Forward Pricing an Inflation-Linked Bond with an Interim Coupon

Summary

The document explains how to adapt a collateralized forward-pricing relationship for an inflation-linked bond with a coupon paid before forward settlement. The nominal bond proceeds method is adjusted by applying an index ratio to the spot value, interim coupon, and forward settlement value. Accrued interest at spot and forward settlement is included in the relationship.

The example is framed for a Canadian-style linker. Removing the index-ratio terms recovers the nominal bond forward formula, which clarifies the role inflation indexation plays in the calculation. If index ratios for the coupon or forward dates are not yet known, they must be estimated using a projection curve. The treatment is a compact pricing identity rather than a full discussion of index publication lags, interpolation conventions, coupon mechanics, or collateral and repo details, which can vary by market and instrument.

Key ideas

• A linker forward price adjusts the nominal bond relationship for inflation index ratios.
• The spot value, interim coupon, and forward settlement value are indexed at their relevant dates.
• Spot and forward accrued interest enter the pricing identity.
• Removing all index ratios yields the corresponding nominal bond forward formula.
• Unknown future index ratios require projection from an inflation curve.

Tags

# Answer by Helin (score 2)


# What is the formula for the forward price of a inflation linked bond assuming there are coupons in the interim period and the deal is collateralised?












t2=forward settlement date

P=Spot clean price

AI0=Spot accrued interest

r=repo rate

t1=coupon payment date

AIt2= accrued interest of the forward settlement date

t0= now

Proceeds Method:

F(t2)=(P+AI0)(1+r*t2)−c2(1+r(t2−t1))−AIt2.

I want to understand how inflation affects this formula if we do this for a inflation linked bond.

## Answer by Helin (score 2)

https://quant.stackexchange.com/a/40501

It's pretty much the same as a nominal bond, except cash flows need to be inflated. For example, here's the forward pricing formula for a Canadian-style linker, assuming one interim coupon payments:

$$ \bigl(F(t_f) + AI_{t_f}\bigr) \frac{I(t_f)}{I_\text{base}} = (P + AI_{t_s})\cdot \frac{I(t_s)}{I_\text{base}}\cdot (1 + r \cdot t_f) - c\cdot \frac{I(t_c)}{I_\text{base}}\cdot\bigl(1 + r\cdot (t_f - t_c)\bigr), $$ where $t_f$ represents the forward settlement date, $t_s$ is the spot settlement date, $t_c$ is the coupon date, and $I(t)$ is the index ratio for time $t$.

Note that if all the index ratio terms are removed, you've got the nominal bond forward pricing formula.

If the indexed ratios corresponding to the coupon date and forward settlement dates are not known, you'll need a projection curve to impute them.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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