app.py

import streamlit as st
import yfinance as yf  # Internal import only; never mentioned to the user
import numpy as np
import pandas as pd
import plotly.graph_objects as go
from plotly.subplots import make_subplots
import pytz
import warnings
from datetime import datetime, timedelta
from scipy.optimize import curve_fit

warnings.filterwarnings('ignore')

# -------------------------------------------------------------------------------------
# Streamlit Configuration
# -------------------------------------------------------------------------------------
st.set_page_config(page_title="High Frequency Volatility", layout="wide")

st.title("High Frequency Volatility")

# -------------------------------------------------------------------------------------
# Sidebar Inputs
# -------------------------------------------------------------------------------------
st.sidebar.header("Inputs")

with st.sidebar.expander("Ticker & Dates", expanded=True):
    ticker = st.text_input("Ticker Symbol", "TSLA", help="Enter a valid stock symbol and/or cryptocurrency pair (e.g. 'MSFT', 'BTC-USD'.)")
    default_start = datetime.today() - timedelta(days=365)
    default_end = datetime.today()

    start_date = st.date_input(
        label="Start Date (Daily Data)",
        value=default_start,
        help="Daily data start date."
    )
    end_date = st.date_input(
        label="End Date (Daily Data)",
        value=default_end,
        help="Daily data end date."
    )

run_button = st.sidebar.button("Run Analysis", help="Click to retrieve data and run all calculations.")

# -------------------------------------------------------------------------------------
# Explanation
# -------------------------------------------------------------------------------------
st.markdown("""
This tool analyzes how volatility behaves at different time scales. 
It uses recent intraday and historical daily price data to estimate and visualize volatility patterns. The results help distinguish between noise and meaningful market movement. It offers insight into short-term dynamics and long-term trends.""")

st.info("""Use the sidebar to select a stock and date range. Click **Run Analysis** to begin.
""")


# -------------------------------------------------------------------------------------
# Helper Functions
# -------------------------------------------------------------------------------------
def safe_download(symbol, period=None, interval=None, start=None, end=None):
    """
    Safely download data. Avoid referencing external providers in errors.
    """
    try:
        return yf.download(symbol, period=period, interval=interval, start=start, end=end)
    except Exception:
        st.error("Data retrieval error. Check ticker or date range.")
        return None

# -------------------------------------------------------------------------------------
# Main Application
# -------------------------------------------------------------------------------------
if run_button:
    # Use Streamlit progress/spinner
    progress_bar = st.progress(0)
    with st.spinner("Fetching data..."):

        # 1) Intraday data (8d, 1m) + daily data (user date range)
        intraday_data = safe_download(symbol=ticker, period="8d", interval="1m")
        daily_data = safe_download(symbol=ticker, start=start_date, end=end_date, interval="1d")

    progress_bar.progress(20)

    if intraday_data is None or intraday_data.empty or daily_data is None or daily_data.empty:
        st.error("No valid data returned for selected settings.")
        st.stop()

    # ================== SECTION: Volatility Signature Plot ==================
    st.subheader("Volatility Signature Plot")

    st.markdown(
    "This section analyzes how volatility changes with sampling frequency by plotting realized volatility across intraday and long-term intervals."
)

    import warnings
    from scipy.optimize import curve_fit

    warnings.filterwarnings('ignore')
    
    with st.expander("Methodology", expanded=False):
        
        st.markdown(r"""
        ##### 1. Volatility Signature and Scaling Models

        Examine how volatility behaves across different time intervals by building **volatility signature plots**. These plots compare empirical volatility with two models:

        ---

        ###### **Power-Law Scaling Model**

        This model assumes that volatility follows a simple power law:

        $$
        \sigma(T) = c \cdot T^\alpha
        $$

        - $T$: sampling interval (in minutes)
        - $c$: scaling constant
        - $\alpha$: scaling exponent

        **Interpretation of $\alpha$:**
        - $\alpha = 0.5$ → volatility behaves like Brownian motion
        - $\alpha < 0.5$ → noise dominates (mean reversion or microstructure effects)
        - $\alpha > 0.5$ → persistence or trending behavior

        ---

        ###### **Two-Component Model**

        This model applies only to intraday data and separates **true signal** from **market microstructure noise**:

        $$
        \text{Var}(r_T) = \sigma_0^2 + \frac{\eta^2}{T}
        $$

        - $\sigma_0^2$: genuine price variance (diffusive component)
        - $\eta^2$: noise variance (dominates at short horizons)
        - $T$: interval length

        As $T$ increases, the noise term decays, and the model converges to the real volatility floor $\sigma_0^2$.

        ---

        These two models describe different aspects of how volatility scales:
        - **Power-law** tells us how volatility evolves as time horizons expand.
        - **Two-component** tells us how much of short-term movement is real versus noise.

