Box Spread
Quick Definition
A combination of a bull call spread and bear put spread at the same strikes, creating a risk-free position that should be worth the present value of the strike difference.
What Is Box Spread?
A box spread combines a bull call spread and a bear put spread using the same two strike prices and expiration date. In theory, a box spread on European options is an arbitrage-free position whose value equals the present value of the difference between the strikes. It effectively creates a synthetic risk-free bond. For example, a box spread with strikes at $50 and $60 should be worth approximately $10 discounted at the risk-free rate. Box spreads are primarily used for arbitrage when options markets misprice relative to interest rates, or for synthetic lending and borrowing. With American-style options, early exercise risk makes box spreads less predictable and potentially unprofitable.
Box Spread Example
- 1A trader constructs a box spread with $100/$110 strikes: buy $100 call, sell $110 call, buy $110 put, sell $100 put. The position should be worth ~$10 at expiration
- 2If a $100/$110 box spread trades at $9.85 but the present value of $10 is $9.95, an arbitrageur can buy the box and earn a risk-free $0.10 per spread
Related Terms
Bull Call Spread
A bullish options strategy that involves buying a lower-strike call and selling a higher-strike call on the same underlying with the same expiration.
Bear Put Spread
A bearish options strategy that involves buying a higher-strike put and selling a lower-strike put on the same underlying with the same expiration.
Vertical Spread
An options strategy involving buying and selling options of the same type and expiration but at different strike prices.
Put-Call Parity
A fundamental pricing relationship stating that the price of a call, put, underlying, and risk-free bond must be in equilibrium for European options.
Synthetic Position
An options strategy that replicates the payoff profile of another position, such as stock ownership, using a combination of options.
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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