Delta Hedging
Quick Definition
A strategy that offsets the directional risk of an options position by trading the underlying asset in proportion to the option's delta.
What Is Delta Hedging?
Delta hedging involves maintaining a position in the underlying asset that offsets the delta exposure of an options position, creating a "delta-neutral" portfolio. For example, if a trader is short a call option with a delta of 0.50, they would buy 50 shares of stock per contract to neutralize directional risk. As the underlying price moves and delta changes (due to gamma), the hedge must be continuously rebalanced — a process called "dynamic hedging." Delta hedging is fundamental to options market making, where dealers must manage the directional risk of their books. Perfect continuous delta hedging (which is impossible in practice due to discrete trading and transaction costs) is the basis of the Black-Scholes model. The cost of delta hedging over time is directly related to realized volatility.
Delta Hedging Example
- 1A market maker sells 10 call contracts (delta 0.60 each) and buys 600 shares to be delta-neutral. If delta changes to 0.65, they buy 50 more shares to rebalance
- 2An options desk delta-hedges its entire book every hour, adjusting stock positions as deltas shift throughout the trading day due to price and volatility changes
Related Terms
Delta (Options)
A Greek that measures how much an option's price changes for a $1 move in the underlying asset, also approximating the probability of expiring in the money.
Gamma (Options)
A Greek that measures the rate of change of delta for a $1 move in the underlying, indicating how quickly an option's directional exposure shifts.
Options Greeks
A set of risk measures (delta, gamma, theta, vega, rho) that quantify how an option's price responds to changes in various market factors.
Black-Scholes Model
The foundational mathematical model for pricing European options, using stock price, strike, time, volatility, and risk-free rate as inputs.
Implied Volatility (IV)
The market's forecast of the likely magnitude of future price movements, derived from current option prices using pricing models.
Call Option
A contract giving the holder the right, but not the obligation, to buy an underlying asset at a specified price within a specified time period.
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