app.py

import streamlit as st
import yfinance as yf
import numpy as np
import pandas as pd
from datetime import datetime
from scipy.optimize import brentq
from scipy.stats import norm, gaussian_kde
from scipy.interpolate import splrep, BSpline
from scipy.integrate import simps
import plotly.graph_objects as go
from plotly.subplots import make_subplots

st.set_page_config(layout="wide", page_title="Forward-Looking Probability")

st.markdown("## Forward-Looking Market-Implied Probability Distribution")  
st.markdown("#### Option-Based Price Forecasting Using Implied Volatility")  


st.write(
    "This tool analyzes the implied probability distribution of a stock's future price using call option data. "
    "It calculates implied volatilities via the Black-Scholes model, derives a risk-neutral probability density function using "
    "the Breeden-Litzenberger formula, and then smooths the result with Kernel Density Estimation (KDE). "
    "A unified strike grid is used for the 3D surface, while 2D analysis focuses on individual expiration dates."
)

with st.expander("How It Works", expanded=False):
    st.write("The analysis is based on the Black-Scholes model for European call options:")
    st.latex(r"C(S,K,T,r,\sigma)=S\Phi(d_1)-Ke^{-rT}\Phi(d_2)")
    st.latex(r"d_1=\frac{\ln\left(\frac{S}{K}\right)+(r+0.5\sigma^2)T}{\sigma\sqrt{T}}")
    st.latex(r"d_2=d_1-\sigma\sqrt{T}")
    st.write("The risk-neutral probability density function (PDF) is derived using the Breeden-Litzenberger formula:")
    st.latex(r"\text{PDF}(K)=e^{rT}\frac{\partial^2C}{\partial K^2}")
    st.write("The resulting PDF is then smoothed using Kernel Density Estimation (KDE).")

# =============================================================================
# SIDEBAR - General Settings
# =============================================================================

st.sidebar.title("Parameters")

with st.sidebar.expander("General Settings", expanded=True):
    ticker_input = st.text_input("Ticker Symbol", value="NVDA")
    lower_pct = st.number_input(
        "Price % Decrease", value=10, min_value=1, max_value=100, step=1,
        help="For 2D plots: lower threshold = current price * (1 - percentage/100)"
    )
    upper_pct = st.number_input(
        "Price % Increase", value=10, min_value=1, max_value=100, step=1,
        help="For 2D plots: upper threshold = current price * (1 + percentage/100)"
    )

# =============================================================================
# SIDEBAR - Advanced Settings
# =============================================================================
with st.sidebar.expander("Advanced Settings", expanded=True):
    risk_free = st.number_input(
        "Risk-Free Rate", value=0.04, step=0.01, format="%.2f",
        help="The annualized risk-free rate used in option pricing."
    )
    min_volume = st.number_input(
        "Minimum Volume", value=20, step=1,
        help="Minimum trading volume required for an option to be considered liquid."
    )
    max_spread_ratio = st.number_input(
        "Max Spread Ratio", value=0.2, step=0.01, format="%.2f",
        help="Maximum acceptable ratio of bid-ask spread to ask price. Options exceeding this will be excluded."
    )

# =============================================================================
# Run Analysis Button (placed outside the expanders)
# =============================================================================
run_analysis = st.sidebar.button("Run Analysis")

# =============================================================================
# HELPER FUNCTIONS
# =============================================================================
def call_bs_price(S, K, T, r, sigma):
    if T <= 0:
        return max(S - K, 0)
    d1 = (np.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
    d2 = d1 - sigma * np.sqrt(T)
    return S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)

def implied_vol_call(price, S, K, T, r):
    if T <= 0:
        return np.nan
    def f(iv):
        return call_bs_price(S, K, T, r, iv) - price
    try:
        return brentq(f, 1e-9, 5.0)
    except:
        return np.nan

def build_pdf(K_grid, iv_spline_tck, S, T, r):
    iv_vals = BSpline(*iv_spline_tck)(K_grid)
    call_prices = [call_bs_price(S, K, T, r, iv) for K, iv in zip(K_grid, iv_vals)]
    dC_dK = np.gradient(call_prices, K_grid)
    d2C_dK2 = np.gradient(dC_dK, K_grid)
    pdf_raw = np.exp(r * T) * d2C_dK2
    return np.clip(pdf_raw, 0, None)

def build_cdf(K_grid, pdf_vals):
    cdf_vals = []
    running = 0.0
    for i in range(len(K_grid)):
        if i == 0:
            cdf_vals.append(0.0)
        else:
            area = simps(pdf_vals[i-1:i+1], K_grid[i-1:i+1])
            running += area
            cdf_vals.append(running)
    cdf_vals = np.array(cdf_vals)
    if cdf_vals[-1] > 0:
        cdf_vals /= cdf_vals[-1]
    return cdf_vals

