Why a Bond Option’s Forward Yield Uses an Earlier Bond Price

Summary

The document addresses a question about replicating a call option on a six-month zero-coupon bond, with the option expiring in six months. The questioner identifies the bond at the option’s expiry as the underlying and asks why the replication equation also uses the price labeled F₀.₅.

The response distinguishes the underlying from the input needed to infer its forward yield. F₁ represents the bond price at the later date, while F₀.₅ is used to determine the yield at which that bond is expected to trade when the option expires. The explanation is brief and offers no derivation, pricing equation, or assumptions about rates or financing, so it clarifies the role of the extra price without laying out the full replication argument.

Key ideas

• The option’s underlying is the bond price at the option expiry, labeled F₁.
• The earlier price F₀.₅ helps determine the forward yield for that bond at expiry.
• The response clarifies the role of the earlier price but does not derive the replication equation.

Tags

# Simple arbitrage pricing of bond option


# Simple arbitrage pricing of bond option












This is Tuckman fixed income security textbook. The text here is trying to price a 990 six month call on a six month zero bond. When we replicate the portfolio, where is the F_.5 coming from?

My understanding is that the underlying is the F_1. Why we are adding F_.5 in the equation but not anything else?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/79854

The underlying is indeed the F_1. But the F_0.5 is required to determine the forward yield. Ie at what yield the F_1 is expected to trade at after 6 months.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.