Volatility Analysis In Trading

Topics
April 8, 2025

We often hear traders say:

“Volatility is too high, I’ll wait.🗣️

“Or worse…😬

“This market’s too quiet. Nothing to do.” 🛌

Truth is — volatility isn’t the enemy. It’s price movement, and movement is where the edge lives. If you understand it, you can anticipate risk, price your trades smarter, and stop reacting emotionally.

Whether you’re a scalper, options trader, or quant-in-the-making, mastering volatility is non-negotiable.

If you know how to read it, volatility tells you:

🧠 When to size up

📈 When premiums are overpriced

🚪 When to stay out

Historical vs Implied Volatility

Historical Volatality shows what past was 🕰️. Its like a rearview mirror.

Implied Volatality whispers what future might be 🔮. Its like a fear gauge.



# calculation for implied volatality

from scipy.optimize import brentq
from scipy.stats import norm
import math

# Black-Scholes Formula
def black_scholes_call(S, K, T, r, sigma):
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)

# Implied Volatility Solver
def implied_volatility(C_market, S, K, T, r):
objective = lambda sigma: black_scholes_call(S, K, T, r, sigma) - C_market
return brentq(objective, 1e-6, 5)

# Example Inputs
S = 22500 # Spot Price
K = 22500 # Strike
T = 7 / 365 # Time to Expiry (7 days)
r = 0.065 # Risk-free rate (6.5%)
C_market = 150 # Option Premium (Call)

iv = implied_volatility(C_market, S, K, T, r)
print(f"Implied Volatility: {iv:.2%}")



Calculation for Historical Volatility

import pandas as pd
import numpy as np
import yfinance as yf

# Load data (e.g., NIFTY or any stock/index)
symbol = "^NSEI" # Nifty 50 Index (change as needed)
data = yf.download(symbol, period="6mo", interval="1d")

# Calculate log returns
data['log_ret'] = np.log(data['Close'] / data['Close'].shift(1))

# Historical Volatility (Annualized)
hv = data['log_ret'].std() * np.sqrt(252)
print(f"Historical Volatility: {hv:.2%}")