Tim Olson
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description, tags
| description | tags | ||||
|---|---|---|---|---|---|
| An arbitrage/volatility strategy combining a long synthetic forward and a short synthetic forward (or bull call spread and bear put spread) at two strikes, locking in a fixed payoff of K1 - K2. |
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Long Box
Section: 2.52 | Asset Class: Options | Type: Arbitrage
Overview
The long box strategy can be viewed as a combination of a long synthetic forward and a short synthetic forward, or as a combination of a bull call spread and a bear put spread. It consists of: a long ITM put at K1, a short OTM put at K2 (lower), a long ITM call at K2, and a short OTM call at K1. The trader's outlook is neutral. This is a capital gain strategy. We assume K1 >= K2 + D.
Construction
- Buy 1 ITM put option at strike K1 (higher)
- Sell 1 OTM put option at strike K2 (lower, K2 < K1)
- Buy 1 ITM call option at strike K2 (same as short put strike)
- Sell 1 OTM call option at strike K1 (same as long put strike)
- All same expiry
Net debit: D (assumed K1 >= K2 + D)
Payoff Profile
f_T = (K1 - S_T)+ - (K2 - S_T)+ + (S_T - K2)+ - (S_T - K1)+ - D = K1 - K2 - D (constant, regardless of S_T)
- P_max = (K1 - K2) - D (fixed payoff at all stock prices)
Key Conditions / Signals
- Used primarily as an arbitrage strategy when the market price of the box (D) is less than the theoretical value (K1 - K2)
- Also used as a tax strategy in some jurisdictions (see footnote 31 in the source)
- No directional risk: the payoff is fixed regardless of stock price at expiry
Notes
The long box has a deterministic payoff of K1 - K2 - D at expiry. If D < K1 - K2 (mispricing), this is a risk-free profit. In practice, transaction costs and bid-ask spreads must be considered. Can also be used as a synthetic loan.