F-spread

What is it?

The F-spread is the credit premium over the government zero-coupon curve expressed on a continuously compounded basis. It answers the same question as the Z-spread — how much extra return the bond offers over risk-free rates across its whole life — but states the answer in the compounding convention used in derivatives pricing.

The spread is solved from the bond's price and then converted:

Bond Price = ∑ ( CashFlow × DiscountFactor ÷ (1 + Spread) ^ Time )

F-Spread (basis points) = ln ( 1 + Spread ) × 10000

• BondPrice – current market price of the bond, including accrued interest.
• CashFlow – coupon payment, or coupon plus redemption amount for the final one, up to the redemption date that produced the yield to worst.
• Time – time from today until the cash flow, in years.
• DiscountFactor – government discount factor for that same term, derived from published benchmark yields.
• Spread – the constant premium being solved for, expressed as a decimal.
• ln – natural logarithm.

Because continuous compounding always produces a slightly smaller number than annual compounding for the same economic premium, the F-spread runs marginally below the Z-spread, and the gap widens as the spread grows: roughly one basis point at a spread of 100, and around twenty at a spread of 600. The metric is used where the rest of the model is built on continuous rates.