In [1]:

import os
import requests
import polars as pl
import numpy as np
from lets_plot import *
LetsPlot.setup_html()

uw_token = os.environ['UW_TOKEN']
headers = {'Accept': 'application/json, text/plain', 'Authorization': uw_token}

In [2]:

def theme_dark():
    darkest_black = '#0d1117'
    darker_black = '#161b22'
    dark_black = '#21262d'
    darkest_gray = '#89929b'
    darker_gray = '#c6cdd5'
    dark_gray = '#ecf2f8'
    white = '#ffffff'
    red = '#fa7970'
    orange = '#faa356'
    green = '#7ce38b'
    sky_blue = 'a2d2fb'
    blue = '#77bdfb'
    purple = '#cea5fb'
    return theme_none() + theme(
        line=element_line(color=dark_gray, size=1),
        rect=element_rect(color=darkest_gray, fill=darkest_black, size=2),
        text=element_text(color=darker_gray),
        axis_ontop=True,
        axis_ticks=element_line(color=darker_gray),
        legend_background=element_rect(size=2, fill=darker_black),
        legend_position='bottom',
        panel_grid_major=element_line(color=darker_gray, size=1, linetype='dashed'),
        panel_grid_minor=element_blank(),
        plot_background=element_rect(fill=darkest_black),
        plot_title=element_text(hjust=0.5, color=dark_gray),
        tooltip=element_rect(fill=darkest_black, color=dark_gray),
        axis_tooltip=element_rect(color=darker_gray)
    )


def theme_light():
    darkest_black = '#0d1117'
    darker_black = '#161b22'
    dark_black = '#21262d'
    darkest_gray = '#89929b'
    darker_gray = '#c6cdd5'
    dark_gray = '#ecf2f8'
    white = '#ffffff'
    red = '#fa7970'
    orange = '#faa356'
    green = '#7ce38b'
    sky_blue = 'a2d2fb'
    blue = '#77bdfb'
    purple = '#cea5fb'
    return theme_none() + theme(
        line=element_line(color=darkest_black, size=1),
        rect=element_rect(color=darkest_black, fill=white, size=2),
        text=element_text(color=darkest_black),
        axis_ontop=True,
        axis_ticks=element_line(color=darker_black),
        legend_background=element_rect(size=2),
        legend_position='bottom',
        panel_grid_major=element_line(color=darker_black, size=1, linetype='dashed'),
        panel_grid_minor=element_blank(),
        # plot_background=element_rect(fill=dark_gray),
        plot_title=element_text(hjust=0.5, color=darkest_black),
        tooltip=element_rect(color=dark_black),
        axis_tooltip=element_rect(color=darker_black)
    )


dark_theme = {
    'darkest_black': '#0d1117',
    'darker_black': '#161b22',
    'dark_black': '#21262d',
    'darkest_gray': '#89929b',
    'darker_gray': '#c6cdd5',
    'dark_gray': '#ecf2f8',
    'white': '#ffffff',
    'red': '#fa7970',
    'orange': '#faa356',
    'green': '#7ce38b',
    'sky_blue': '#a2d2fb',
    'blue': '#77bdfb',
    'purple': '#cea5fb'
}


def create_uw_iv_rv_df(ticker: str) -> pl.DataFrame:
    """
    Return a Polars DataFrame containing queried data from
    the Unusual Whales API endpoint for realized volatilty.
    """
    # Collect implied volatility and closing price data
    # # from the Unusual Whales API
    base_url = ('https://api.unusualwhales.com/api/'
                'stock/{}/volatility/realized?timeframe={}')
    full_url = base_url.format(ticker, '2Y')
    r = requests.get(full_url, headers=headers)

    df = pl.DataFrame(r.json()['data'])
    df = (
        df
        .with_columns(
            [
                pl.col('date').cast(pl.Date),
                pl.col('implied_volatility').cast(pl.Float64) * 100,
                pl.col('price').cast(pl.Float64),
                pl.col('realized_volatility').cast(pl.Float64) * 100
            ]
        )
    )
    return (
        df
        .with_columns(
            [
                (
                    (pl.col('price') / pl.col('price').shift(1) - 1) * 100
                ).alias('price_pct_change_from_yesterday'),
                (
                    pl.col('implied_volatility') - pl.col('implied_volatility').shift(1)
                ).alias('iv_change_from_yesterday')
            ]
        )
    )