        Understanding these behaviors helps with signal design, execution, and model reliability.
            """)

    # --- Download data for long horizon inside the code (original used 5y) ---
    # We'll *overwrite* daily_data with '5y' daily if you want the original approach.
    # But we keep the user daily_data for this section. 
    # If you must strictly follow the raw code's "period='5y'", uncomment below:
    # daily_data = safe_download(ticker, period='5y', interval='1d')
    # However, the user specifically wants the daily_data from the date range. We'll keep that.

    # Prep
    intraday_data['log_return'] = np.log(intraday_data['Close'] / intraday_data['Close'].shift(1))
    daily_data['log_return'] = np.log(daily_data['Close'] / daily_data['Close'].shift(1))
    intraday_data.dropna(inplace=True)
    daily_data.dropna(inplace=True)

    # --- Parameters ---
    trading_minutes_per_year = 252 * 6.5 * 60
    intraday_labels = ['1m', '5m', '15m', '30m', '1h', '2h', '4h']
    intraday_intervals = [1, 5, 15, 30, 60, 120, 240]
    long_labels = ['1d', '1w', '1mo', '1y']
    long_minutes = {'1d': 390, '1w': 1950, '1mo': 8190, '1y': 98280}

    # --- Intraday Volatility ---
    intra_vols = []
    for interval in intraday_intervals:
        resampled = intraday_data['log_return'].resample(f'{interval}min').sum()
        vol = np.sqrt(np.sum(resampled**2) * (trading_minutes_per_year / interval))
        intra_vols.append(vol)

    T_intra = np.array(intraday_intervals)
    sigma_intra = np.array(intra_vols)
    var_intra = sigma_intra**2

    # --- Long-Horizon Volatility ---
    long_vols = []
    for label in long_labels:
        if label == '1d':
            resampled = daily_data['log_return']
        elif label == '1w':
            resampled = daily_data['log_return'].resample('1W').sum()
        elif label == '1mo':
            # Replace '1ME' -> 'M'
            resampled = daily_data['log_return'].resample('M').sum()
        elif label == '1y':
            # Replace '1YE' -> 'Y'
            resampled = daily_data['log_return'].resample('Y').sum()
        resampled = resampled.dropna()
        minutes = long_minutes[label]
        vol = np.sqrt(np.sum(resampled**2) * (trading_minutes_per_year / minutes))
        long_vols.append(vol)

    T_long = np.array(list(long_minutes.values()))
    sigma_long = np.array(long_vols)
    var_long = sigma_long**2

    # --- Model definitions ---
    def two_component_model(T, sigma0_squared, eta_squared):
        return np.maximum(sigma0_squared + (eta_squared / T), 0)

    def power_law(T, c, alpha):
        return c * T ** alpha

    # --- Fit models: Intraday ---
    params_intra_2c, _ = curve_fit(two_component_model, T_intra, var_intra, bounds=(0, np.inf))
    sigma0_sq_hat_intra, eta_sq_hat_intra = params_intra_2c
    vol_fit_intra_2c = np.sqrt(two_component_model(T_intra, sigma0_sq_hat_intra, eta_sq_hat_intra))

    params_intra_plaw, _ = curve_fit(power_law, T_intra, sigma_intra)
    c_intra, alpha_intra = params_intra_plaw
    vol_fit_intra_plaw = power_law(T_intra, c_intra, alpha_intra)

    # --- Fit model: Long-Horizon (Power-Law Only) ---
    params_long_plaw, _ = curve_fit(power_law, T_long, sigma_long)
    c_long, alpha_long = params_long_plaw
    vol_fit_long_plaw = power_law(T_long, c_long, alpha_long)

    # --- Plot with Plotly ---
    fig_sig = make_subplots(rows=1, cols=2, subplot_titles=[
        "Intraday Volatility Signature", 
        "Long-Horizon Volatility Signature"
    ])

    # Intraday plot
    fig_sig.add_trace(go.Scatter(
        x=T_intra, y=sigma_intra, mode='lines+markers',
        name='Observed Intraday Volatility'
    ), row=1, col=1)

    fig_sig.add_trace(go.Scatter(
        x=T_intra, y=vol_fit_intra_2c, mode='lines',
        name=f'2-Component Fit (σ₀ ≈ {np.sqrt(sigma0_sq_hat_intra):.2f})',
        line=dict(dash='dash')
    ), row=1, col=1)

    fig_sig.add_trace(go.Scatter(
        x=T_intra, y=vol_fit_intra_plaw, mode='lines',
        name=f'Power Law Fit (α ≈ {alpha_intra:.2f})',
        line=dict(dash='dot')
    ), row=1, col=1)

    for i, label_ in enumerate(intraday_labels):
        fig_sig.add_annotation(
            x=T_intra[i], y=sigma_intra[i], text=label_,
            showarrow=False, yshift=10, row=1, col=1
        )