# Function to filter illiquid options
def filter_liquid_options(df, min_volume=20, max_spread_ratio=0.2):
    spread = df["ask"] - df["bid"]
    return df[(spread / df["ask"] < max_spread_ratio) & (df["bid"] > 0) & (df["volume"] >= min_volume)]

# =============================================================================
# 3D ANALYSIS FUNCTION (CALLS ONLY)
# =============================================================================
def compute_3d_pdf(data_ticker, current_price, r, min_volume, max_spread_ratio):
    all_expirations = data_ticker.options
    valid_expiries = []
    days_list = []
    calls_data_dict = {}

    # First pass: collect calls data from valid expiries.
    for exp_date in all_expirations:
        try:
            expiry_dt = datetime.strptime(exp_date, "%Y-%m-%d")
        except:
            continue
        days_forward = (expiry_dt - datetime.now()).days
        if days_forward < 1:
            continue
        try:
            chain = data_ticker.option_chain(exp_date)
        except Exception:
            continue
        calls_df = chain.calls[['strike', 'lastPrice', 'bid', 'ask', 'volume']].dropna().copy()
        calls_df = filter_liquid_options(calls_df, min_volume, max_spread_ratio)
        calls_df = calls_df[calls_df['lastPrice'] > 0].sort_values('strike')
        if calls_df.empty:
            continue
        valid_expiries.append(exp_date)
        days_list.append(days_forward)
        calls_data_dict[exp_date] = calls_df

    if not valid_expiries:
        raise ValueError("No valid expiries with call data.")

    K_grid_3d = np.linspace(current_price * 0.25, current_price * 3, 300)
    pdf_list = []

    # Second pass: compute smoothed PDF for each expiry.
    for exp_date in valid_expiries:
        expiry_dt = datetime.strptime(exp_date, "%Y-%m-%d")
        T_val = (expiry_dt - datetime.now()).days / 365.0
        calls_df = calls_data_dict[exp_date]
        iv_vals = []
        for _, row in calls_df.iterrows():
            vol = implied_vol_call(row['lastPrice'], current_price, row['strike'], T_val, r)
            iv_vals.append(vol)
        calls_df['iv'] = iv_vals
        calls_df.dropna(subset=['iv'], inplace=True)
        if calls_df.empty:
            pdf_list.append(np.zeros_like(K_grid_3d))
            continue
        strikes = calls_df['strike'].values
        ivs = calls_df['iv'].values
        try:
            iv_spline_tck = splrep(strikes, ivs, s=10, k=3)
        except Exception:
            pdf_list.append(np.zeros_like(K_grid_3d))
            continue
        pdf_raw = build_pdf(K_grid_3d, iv_spline_tck, current_price, T_val, r)
        try:
            kde = gaussian_kde(K_grid_3d, weights=pdf_raw)
            pdf_smooth = kde(K_grid_3d)
            area = np.trapz(pdf_smooth, K_grid_3d)
            if area > 0:
                pdf_smooth /= area
        except Exception:
            pdf_smooth = pdf_raw
        pdf_list.append(pdf_smooth)

    pdf_matrix = np.array(pdf_list)
    days_array = np.array(days_list)

    TT, KK = np.meshgrid(days_array, K_grid_3d, indexing='ij')

    fig = go.Figure(data=[go.Surface(
        x=KK,
        y=TT,
        z=pdf_matrix,
        colorscale='Viridis',
        opacity=0.8
    )])
    fig.update_layout(
        scene=dict(
            xaxis_title='Strike',
            yaxis_title='Days to Expiry',
            zaxis_title='PDF'
        ),
        title="3D Smoothed Implied PDF Across Expiries",
        width=900,
        height=700
    )
    fig.add_annotation(
        x=0.98, y=0.98, xref="paper", yref="paper",
        text=f"Current Price: {current_price:.2f}",
        showarrow=False,
        align="right",
        font=dict(size=12),
        bordercolor="black",
        borderwidth=1,
        #bgcolor="white",
        opacity=0.8
    )
    return fig, valid_expiries

