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Intraday Trend Following and Conditional Mean Reversion Yanyi Huang Abstract This study examines whether transparent intraday trend-following and conditional mean-reversion rules can generate statistically robust net returns in the Invesco QQQ Trust (QQQ), and whether those rules can be translated into a resilient broker-facing trading process. Two trend strategies are considered. The first combines exponential moving-average direction, MACD confirmation, ADX trend strength, and a volatility-expansion filter. The second compares a short volume-weighted moving average with a longer price average. A third strategy enters Bollinger %B mean-reversion trades only when a rolling Hurst estimate or variance-ratio statistic indicates a reversion-compatible state. ...

Task 3. VaR Backtesting VaR Backtesting most of the time, we assume daily return follow normal distribution and as the question say, Var is caculated at 99% confidence. Import Libraries 1 await __import__("piplite").install('numpy', 'scipy', 'matplotlib', 'pandas', 'tabulate') 1 2 # hyy:fix the import failed issue await __import__("piplite").install('tabulate') 1 2 # hyy:fix excel issue, miss the excel read library, install here. await __import__("piplite").install('openpyxl') 1 2 3 4 5 import numpy as np import pandas as pd from scipy import stats import matplotlib.pyplot as plt from tabulate import tabulate 1 2 # set precision pd.set_option('display.precision', 4) Load Data ...

Pricing European and Binary Options using Monte Carlo Simulation 1. Introduction This report investigates the pricing of European and Binary call options using Monte Carlo simulation under the risk-neutral framework. According to the Fundamental Theorem of Asset Pricing, the value of an option $V(S,t)$ is the expected value of its discounted payoff under the risk-neutral measure $\mathbb{Q}$: $$V(S, t) = e^{-r(T-t)} \mathbb{E}^\mathbb{Q} [\text{Payoff}(S_T)]$$ We assume the underlying asset follows Geometric Brownian Motion (GBM) governed by the Stochastic Differential Equation (SDE): $$dS_t = r S_t dt + \sigma S_t dW_t$$ where $r$ is the risk-free rate, $\sigma$ is the volatility, and $dW_t$ is a Wiener process. ...