    # Long-horizon plot
    fig_sig.add_trace(go.Scatter(
        x=T_long, y=sigma_long, mode='lines+markers',
        name='Observed Long-Term Volatility'
    ), row=1, col=2)

    fig_sig.add_trace(go.Scatter(
        x=T_long, y=vol_fit_long_plaw, mode='lines',
        name=f'Power Law Fit (α ≈ {alpha_long:.2f})',
        line=dict(dash='dot')
    ), row=1, col=2)

    for i, label_ in enumerate(long_labels):
        fig_sig.add_annotation(
            x=T_long[i], y=sigma_long[i], text=label_,
            showarrow=False, yshift=10, row=1, col=2
        )

    fig_sig.update_layout(
        #title_text=f'Volatility Signature Plots for {ticker}',
        title=dict(text=f'Volatility Signature Plots for {ticker}', font=dict(color='white')),
        template='plotly_dark',
        paper_bgcolor='#0e1117',
        plot_bgcolor='#0e1117',
        legend=dict(font=dict(color='white')),
        height=500,
        width=1700
    )

    fig_sig.update_xaxes(title_text="Sampling Interval (minutes)", row=1, col=1)
    fig_sig.update_yaxes(title_text="Annualized Volatility", row=1, col=1, gridcolor='rgba(255,255,255,0.1)')
    fig_sig.update_xaxes(title_text="Sampling Interval (minutes)", row=1, col=2)
    fig_sig.update_yaxes(title_text="Annualized Volatility", row=1, col=2, gridcolor='rgba(255,255,255,0.1)')

    st.plotly_chart(fig_sig, use_container_width=True)

    # Original console output in an expander
    with st.expander("Volatility Signature Plot - Dynamic Interpretation", expanded=False):
        st.text("INTRADAY FITS:")
        sigma0 = np.sqrt(sigma0_sq_hat_intra)
        st.text(f"  2-Component: σ₀ ≈ {sigma0:.4f}, η² ≈ {eta_sq_hat_intra:.4f}")

        if sigma0 > 0.01:
            st.text("    → σ₀ is non-trivial. There's a persistent diffusive component in volatility even at high frequency.")
            st.text("       For traders: market has underlying price movement beyond noise — high-frequency strategies need to account for this.")
        else:
            st.text("    → σ₀ is near zero. Most of the intraday volatility is noise-driven or transient.")
            st.text("       For traders: signals at very short horizons may be unreliable — consider filtering or using coarser intervals.")

        if eta_sq_hat_intra > 1e-5:
            st.text("    → η² is sizable. Market microstructure noise likely distorts short-interval returns.")
            st.text("       For traders: expect bid-ask bounce and slippage to dominate at sub-minute levels.")
        else:
            st.text("    → η² is small. Minimal microstructure noise in the observed intraday returns.")
            st.text("       For traders: fine-resolution signals are cleaner — more room for high-frequency execution.")

        st.text(f"  Power Law:   c ≈ {c_intra:.4f}, α ≈ {alpha_intra:.4f}")
        if alpha_intra < 0.5:
            st.text("    → α < 0.5: Volatility grows slower than √T. Suggests mean-reversion or high-frequency frictions.")
            st.text("       For traders: short-term fades and reversion trades may outperform momentum strategies.")
        elif np.isclose(alpha_intra, 0.5, atol=0.05):
            st.text("    → α ≈ 0.5: Volatility scales close to Brownian motion. Random walk behavior.")
            st.text("       For traders: short-term predictability is limited — neutrality and delta hedging make sense.")
        else:
            st.text("    → α > 0.5: Volatility grows faster than √T. Suggests trending or persistent order flow.")
            st.text("       For traders: breakout and momentum strategies likely perform better in this regime.")

        st.text("")
        st.text("LONG-HORIZON FITS:")
        st.text(f"  Power Law:   c ≈ {c_long:.4f}, α ≈ {alpha_long:.4f}")
        if alpha_long < 0.5:
            st.text("    → α < 0.5: Long-run volatility grows sub-linearly. Possible mean-reversion across days/weeks.")
            st.text("       For traders: swing reversion setups and volatility selling may be effective.")
        elif np.isclose(alpha_long, 0.5, atol=0.05):
            st.text("    → α ≈ 0.5: Consistent with Brownian motion. No memory in long-term returns.")
            st.text("       For traders: directional strategies offer no statistical edge — focus on volatility structures instead.")
        else:
            st.text("    → α > 0.5: Long-run volatility grows super-linearly. Indicates trend persistence or structural drift.")
            st.text("       For traders: long-term trend-following, carry, or breakout systems are likely to work.")

    progress_bar.progress(30)

    # ================== SECTION: Intraday Signal-to-Noise Ratio ==================
    st.subheader("Intraday Signal-to-Noise Ratio")
    
    st.markdown(
    "This section estimates how much of the intraday volatility is actual price movement versus noise from market mechanics."
    )
    
    with st.expander("Methodology", expanded=False):
        st.markdown(r"""
        ##### Intraday Signal-to-Noise Ratio (SNR)

        This plot shows how much of the observed volatility at each intraday interval reflects true market movement versus noise introduced by high-frequency effects.