# =============================================================================
# 2D ANALYSIS FUNCTION (CALLS ONLY)
# =============================================================================
def compute_2d_pdf(exp_date, data_ticker, current_price, r, lower_pct, upper_pct, min_volume, max_spread_ratio):
    try:
        expiry_dt = datetime.strptime(exp_date, "%Y-%m-%d")
    except:
        return None
    days_forward = (expiry_dt - datetime.now()).days
    if days_forward < 1:
        return None
    T_val = days_forward / 365.0
    try:
        chain = data_ticker.option_chain(exp_date)
    except:
        return None
    calls_df = chain.calls[['strike', 'lastPrice', 'bid', 'ask', 'volume']].dropna().copy()
    calls_df = filter_liquid_options(calls_df, min_volume, max_spread_ratio)
    calls_df = calls_df[calls_df['lastPrice'] > 0].sort_values('strike')
    if calls_df.empty:
        return None

    iv_list = []
    for _, row in calls_df.iterrows():
        vol = implied_vol_call(row['lastPrice'], current_price, row['strike'], T_val, r)
        iv_list.append(vol)
    calls_df['iv'] = iv_list
    calls_df.dropna(subset=['iv'], inplace=True)
    if calls_df.empty:
        return None

    strikes = calls_df['strike'].values
    ivs = calls_df['iv'].values
    try:
        iv_spline_tck = splrep(strikes, ivs, s=10, k=3)
    except:
        return None

    K_min = strikes.min()
    K_max = strikes.max()
    K_grid_2d = np.linspace(K_min, K_max, 300)
    pdf_raw = build_pdf(K_grid_2d, iv_spline_tck, current_price, T_val, r)
    try:
        kde = gaussian_kde(K_grid_2d, weights=pdf_raw)
        pdf_smooth = kde(K_grid_2d)
        area = np.trapz(pdf_smooth, K_grid_2d)
        if area > 0:
            pdf_smooth /= area
    except:
        pdf_smooth = pdf_raw

    cdf = build_cdf(K_grid_2d, pdf_smooth)

    lower_thresh = current_price * (1 - lower_pct / 100)
    upper_thresh = current_price * (1 + upper_pct / 100)
    mask_below = K_grid_2d < lower_thresh
    mask_between = (K_grid_2d >= lower_thresh) & (K_grid_2d <= upper_thresh)
    mask_above = K_grid_2d > upper_thresh
    p_below = np.trapz(pdf_smooth[mask_below], K_grid_2d[mask_below])
    p_between = np.trapz(pdf_smooth[mask_between], K_grid_2d[mask_between])
    p_above = np.trapz(pdf_smooth[mask_above], K_grid_2d[mask_above])

    fig_pdf_cdf = make_subplots(rows=1, cols=2, subplot_titles=("Smoothed PDF", "Smoothed CDF"))
    fig_pdf_cdf.add_trace(go.Scatter(
        x=K_grid_2d, y=pdf_smooth, mode='lines', name='PDF', line=dict(color='blue')
    ), row=1, col=1)
    fig_pdf_cdf.add_vline(x=current_price, line=dict(color='red', dash='dash'), row=1, col=1)
    fig_pdf_cdf.update_xaxes(title_text="Strike", row=1, col=1)
    fig_pdf_cdf.update_yaxes(title_text="PDF", row=1, col=1)
    fig_pdf_cdf.add_trace(go.Scatter(
        x=K_grid_2d, y=cdf, mode='lines', name='CDF', line=dict(color='blue')
    ), row=1, col=2)
    fig_pdf_cdf.add_vline(x=current_price, line=dict(color='red', dash='dash'), row=1, col=2)
    fig_pdf_cdf.update_xaxes(title_text="Strike", row=1, col=2)
    fig_pdf_cdf.update_yaxes(title_text="CDF", row=1, col=2)
    fig_pdf_cdf.update_layout(title_text="2D Analysis: PDF and CDF")
    fig_pdf_cdf.add_annotation(
        x=0.98, y=0.98, xref="paper", yref="paper",
        text=f"Current Price: {current_price:.2f}",
        showarrow=False,
        align="right",
        font=dict(size=12),
        #bordercolor="white",
        borderwidth=1,
        opacity=0.8
    )

