Box spread
Combine four option legs into a fixed expiry cash flow, then compare its price with funding.

The idea · in two minutes

Jack arranges four tickets into a box with a fixed payout

Jack wants 90-day financing. He buys the 90 call, sells the 100 call, buys the 100 put and sells the 90 put. Rose adds the expiry lines: whether the underlying ends above 100, below 90 or between them, the long box pays 10.

If Jack pays 9.90 today and receives 10 in 90 days, the model return is about 1.01% for the period, or 4.17% effective annualised. That resembles borrowing, not a directional bet. Selling the box reverses the cash-flow direction.

Rose asks what happens if the legs do not fill together, a short option is assigned early, or margin rises. The box payoff is fixed only under matching contracts and settlement. Execution, funding, clearing and operational risk remain real. European cash-settled index options fit the assumptions more closely than American single-stock options.

• Sₜ ≤ 90Below the lower strike, the put legs still net to the 10-point strike width; subtract the 9.90 debit.
• Sₜ = 95Between strikes, the call and put spreads still add to the same 10-point payment.
• Sₜ ≥ 100Above the upper strike, the call legs also leave the same fixed payment.

Illustrative research examples only. They are not live signals or a recommendation.

The mechanics · payoff and exposure

The four matched legs cancel the underlying price exposure and leave the strike width less the entry debit.

K₁ and K₂ are the shared strikes, with K₁<K₂; D is the full debit to buy the box. Payoffs are per underlying unit before contract multipliers and settlement currency.

Greeks: the directional intuition

Delta

Measures first-order sensitivity to the underlying price.

Gamma

Measures how quickly delta changes as the underlying moves.

Theta

Captures the effect of time passing, all else equal.

Vega

Measures sensitivity to implied volatility.

The four matched legs cancel the underlying price exposure and leave the strike width less the entry debit.

Practical context · published observations

Long box net payoff: read the record with its caveats.

The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.

假設四腿同時按指定價格成交、同到期且採不會提前行權干擾的結算方式；未計清算費、買賣價差、融資及保證金成本。 Source ↗ · Methodology ↗