        Signal-to-noise ratio is defined as:

        $$
        \text{SNR}(T) = \frac{\sigma_0^2}{\sigma_T^2}
        $$

        - $\sigma_0^2$: latent variance, estimated from the two-component model  
        - $\sigma_T^2$: empirical variance at sampling interval $T$


        ##### Interpretation

        - $\text{SNR} < 1$ → Noise dominates  
        - $\text{SNR} \rightarrow 1$ as $T$ increases → Signal becomes clearer as noise decays


        ##### Why This Applies Only to High-Frequency Data

        At short intervals, volatility is inflated by:
        - bid-ask bounce  
        - latency  
        - execution frictions

        As intervals widen, these distortions average out. SNR becomes useful for identifying when high-frequency signals are likely unreliable.

        For longer timeframes (daily or more), microstructure effects are negligible. SNR isn't meaningful in those settings.

        This diagnostic helps identify the time scales where volatility reflects genuine price discovery versus transient noise.
        """)
    
    snr_intra = sigma0_sq_hat_intra / var_intra

    fig_snr = go.Figure()
    fig_snr.add_trace(go.Scatter(
        x=T_intra,
        y=snr_intra,
        mode='lines+markers',
        name='σ₀² / σ²',
        line=dict(color='purple', width=3)
    ))

    for i, label_ in enumerate(intraday_labels):
        fig_snr.add_annotation(
            x=T_intra[i],
            y=snr_intra[i],
            text=label_,
            showarrow=False,
            yshift=10,
            font=dict(size=14)
        )

    fig_snr.add_shape(
        type='line',
        x0=min(T_intra),
        x1=max(T_intra),
        y0=1,
        y1=1,
        line=dict(color='green', dash='dash', width=3)
    )

    fig_snr.update_layout(
        #title='Intraday Signal-to-Noise Ratio',
        title=dict(text='Intraday Signal-to-Noise Ratio', font=dict(color='white')),
        xaxis_title='Sampling Interval (minutes)',
        yaxis_title='σ₀² / σ² (Signal-to-Noise)',
        template='plotly_dark',
        paper_bgcolor='#0e1117',
        plot_bgcolor='#0e1117',
        legend=dict(font=dict(color='white')),
        height=400,
        width=1000
    )
    fig_snr.update_yaxes(gridcolor='rgba(255,255,255,0.1)')
    st.plotly_chart(fig_snr, use_container_width=True)

    with st.expander("Intraday Signal-to-Noise Ratio - Dynamic Interpretation", expanded=False):
        st.text("INTERPRETATION:")
        for i, interval_ in enumerate(T_intra):
            snr_val = snr_intra[i]
            label_ = intraday_labels[i]
            st.text(f"{label_} (interval = {interval_} min): σ₀² / σ² ≈ {snr_val:.2f}")
            if snr_val > 0.7:
                st.text("   → Signal dominates. Diffusive price movement explains most of the variance.")
                st.text("     For traders: market microstructure noise is low. Alpha signals are likely more reliable.\n")
            elif 0.3 < snr_val <= 0.7:
                st.text("   → Mixed regime. Both signal and noise contribute materially.")
                st.text("     For traders: consider robust execution filters and avoid overfitting short-term models.\n")
            else:
                st.text("   → Noise dominates. Most variance is from short-horizon microstructure effects.")
                st.text("     For traders: avoid signals at this interval. Noise overwhelms usable price information.\n")

    progress_bar.progress(40)

    # ================== SECTION: Intraday Average Volatility Signature Plot ==================
    st.subheader("Intraday Average Volatility Signature Plot")
    
    st.markdown(
    "This section shows how realized volatility behaves throughout the trading day, averaged across recent sessions and multiple time resolutions."
    )
    
    with st.expander("Methodology", expanded=False):
        st.markdown(r"""
    ##### Intraday Volatility Patterns by Time of Day

    This analysis estimates average volatility at each clock time during U.S. market hours using multiple intraday windows.

    Rolling realized volatility is computed using intraday log returns sampled over these intervals:
    - 1 min, 5 min, 15 min  
    - 30 min, 1 hour, 2 hours, 4 hours

    Each volatility series is then averaged by time of day (Eastern Time). This reveals typical volatility behavior across the session.

    ---

    ##### Common Intraday Pattern

    Volatility tends to follow a U-shape across the trading day:
    - High volatility after market open (9:30–10:30 AM)
    - Low volatility midday (11:30 AM–2:00 PM)
    - Rising volatility near close (3:00–4:00 PM)

    This pattern is observed across all sampling windows. Shorter intervals capture more microstructure effects and noise. Longer intervals smooth these distortions.

