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@@ -1,6 +1,5 @@
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import json
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from decimal import Decimal, getcontext
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-
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import pandas as pd
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import threading
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from collections import deque
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@@ -145,6 +144,31 @@ def objective_function(params, delta_max, log_lambda_hat_value, log_integral_phi
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return np.sum(residuals)
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+def calculate_delta_sum(gamma, sigma_squared, T_minus_t, k):
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+ term1 = gamma * sigma_squared * T_minus_t
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+ term2 = (2 / gamma) * np.log(1 + (gamma / k))
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+ delta_sum = term1 + term2
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+ return delta_sum
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+
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+
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+def calculate_sigma_squared(prices, timestamps):
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+ """
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+ 计算 σ^2 的值
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+ :param prices: 时间序列的价格数据
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+ :param timestamps: 时间戳数组
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+ :return: σ^2 的值
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+ """
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+ n = len(prices)
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+ if n < 2:
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+ return 0.0
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+
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+ time_diff = int(int((timestamps[-1] - timestamps[0]).total_seconds() * 1000) / 100)
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+ price_diff_squared = [(prices[i] - prices[i - 1]) ** 2 for i in range(1, n)]
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+ sigma_squared = np.sum(price_diff_squared) / time_diff
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+
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+ return sigma_squared
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+
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+
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def process_depth_data():
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global order_book_snapshots, trade_snapshots, spread_delta_snapshots
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global k_initial, A_initial, S0
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@@ -192,9 +216,13 @@ def process_depth_data():
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if result.success:
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A_initial, k_initial = result.x
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+ # logger.info(f"Optimal k: {k_initial}, delta_max: {delta_max}")
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- logger.info(f"Optimal k: {k_initial}, delta_max: {delta_max}")
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- # else:
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- # logger.error("Optimization failed")
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+ # ========================== 计算 σ^2 ==========================
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+ sigma_squared = calculate_sigma_squared(S_values, order_book_timestamps)
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- # logger.info("log(λ(δ)): {}, log(∫ φ(k, ξ) dξ): {}".format(log_lambda_hat_value, log_integral_phi_value))
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+ # ========================== 计算 δ^a + δ^b ==========================
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+ gamma = 1.0
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+ T_minus_t = 1.0
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+ delta_sum = calculate_delta_sum(gamma, sigma_squared, T_minus_t, k_initial)
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+ logger.info(f"δ^a + δ^b: {delta_sum}")
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