Valuation models

Bond options

Calls and puts on a fixed coupon bond, Black-76 on the forward clean price with a price vol or implied from a premium, or Hull-White fitted to the curve for European, Bermudan and American exercise.

Inputs

Results

Every input and result then gets a + calc button.

Explain this result

Get a plain-English reading of the numbers above and what drives them.

Preview: rule-based reading. AI-assisted explanations run on the analytics core.

Methodology

Conventions

  • Black-76: the forward clean price at expiry is lognormal; strike is a clean price.
  • Hull-White: the bond is valued on a tree fitted to the curve plus the z-spread; the call is straight − callable.
  • Bermudan and American exercise need Hull-White.

References

  • Hull, Options, Futures, and Other Derivatives, ch. 29
  • Brigo and Mercurio, Interest Rate Models

Formulas

Forward
F = (P_dirty − PV(coupons to T)) / D(T) − AI(T)
Call
C = D(T) [F N(d1) − K N(d2)]