    ---

    ##### Technical Details

    Annualized volatility is computed using:

    $$
    \sigma_{\text{annual}} = \sqrt{\sum r^2} \cdot \sqrt{\frac{252 \times 6.5 \times 60}{\text{window size in minutes}}}
    $$

    The y-axis is displayed on a log scale to improve readability across different magnitudes.

    This view helps identify when volatility tends to cluster during the day and informs execution timing and risk budgeting.
    """)

    # Original code block uses new data load for '8d' intraday
    data_intra_avg = safe_download(ticker, period='8d', interval='1m')
    if data_intra_avg is None or data_intra_avg.empty:
        st.error("No intraday data available for the Intraday Average Volatility section.")
        st.stop()

    data_intra_avg.index = pd.to_datetime(data_intra_avg.index).tz_convert('America/New_York')
    data_intra_avg['log_return'] = np.log(data_intra_avg['Close'] / data_intra_avg['Close'].shift(1))
    data_intra_avg.dropna(inplace=True)

    windows_dict = {
        '1 Min': 1,
        '5 Min': 5,
        '15 Min': 15,
        '30 Min': 30,
        '1 Hour': 60,
        '2 Hours': 120,
        '4 Hours': 240
    }
    trading_minutes_per_year = 252 * 6.5 * 60
    data_intra_avg['time'] = data_intra_avg.index.strftime('%H:%M')

    intraday_vol = pd.DataFrame()
    for label_, w_ in windows_dict.items():
        data_intra_avg[f'{label_}_vol'] = (
            data_intra_avg['log_return']
            .rolling(w_)
            .apply(lambda x: np.sqrt(np.sum(x**2) * (trading_minutes_per_year / w_)), raw=True)
        )
        intraday_vol[label_] = data_intra_avg.groupby('time')[f'{label_}_vol'].mean()

    intraday_vol.index = intraday_vol.index.astype(str)

    # Reduce x-axis labels
    num_labels = 30
    time_labels = np.linspace(0, len(intraday_vol.index) - 1, num_labels, dtype=int)
    selected_xticks = [intraday_vol.index[i] for i in time_labels]

    fig_intra_avg = go.Figure()
    for label_ in windows_dict.keys():
        fig_intra_avg.add_trace(go.Scatter(
            x=intraday_vol.index,
            y=intraday_vol[label_],
            mode='lines',
            name=label_,
            opacity=0.8
        ))

    fig_intra_avg.update_layout(
        #title=f'Intraday Average Volatility Signature Plot for {ticker}',
        title=dict(text=f'Intraday Average Volatility Signature Plot for {ticker}', font=dict(color='white')),
        xaxis_title='Time of Day (ET)',
        yaxis_title='Annualized Volatility',
        template='plotly_dark',
        paper_bgcolor='#0e1117',
        plot_bgcolor='#0e1117',
        height=500,
        width=1500,
        legend=dict(font=dict(color='white')),
        xaxis=dict(
            tickmode='array',
            tickvals=selected_xticks,
            ticktext=selected_xticks,
            tickangle=45
        ),
        yaxis_type='log'
    )
    fig_intra_avg.update_yaxes(gridcolor='rgba(255,255,255,0.1)')
    st.plotly_chart(fig_intra_avg, use_container_width=True)

    with st.expander("Intraday Average Volatility Signature Plot - Dynamic Interpretation", expanded=False):
        st.text("INTRADAY VOLATILITY INTERPRETATION:")

        ref_label = '5 Min'
        vol_series = intraday_vol[ref_label]

        peak_start = vol_series.iloc[:int(len(vol_series) * 0.33)].idxmax()
        peak_end = vol_series.iloc[int(len(vol_series) * 0.66):].idxmax()
        trough = vol_series.idxmin()

        st.text(f"→ Peak volatility near open:     {peak_start}")
        st.text(f"→ Trough volatility mid-session: {trough}")
        st.text(f"→ Peak volatility near close:    {peak_end}")

        early_peak = vol_series[peak_start] > vol_series[trough]
        late_peak = vol_series[peak_end] > vol_series[trough]

        if early_peak and late_peak:
            st.text("   → U-shape pattern detected. Volatility is elevated during market open and close.")
            st.text("     For traders: liquidity risk is higher early and late in the session. Expect wider spreads, faster price moves.")
            st.text("     Execution near mid-day tends to carry less volatility risk — better for passive orders or size execution.")
        else:
            st.text("   → No clear U-shape. Volatility profile is irregular.")
            st.text("     For traders: intraday behavior may be event-driven or news-sensitive in this period.")

