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