    fig_threshold = go.Figure()
    fig_threshold.add_trace(go.Scatter(
        x=K_grid_2d, y=pdf_smooth, mode='lines', name='PDF', line=dict(color='blue')
    ))
    fig_threshold.add_vline(
        x=lower_thresh,
        line=dict(color='orange', dash='dash'),
        annotation_text=f'Lower: {lower_thresh:.2f}',
        annotation_position="top left",
        annotation_xshift=10,
        annotation_yshift=-10
    )
    fig_threshold.add_vline(
        x=upper_thresh,
        line=dict(color='purple', dash='dash'),
        annotation_text=f'Upper: {upper_thresh:.2f}',
        annotation_position="top right",
        annotation_xshift=-10,
        annotation_yshift=-10
    )
    fig_threshold.add_vline(
        x=current_price,
        line=dict(color='red', dash='dash'),
        annotation_text=f'Current: {current_price:.2f}',
        annotation_position="bottom right",
        annotation_xshift=-10,
        annotation_yshift=10
    )
    fig_threshold.add_trace(go.Scatter(
        x=K_grid_2d[mask_below], y=pdf_smooth[mask_below], mode='lines',
        fill='tozeroy', line=dict(color='lightblue'), showlegend=False
    ))
    fig_threshold.add_trace(go.Scatter(
        x=K_grid_2d[mask_between], y=pdf_smooth[mask_between], mode='lines',
        fill='tozeroy', line=dict(color='lightgrey'), showlegend=False
    ))
    fig_threshold.add_trace(go.Scatter(
        x=K_grid_2d[mask_above], y=pdf_smooth[mask_above], mode='lines',
        fill='tozeroy', line=dict(color='lightcoral'), showlegend=False
    ))
    fig_threshold.update_layout(
        title="Threshold Probability Plot",
        xaxis_title="Strike",
        yaxis_title="PDF"
    )
    annotation_text = (
        f"Probability below {lower_thresh:.2f} is {p_below:.2%}<br>"
        f"Probability between {lower_thresh:.2f} and {upper_thresh:.2f} is {p_between:.2%}<br>"
        f"Probability above {upper_thresh:.2f} is {p_above:.2%}"
    )
    fig_threshold.add_annotation(
        x=0.75, y=0.5, xref="paper", yref="paper",
        text=annotation_text,
        showarrow=False,
        align="left",
        font=dict(size=12),
        #bordercolor="white",
        borderwidth=1,
        opacity=0.8
    )
    fig_threshold.add_annotation(
        x=0.98, y=0.98, xref="paper", yref="paper",
        text=f"Current Price: {current_price:.2f}",
        showarrow=False,
        align="right",
        font=dict(size=12),
        bordercolor="black",
        borderwidth=1,
        #bgcolor="white",
        opacity=0.8
    )

    result = {
        "K_grid_2d": K_grid_2d,
        "pdf_smooth": pdf_smooth,
        "cdf": cdf,
        "lower_thresh": lower_thresh,
        "upper_thresh": upper_thresh,
        "p_below": p_below,
        "p_between": p_between,
        "p_above": p_above,
        "fig_pdf_cdf": fig_pdf_cdf,
        "fig_threshold": fig_threshold,
        "days_to_exp": days_forward
    }
    return result

# =============================================================================
# MAIN RUN (only run when the button is clicked)
# =============================================================================
if run_analysis:
    with st.spinner("Running analysis, please wait..."):
        try:
            data_ticker = yf.Ticker(ticker_input)
            hist_data = data_ticker.history(period="1d")
            if hist_data.empty:
                st.error("No price data found.")
                st.stop()
            current_price = hist_data["Close"].iloc[-1]
        except Exception as e:
            st.error(f"Error fetching data: {e}")
            st.stop()

        st.write(f"Current Price: {round(current_price, 2)}")
        r = risk_free

        try:
            fig3d, valid_expiries_3d = compute_3d_pdf(data_ticker, current_price, r, min_volume, max_spread_ratio)
        except Exception as e:
            st.error(f"3D analysis error: {e}")
            st.stop()

        results_2d = {}
        for exp_date in data_ticker.options:
            res = compute_2d_pdf(exp_date, data_ticker, current_price, r, lower_pct, upper_pct, min_volume, max_spread_ratio)
            if res is not None:
                results_2d[exp_date] = res

        if not results_2d:
            st.error("No valid expirations for 2D analysis.")
            st.stop()

        st.session_state.analysis_data = {
            "current_price": current_price,
            "expirations": list(results_2d.keys()),
            "results": results_2d,
            "fig3d": fig3d
        }

# =============================================================================
# DISPLAY RESULTS (if analysis data exists)
# =============================================================================
if "analysis_data" in st.session_state:
    ad = st.session_state.analysis_data
    st.write(f"**Current Price:** {round(ad['current_price'], 2)}")
    st.markdown("## 3D Probability Surface")
    st.plotly_chart(ad["fig3d"], use_container_width=True)
    st.markdown("## 2D Plots for Selected Expiration Date")
    chosen = st.selectbox("Choose expiration date:", options=ad["expirations"])
    res2d = ad["results"][chosen]
    st.plotly_chart(res2d["fig_pdf_cdf"], use_container_width=True)
    st.plotly_chart(res2d["fig_threshold"], use_container_width=True)
    st.write("The 2D plots use calls data only. The 3D surface uses a unified strike grid.")
else:
    st.info("Click 'Run Analysis' to start.")


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