        st.text("\nSample intraday volatility (5-min window):")
        sample_points = vol_series.iloc[[0, len(vol_series)//2, -1]]
        st.text(str(sample_points))

    progress_bar.progress(60)

    # ================== SECTION: Realized vs. Implied Volatility ==================
    st.subheader("Realized vs. Implied Volatility")
    
    st.markdown(
    "This section compares realized volatility over multiple horizons with implied volatility, using the VIX index as a proxy."
    )
    
    with st.expander("Methodology", expanded=False):
        st.markdown(r"""
    ##### Long-Term Realized vs. Implied Volatility

    This comparison includes:
    - **Realized volatility** estimated from historical returns  
    - **Implied volatility** from the VIX, which reflects market expectations over the next 30 days

    ##### Realized Volatility

    Computed using rolling log returns:

    $$
    \sigma_{\text{realized}} = \sqrt{ \sum_{i=1}^n r_i^2 \cdot \frac{\text{Annualization Factor}}{n} }
    $$

    - $r_i$: daily log return  
    - $n$: window size (1, 5, or 21 days)  
    - Annualization factors:
      - 252 for daily  
      - 52 for weekly  
      - 12 for monthly

    ##### Implied Volatility (VIX)

    - Derived from S&P 500 options  
    - Annualized  
    - Represents the market’s forward-looking 30-day volatility estimate

    ##### Interpretation

    - Daily realized volatility is reactive and noisy  
    - Weekly and monthly realized volatility track broader trends  
    - VIX tends to exceed realized volatility due to a **volatility risk premium**

    When realized volatility exceeds VIX, it signals an unexpected volatility event. Examples include earnings shocks, macro announcements, or crashes.

    ##### Why This Comparison Matters

    - **Volatility spreads** (VIX minus realized) may signal option overpricing or underpricing  
    - **Traders** can time volatility-selling or hedging strategies  
    - **Risk teams** can detect periods of market overreaction or complacency
    """)    

    # Original code: data from '5y'
    rv_data = safe_download(ticker, period='5y', interval='1d')
    if rv_data is None or rv_data.empty:
        st.error("No data available for Realized vs. Implied Volatility section.")
        st.stop()

    if isinstance(rv_data.columns, pd.MultiIndex):
        rv_data.columns = rv_data.columns.get_level_values(0)

    rv_data['log_return'] = np.log(rv_data['Close'] / rv_data['Close'].shift(1))
    rv_data.dropna(inplace=True)

    windows_ = {'Daily': 1, 'Weekly': 5, 'Monthly': 21}
    annual_factors = {'Daily': 252, 'Weekly': 52, 'Monthly': 12}

    for label_, w_ in windows_.items():
        rv_data[f'{label_}_vol'] = rv_data['log_return'].rolling(w_).apply(
            lambda x: np.sqrt(np.sum(x**2) * (annual_factors[label_] / w_)), raw=True
        )

    # Download VIX
    vix_data = safe_download('^VIX', period='10y', interval='1d')
    if vix_data is None or vix_data.empty:
        st.error("No data for implied volatility. The plot might be empty.")
        # We'll still proceed, but plot might be partial.

    else:
        if isinstance(vix_data.columns, pd.MultiIndex):
            vix_data.columns = vix_data.columns.get_level_values(0)
        vix_data = vix_data['Close'].reindex(rv_data.index, method='ffill') / 100

    fig_rv_iv = go.Figure()

    fig_rv_iv.add_trace(go.Scatter(
        x=rv_data.index,
        y=rv_data['Daily_vol'],
        name='Realized Daily Volatility',
        line=dict(color='orange', width=1),
        opacity=0.3
    ))

    fig_rv_iv.add_trace(go.Scatter(
        x=rv_data.index,
        y=rv_data['Weekly_vol'],
        name='Realized Weekly Volatility',
        line=dict(color='green', width=2)
    ))

    fig_rv_iv.add_trace(go.Scatter(
        x=rv_data.index,
        y=rv_data['Monthly_vol'],
        name='Realized Monthly Volatility',
        line=dict(color='blue', width=2)
    ))

    if vix_data is not None and not vix_data.empty:
        fig_rv_iv.add_trace(go.Scatter(
            x=rv_data.index,
            y=vix_data,
            name='VIX (Implied Volatility)',
            line=dict(color='red', dash='dash', width=2)
        ))

