|
| 1 | +from datetime import date, datetime, time, timedelta |
| 2 | + |
| 3 | +import numpy as np |
| 4 | +import pandas as pd |
| 5 | + |
| 6 | +from moddata.src.constants import MICRO_SECS_PER_DAY |
| 7 | + |
| 8 | + |
| 9 | +def make_milisec_data( |
| 10 | + inter_arrival_time_milisecs: float = 50, |
| 11 | + start_value: float = 5.00, |
| 12 | + daily_sigma: float = 0.02, |
| 13 | + day: date = date(2021, 1, 1), |
| 14 | + seed: int = 123_456 |
| 15 | +): |
| 16 | + """ |
| 17 | + Generate 1 day of data using GBM without drift. |
| 18 | + Arrivals have exponential distribution. |
| 19 | +
|
| 20 | + :param inter_arrival_time_milisecs: |
| 21 | + :param start_value: starting value of the GBM process |
| 22 | + :param daily_sigma: standard deviation of the GBM for 1d period |
| 23 | + :param day: date to use in the simulation |
| 24 | + :param seed: random seed |
| 25 | + :return: pd.DataFrame with columns quote_time and price |
| 26 | + """ |
| 27 | + dt: datetime = datetime.combine(day, time(0, 0, 0, 0)) |
| 28 | + time_grid: list[datetime] = [dt] |
| 29 | + prices: list[float] = [start_value] |
| 30 | + np.random.seed(seed) |
| 31 | + |
| 32 | + while dt.date() == day: |
| 33 | + time_diff = int(np.random.exponential( |
| 34 | + scale=inter_arrival_time_milisecs)) + 1 |
| 35 | + dt += timedelta(milliseconds=time_diff) |
| 36 | + time_grid.append(dt) |
| 37 | + prices.append( |
| 38 | + prices[-1] * ( |
| 39 | + 1 + |
| 40 | + np.random.standard_normal(size=1)[0] * |
| 41 | + np.sqrt(time_diff / MICRO_SECS_PER_DAY) * |
| 42 | + daily_sigma |
| 43 | + ) |
| 44 | + ) |
| 45 | + |
| 46 | + return pd.DataFrame(data={"quote_time": time_grid, "price": prices}) |
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