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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Computes the spread duration of a bond by finite differences, repricing the instrument for an up and a down move in the credit spread: (V− − V+)/(2·V0·Δs). While duration measures sensitivity to changes in the risk-free rate, spread duration isolates sensitivity to the credit spread, the premium the market charges for issuer risk. It's essential for managing credit portfolios, where spread risk often dominates. Enter the base price, the prices with higher and lower spread and the spread change used.
Risk Reversal
Computes the net premium of a risk reversal: buying a higher-strike call and selling a lower-strike put, building a synthetic long position in the asset. Depending on the premium gap, the structure comes out as a debit (you pay) or a credit (you receive) — and when the two cancel, it becomes the classic zero-cost reversal. In FX, it also gauges the slope of the volatility smile. Enter the put and call strikes and the two premiums.
Synthetic Forward (Put-Call Parity)
Computes the synthetic forward price implied by the prices of a European call and put with the same strike and expiry, via put-call parity: F = (C − P)·e^(rT) + K. Instead of starting from the spot price and cost of carry, it extracts the forward directly from the options market, which is useful for checking arbitrage between the two markets. Enter the call and put premiums, the strike, the interest rate and the term.
Calendar Spread
Computes the net debit of a calendar spread, also called a horizontal spread: selling a short-dated option and buying a longer-dated one at the same strike. The strategy exploits the fact that the short option loses value to time (theta) faster than the longer one. The result is the cost of setting up the position. Enter the premium of the short option sold and that of the long option bought.
Z-spread (Zero-Volatility Spread)
Computes a bond's Z-spread: the constant spread added to the entire zero (spot) rate curve so the present value of its cashflows equals the market price. Unlike the nominal spread, which uses a single point, it accounts for the whole shape of the curve; for an option-free bond the Z-spread equals the OAS. Enter the cashflow times and amounts, the zero rate at each node and the price; the result is in basis points.
FRA Settlement (Forward Rate Agreement)
Computes the settlement amount of an FRA (Forward Rate Agreement), the contract that locks in today an interest rate for a future period. At fixing, the contracted rate is compared with the market reference rate, and the difference is paid at the start of the period — which is why it's discounted: N·(L − R)·(d/B)/(1 + L·d/B). When the market rate exceeds the contracted one, the party who locked in gains. It's used to hedge loans and deposits against rate moves. Enter the notional, the contracted rate, the reference rate, the days in the period and the day-count basis.
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.