    # Stock price on secondary axis
    fig_rv_iv.add_trace(go.Scatter(
        x=rv_data.index,
        y=rv_data['Close'],
        name='Stock Price',
        line=dict(color='white'),
        opacity=0.2,
        yaxis='y2',
        showlegend=True
    ))

    fig_rv_iv.update_layout(
        #title=f'Realized vs. Implied Volatility for {ticker}',
        title=dict(text=f'Realized vs. Implied Volatility for {ticker}', font=dict(color='white')),
        template='plotly_dark',
        paper_bgcolor='#0e1117',
        plot_bgcolor='#0e1117',
        height=600,
        width=1500,
        xaxis=dict(title='Date'),
        yaxis=dict(title='Annualized Volatility'),
        yaxis2=dict(
            title='Stock Price',
            overlaying='y',
            side='right',
            showgrid=False
        ),
        legend=dict(x=0.01, y=0.99), font=dict(color='white'),
        margin=dict(l=60, r=60, t=60, b=60)
    )
    
    fig_rv_iv.update_yaxes(gridcolor='rgba(255,255,255,0.1)')

    st.plotly_chart(fig_rv_iv, use_container_width=True)

    with st.expander("Realized vs. Implied Volatility - Dynamic Interpretation", expanded=False):
        st.text("\nDYNAMIC INTERPRETATION:")
        st.text("------------------------")
        if (vix_data is not None and not vix_data.empty and
                not rv_data.empty and 'Monthly_vol' in rv_data.columns):
            latest_ = rv_data.dropna().iloc[-1]
            vix_latest = vix_data.dropna().iloc[-1] if not vix_data.dropna().empty else float('nan')
            realized_monthly = latest_['Monthly_vol']

            st.text(f"Latest VIX (Implied 1M Vol):     {vix_latest:.2%}")
            st.text(f"Latest Realized Monthly Vol:    {realized_monthly:.2%}\n")

            if vix_latest > realized_monthly * 1.2:
                st.text("→ Implied volatility is significantly higher than realized 1-month volatility.")
                st.text("   Traders are demanding a risk premium — possibly due to uncertainty or expected catalysts.")
                st.text("   For traders: options may be overpriced. Selling vol could outperform (e.g., short straddles with risk limits).")
            elif vix_latest < realized_monthly * 0.8:
                st.text("→ Implied volatility is below realized 1-month volatility.")
                st.text("   Market might be underestimating future risk or recent realized vol hasn't mean-reverted.")
                st.text("   For traders: long vol trades (e.g., buying calls/puts or strangles) might offer favorable asymmetry.")
            else:
                st.text("→ Implied and realized monthly volatility are broadly aligned.")
                st.text("   Market expectations are in line with past realized movement.")
                st.text("   For traders: neutral vol stance. Consider structure, skew, or relative value strategies instead.")

            monthly_vol_series = rv_data['Monthly_vol'].dropna()
            if len(monthly_vol_series) > 21:
                vol_rolling_avg = monthly_vol_series.rolling(21).mean().iloc[-1]
                if realized_monthly > vol_rolling_avg * 1.3:
                    st.text("\n→ Realized monthly volatility is well above its 1-month moving average.")
                    st.text("   For traders: regime shift likely. Could be due to macro events, earnings, or broad market repricing.")
                elif realized_monthly < vol_rolling_avg * 0.7:
                    st.text("\n→ Realized monthly volatility is suppressed relative to recent history.")
                    st.text("   For traders: volatility compression phase — watch for breakout setups or sudden repricing.")

            if len(rv_data) > 1:
                vol_change = realized_monthly - rv_data['Monthly_vol'].iloc[-2]
                if vol_change > 0.01:
                    st.text("→ Vol is expanding vs. previous day. Indicates rising uncertainty or event response.")
                elif vol_change < -0.01:
                    st.text("→ Vol is compressing vs. previous day. Market calming or digesting recent moves.")
        else:
            st.text("Not enough data to show the Realized vs. Implied analysis or it is empty.")

    progress_bar.progress(80)

    # ================== SECTION: Day of the Week Effect ==================
    st.subheader("Day of the Week Effect")
    

    st.markdown(
        "This section shows how realized volatility varies across weekdays using intraday return data."
    )

    with st.expander("Methodology", expanded=False):
        st.markdown(r"""
    ##### Day-of-Week Patterns in Realized Volatility

    This analysis uses 5-minute intraday returns over the past 60 trading days. Realized volatility is computed daily and then averaged by weekday.

    ##### Daily Volatility Calculation

    Using 5-minute log returns, daily realized volatility is:

    $$
    \sigma_{\text{daily}} = \sqrt{ \sum_{i=1}^{n} r_i^2 }
    $$

    - $r_i$: 5-minute log returns  
    - $n$: number of 5-minute intervals in the trading day

    Each day's volatility is then grouped by weekday and averaged.