def create_pct_price_vs_iv_plot(ticker: str,
                                df: pl.DataFrame,
                                dark_color: bool = True) -> ggplot:
    """
    Create a scatter plot of the percentage change in price vs the
    percentage change in implied volatility then add a line of best
    fit to the plot.
    """
    price_pct_raw = df['price_pct_change_from_yesterday'].to_numpy()
    iv_pct_raw = df['iv_change_from_yesterday'].to_numpy()
    price_pct = price_pct_raw[1:] # remove the known first value, it's a NaN 
    iv_pct = iv_pct_raw[1:] # remove the known first value, it's a NaN
    
    # Linear regression
    coefficients = np.polyfit(price_pct, iv_pct, 1)
    slope, intercept = coefficients
    linear_regression = slope * price_pct + intercept

    if dark_color:
        return ggplot(df, aes(x='price_pct_change_from_yesterday',
                              y='iv_change_from_yesterday')) + \
            geom_point(color=dark_theme['sky_blue']) + \
                geom_line(aes(x=price_pct,
                              y=linear_regression),
                              color=dark_theme['orange'],
                              size=1) + \
                    ggtitle(f'Spot-to-Implied Volatility Correlation: {ticker}') + \
                        xlab('Price % Change from Yesterday') + \
                            ylab('Implied Volatility % Change from Yesterday') + \
                                ggsize(600, 600) + \
                                    theme_dark()
    else:
        return ggplot(df, aes(x='price_pct_change_from_yesterday',
                              y='iv_change_from_yesterday')) + \
            geom_point(color=dark_theme['blue']) + \
                geom_line(aes(x=price_pct,
                              y=linear_regression),
                              color=dark_theme['red'],
                              size=1) + \
                    ggtitle(f'Spot-to-Implied Volatility Correlation: {ticker}') + \
                        xlab('Price % Change from Yesterday') + \
                            ylab('Implied Volatility % Change from Yesterday') + \
                                ggsize(600, 600) + \
                                    theme_light()


def create_linear_regression_str(df: pl.DataFrame) -> str:
    """
    Calculate the line of best fit (linear regression) for the
    price pct change since yesterday and iv pct change since
    yesterday data provided in the DataFrame and return a string
    for easy printing.
    """
    price_pct_raw = df['price_pct_change_from_yesterday'].to_numpy()
    iv_pct_raw = df['iv_change_from_yesterday'].to_numpy()
    price_pct = price_pct_raw[1:] # remove the known first value, it's a NaN 
    iv_pct = iv_pct_raw[1:] # remove the known first value, it's a NaN
    
    # Linear regression
    coefficients = np.polyfit(price_pct, iv_pct, 1)
    slope, intercept = coefficients
    linear_regression = slope * price_pct + intercept
    
    # Calculate R-squared
    ss_tot = np.sum((iv_pct - np.mean(iv_pct)) ** 2)
    ss_res = np.sum((iv_pct - linear_regression) ** 2)
    r_squared = 1 - (ss_res / ss_tot)

    return (f'Linear regression (y=mx+b): y={slope:.6f}x + {intercept:.6f} || R^2 = {r_squared:.6f}')

In [3]:

ticker = 'TSLA'
df = create_uw_iv_rv_df(ticker)
df

Out[3]:

shape: (502, 6)

date	implied_volatility	price	realized_volatility	price_pct_change_from_yesterday	iv_change_from_yesterday
date	f64	f64	f64	f64	f64
2022-11-16	63.293183	186.92	61.917333	null	null
2022-11-17	62.165243	183.17	62.677051	-2.006206	-1.127939
2022-11-18	63.608796	180.19	62.288186	-1.626904	1.443553
2022-11-21	65.735118	167.87	68.509445	-6.837227	2.126322
2022-11-22	64.523037	169.91	63.968654	1.215226	-1.212081
…	…	…	…	…	…
2024-11-11	67.699666	350.0	null	8.959592	7.900809
2024-11-12	60.843296	328.49	null	-6.145714	-6.85637
2024-11-13	60.695861	330.24	null	0.532741	-0.147435
2024-11-14	56.223077	311.18	null	-5.77156	-4.472783
2024-11-15	58.584288	318.0503	null	2.207822	2.361211

