Box Spread (Arbitrage)
Computes the fair value and arbitrage of a box spread: combining a call spread and a put spread at the same strikes, creating a fixed payoff of (Kh − Kl) at expiry, equivalent to a riskless bond. The fair value is that payoff discounted: (Kh − Kl)·e^(−rT). If you set up the box for less than that, you lock in a risk-free profit. The tool returns the payoff, the fair value and the arbitrage against the cost you enter. Enter the two strikes, the rate, the term and the cost.
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Box Spread (Arbitrage)
Computes the fair value and arbitrage of a box spread: combining a call spread and a put spread at the same strikes, creating a fixed payoff of (Kh − Kl) at expiry, equivalent to a riskless bond. The fair value is that payoff discounted: (Kh − Kl)·e^(−rT). If you set up the box for less than that, you lock in a risk-free profit. The tool returns the payoff, the fair value and the arbitrage against the cost you enter. Enter the two strikes, the rate, the term and the cost.
A riskless bond made of options
The box spread is one of those constructions that look like magic. By combining a call spread and a put spread at the same two strikes, the payoff at expiry is always the same, no matter where the asset is: exactly the difference between the strikes. In other words, you've manufactured a riskless bond using only options.
If the payoff is fixed, the box's fair price today is that future value discounted at the risk-free rate: (Kh − Kl)·e^(−rT). The opportunity shows up when the market lets you set up the box for less than that, locking in a risk-free arbitrage profit. In practice, traders also use the box as a synthetic way to borrow or lend money at an implied rate.
Enter the two strikes, the risk-free rate, the term and the net cost to set up the box. The tool returns the guaranteed payoff, the discounted fair value and the arbitrage profit. Mind the discounting convention: here we use continuous compounding (e^(−rT)), consistent with rates quoted that way.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.