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Breakeven Inflation Rate

Computes the breakeven inflation embedded in the gap between a nominal bond and an inflation-linked bond, using the exact Fisher equation: (1 + nominal)/(1 + real) − 1. It's the inflation rate that would equalize the return of the two instruments — above it, the linker wins; below it, the nominal one. The exact version avoids the error of the simple approximation (nominal − real), which overstates inflation by a few basis points. Enter the nominal yield and the real yield.

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Breakeven Inflation Rate

Computes the breakeven inflation embedded in the gap between a nominal bond and an inflation-linked bond, using the exact Fisher equation: (1 + nominal)/(1 + real) − 1. It's the inflation rate that would equalize the return of the two instruments — above it, the linker wins; below it, the nominal one. The exact version avoids the error of the simple approximation (nominal − real), which overstates inflation by a few basis points. Enter the nominal yield and the real yield.

The inflation the market is betting on

There's a way to know how much inflation the market expects over the coming years, and it doesn't involve guessing. Just compare two bonds of the same maturity: one paying a fixed nominal rate and another linked to inflation, paying a real rate. The gap between them is the breakeven, or implied, inflation, the rate at which it makes no difference which one you hold.

The right calculation isn't simply to subtract one from the other. The Fisher relationship is multiplicative: (1 + nominal) divided by (1 + real), minus one. The plain subtraction works as a shortcut, but it always overstates inflation, and the error grows as rates rise. At higher rate levels, that difference stops being a footnote and becomes basis points that matter in pricing.

Enter the nominal yield and the real yield, and the tool returns the exact breakeven inflation and, alongside it, the simple approximation, so you can see the size of the error. Keep in mind this number also embeds an inflation risk premium, so it's the expectation the market prices, not a guaranteed forecast.

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Bond Equivalent Yield (BEY)

Computes the Bond Equivalent Yield (BEY) of a discount instrument, such as a treasury bill sold below face value. The formula annualizes the percentage gain on the price paid on a 365-day basis: BEY = ((F − P)/P)·(365/t). It lets you compare, on the same ruler, a discount instrument with a coupon-paying bond. Be careful not to confuse it with the bank discount yield, which divides by face value and uses 360 days. Enter the face value, the purchase price and the days to maturity.

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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.

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Bond Accrued Interest

Computes the accrued interest of a fixed-income bond, the slice of coupon that has built up since the last coupon payment up to the settlement date. It uses the linear (actual-days) convention, proportional to elapsed days: interest = face value × (coupon rate ÷ frequency) × (days elapsed ÷ days in period). This is the amount the buyer pays the seller on top of the price, because the whole coupon goes to whoever holds the bond on the payment date. Enter the face value, the annual coupon rate, the number of coupons per year, the days since the last coupon and the days in the period.

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Bond Dirty Price

Computes the dirty price of a bond: the clean price plus the interest accrued since the last coupon. The clean price is what shows up in quotes, but what actually changes hands at settlement is the dirty price, because the buyer has to reimburse the seller for the interest already run up. The tool works out the accrued interest on a linear basis and adds it to the clean price, returning both parts. Enter the clean price, the face value, the annual coupon rate, the coupon frequency, the days since the last coupon and the days in the period.

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Effective Convexity (Numerical)

Computes the effective convexity of a bond by finite differences, repricing the instrument for an up and a down yield move: (V− + V+ − 2·V0)/(V0·Δy²). Unlike analytical convexity, the effective version works even for bonds with uncertain cash flows, such as those with embedded options, because it only needs the three prices. It complements duration to better estimate the price change in large rate moves. Enter the three prices and the yield change used.

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Payer Swaption (Black Model)

Computes the premium of a payer swaption with the Black model: the right to enter an interest rate swap paying a pre-agreed fixed rate. The price is the swap's annuity multiplied by a Black formula on the forward swap rate. Swaptions are the central instrument for those managing long-term interest rate risk, like banks and insurers. Enter the forward swap rate, the strike, the volatility, the expiry, the annuity (PV01) and the notional.

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.