In [3]:

ticker = 'SPY'
df = create_uw_iv_rv_df(ticker)
linreg_str = create_linear_regression_str(df)
print(linreg_str)
p = create_pct_price_vs_iv_plot(ticker, df, dark_color=False)
p.show()

Linear regression (y=mx+b): y=-0.719900x + 0.037563 || R^2 = 0.425913

SPY Spot-to-Implied Volatility Correlation Chart (above)

Pretty tight R² of 0.4259
Slope of the linear regression is -0.719900 which tells us that, based on the last two years, it is expected that for every +1% move in the SPY its 30-calendar day implied volatility will drop by 0.7199 points
30-calendar day implied volatility in SPY is very similar to VIX (though of course VIX is derived from SPX options)
This past Friday (2024-09-27) was very unusual since SPY declined close-to-close by -0.15% but the VIX was up +1.59 points... using our linear regression we can say that a +1.59 point increase in VIX would be much more expected if SPY was down by more than -2%

In [4]:

ticker = 'QQQ'
df = create_uw_iv_rv_df(ticker)
linreg_str = create_linear_regression_str(df)
print(linreg_str)
p = create_pct_price_vs_iv_plot(ticker, df, dark_color=False)
p.show()

Linear regression (y=mx+b): y=-0.541614x + 0.034197 || R^2 = 0.334099

QQQ Spot-to-Implied Volatility Correlation Chart (above)

Less tight than SPY but still respectable R² of 0.3341
Slope of the linear regression is -0.5416 which tells us that, based on the last two years, it is expected that for every +1% move in the QQQ its 30-calendar day implied volatility will drop by 0.5416 points
30-calendar day implied volatility in QQQ is very similar to VXN (though of course VXN is calculated from NDX options, which are much thinner trading-wise than SPX options)
Not nearly as extreme a reaction in the QQQ/implied volatility relationship this past Friday as QQQ was down by -0.56% and VXN was up by +0.75 points
Whatever was driving the outsize reaction in S&P500 implied volatility this past Friday was not as pronounced in the Nasdaq 100

In [5]:

ticker = 'MSTR'
df = create_uw_iv_rv_df(ticker)
linreg_str = create_linear_regression_str(df)
print(linreg_str)
p = create_pct_price_vs_iv_plot(ticker, df, dark_color=False)
p.show()

Linear regression (y=mx+b): y=-0.001678x + -0.040973 || R^2 = 0.000003

MSTR Spot-to-Implied Volatility Correlation Chart (above)

Hmm... R² at zero and slope of the regression roughly the same
Does this mean that implied volatility does not move with spot price?
... of course not lol. But this DOES tell us that moves in implied volatility are just as likely to come with price increases as they are with price decreases, which is very interesting for equity where the risk is much more likely to be down than up.
... very commodity-like.

In [6]:

ticker = 'GME'
df = create_uw_iv_rv_df(ticker)
linreg_str = create_linear_regression_str(df)
print(linreg_str)
p = create_pct_price_vs_iv_plot(ticker, df, dark_color=False)
p.show()

Linear regression (y=mx+b): y=1.288279x + -0.330326 || R^2 = 0.477297

GME Spot-to-Implied Volatility Correlation Chart (above)

C'mon, you knew I was going to pick a fun one for the very end, and what's more fun than GME!?
Remarkably high R² at 0.4773
And you're reading that right, 30-calendar day implied volatility is expected to INCREASE by 1.2883 pts for every +1% move in GME
Fundamentally this makes sense considering GME's history... the risk is to the upside here