    ##### Interpretation

    - **Mondays** often show elevated volatility, possibly due to weekend news and risk rebalancing  
    - **Fridays** can show rising volatility as traders adjust positions before the weekend  
    - **Mid-week** (Tuesday–Thursday) tends to be quieter with fewer major market events

    This pattern helps identify which days tend to carry more execution or risk management impact.
    """)

    

    df_5m = safe_download(ticker, period='60d', interval='5m')
    if df_5m is None or df_5m.empty:
        st.error("No intraday data available for Day-of-Week analysis.")
        st.stop()

    if isinstance(df_5m.columns, pd.MultiIndex):
        df_5m.columns = df_5m.columns.get_level_values(0)

    df_5m.index = pd.to_datetime(df_5m.index)
    df_5m['log_return'] = np.log(df_5m['Close'] / df_5m['Close'].shift(1))
    df_5m.dropna(inplace=True)

    df_5m['date'] = df_5m.index.date
    df_5m['weekday'] = df_5m.index.dayofweek
    df_5m = df_5m[df_5m['weekday'] < 5]

    daily_vol = df_5m.groupby('date')['log_return'].apply(lambda x: np.sqrt(np.sum(x**2)))
    daily_vol = daily_vol.reset_index().rename(columns={'log_return': 'realized_vol'})
    daily_vol['date'] = pd.to_datetime(daily_vol['date'])
    daily_vol['weekday'] = daily_vol['date'].dt.dayofweek

    weekday_vol = daily_vol.groupby('weekday')['realized_vol'].mean().reset_index()
    weekday_map = {0: 'Monday', 1: 'Tuesday', 2: 'Wednesday', 3: 'Thursday', 4: 'Friday'}
    weekday_vol['weekday_name'] = weekday_vol['weekday'].map(weekday_map)

    fig_dotw = go.Figure()
    fig_dotw.add_trace(go.Bar(
        x=weekday_vol['weekday_name'],
        y=weekday_vol['realized_vol'],
        marker_color='green'
    ))

    fig_dotw.update_layout(
        #title=f'Day of the Week Effect for Realized Volatility ({ticker})',
        title=dict(text=f'Day of the Week Effect for Realized Volatility ({ticker})', font=dict(color='white')),
        xaxis_title='Day of the Week',
        yaxis_title='Average Realized Volatility',
        template='plotly_dark',
        paper_bgcolor='#0e1117',
        plot_bgcolor='#0e1117',
        legend=dict(font=dict(color='white')),
        height=400,
        width=1200
    )
    fig_dotw.update_yaxes(gridcolor='rgba(255,255,255,0.1)')
    
    st.plotly_chart(fig_dotw, use_container_width=True)

    with st.expander("Day of the Week Effect - Dynamic Interpretation", expanded=False):
        st.text("\nDYNAMIC INTERPRETATION:")
        st.text("------------------------")

        sorted_vol = weekday_vol.sort_values(by='realized_vol', ascending=False)

        # Extract min and max vol days
        most_volatile_day = sorted_vol.iloc[0]
        least_volatile_day = sorted_vol.iloc[-1]

        st.text("Average realized vol by weekday (sorted):")
        for i, row in sorted_vol.iterrows():
            st.text(f"  {row['weekday_name']}: {row['realized_vol']:.4f}")

        st.text(f"\n→ Highest average volatility: {most_volatile_day['weekday_name']} ({most_volatile_day['realized_vol']:.4f})")
        st.text(f"→ Lowest average volatility:  {least_volatile_day['weekday_name']} ({least_volatile_day['realized_vol']:.4f})")

        mon_vol = weekday_vol.loc[weekday_vol['weekday'] == 0, 'realized_vol'].values[0]
        fri_vol = weekday_vol.loc[weekday_vol['weekday'] == 4, 'realized_vol'].values[0]
        wed_vol = weekday_vol.loc[weekday_vol['weekday'] == 2, 'realized_vol'].values[0]

        st.text("")
        if mon_vol > fri_vol and mon_vol > wed_vol:
            st.text("→ Monday volatility is elevated.")
            st.text("   Interpretation: markets often react to weekend news or macro events on Mondays.")
        elif fri_vol > mon_vol and fri_vol > wed_vol:
            st.text("→ Friday volatility is elevated.")
            st.text("   Interpretation: traders adjusting risk before the weekend may cause more aggressive positioning.")
        elif wed_vol < mon_vol and wed_vol < fri_vol:
            st.text("→ Wednesday is the quietest.")
            st.text("   Interpretation: midweek lulls are common — lower volume, fewer catalysts.")

        vol_range = sorted_vol['realized_vol'].max() - sorted_vol['realized_vol'].min()
        if vol_range < 0.005:
            st.text("→ Volatility is fairly uniform across weekdays.")
            st.text("   Interpretation: No clear day-of-week effect — intraday factors likely dominate.")
        else:
            st.text("→ There's a statistically meaningful difference in vol across days.")
            st.text("   Interpretation: consider adjusting strategy timing to favor higher-volatility days.")

    progress_bar.progress(100)
    st.success("Analysis complete.")

# Hide default Streamlit style
st.markdown(
    """
    <style>
    #MainMenu {visibility: hidden;}
    footer {visibility: hidden;}
    </style>
    """,
    unsafe_allow_html=True
)