Volatility Modeling

Volatility, the magnitude of price fluctuations, is arguably the single most important quantity in trading. It drives position sizing, stop placement, option pricing, and regime detection. This skill covers estimation, forecasting, and practical application of volatility in crypto markets.

Why Volatility Matters

Use Case	How Volatility Is Used
Position sizing	Scale position inversely with vol so each trade risks a consistent dollar amount
Stop placement	ATR-based stops widen in high-vol regimes, tighten in low-vol
Strategy selection	Mean-reversion works in low vol; momentum works in high vol
Risk budgeting	Vol-target portfolios maintain constant portfolio-level risk
Regime detection	Vol regime shifts signal changing market dynamics
Option pricing	Implied vs realized vol gap creates trading opportunities

Types of Volatility

Historical (Realized) Volatility

Computed from observed past returns. The most common and directly measurable form. Multiple estimators exist with different statistical efficiency.

Implied Volatility

Derived from option prices via Black-Scholes or similar models. Limited in crypto DeFi where liquid options markets are sparse, but available on Deribit for BTC/ETH.

Forecast Volatility

Predicted future volatility from models like EWMA or GARCH. Used for forward-looking position sizing and risk budgets.

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Estimation Methods

1. Close-to-Close (Standard Deviation of Log Returns)

The simplest estimator. Compute the standard deviation of log returns and annualize.

import numpy as np

log_returns = np.log(closes[1:] / closes[:-1])
vol_daily = np.std(log_returns, ddof=1)
vol_annual = vol_daily * np.sqrt(365)  # crypto trades 365 days

• Pros: Simple, widely understood.
• Cons: Uses only close prices, ignores intraday range.

2. Parkinson (High-Low Range)