 57.9895 1.05767544 58.9424 0.96671557 59.8953 0.88239975 60.8483 0.80438895 61.8012 0.73236428 62.7541 0.66598134 63.707 0.60490658 64.6599 0.54881145 65.6129 0.49736946 66.5658 0.45027915 67.5187 0.40723327 68.4716 0.36794202 69.4246 0.33212478 70.3775 0.29952534 71.3304 0.26988987 72.2833 0.24298246 73.2362 0.21858119 74.1892 0.19647582 75.1421 0.17647659 76.095 0.15839992 77.0479 0.14207752 78.0008 0.12735344 49.6705 39.6268 39.3218
0.1770287532 0.2739140822 0.2770257455