Handling Publication Lags in Inflation Index Simulations
Summary
The document asks how to value inflation-linked instruments in a Monte Carlo model when an index is published after the reference month. The example uses the UK RPI index and a Jarrow–Yildirim setup in which inflation evolves alongside nominal and real interest rates. The proposed answer is to distinguish the valuation date from the index observation date: payoffs refer to index levels under a lag convention, and may use a published level or an interpolation between levels depending on that convention.
For a simulation valued at the current date, the model still needs a spot index level for that valuation date. The answer recommends obtaining or interpolating that level from published observations according to the relevant lag convention, while retaining model parameters calibrated for the valuation date. This addresses why simply shifting all market data back to the month of the last published index is not the right framing. The exchange explains the convention conceptually but does not provide implementation detail for a specific product or calibration.
Key ideas
- Inflation-linked payoffs refer to index levels according to contractual lag conventions.
- A payoff date may reference an already published index or an interpolated value between observations.
- A simulation needs the spot inflation index level corresponding to its valuation date.
- Publication lag does not by itself require treating all valuation market data as if observed earlier.
- The explanation does not specify product-specific implementation or calibration steps.
Tags
Full text
# How do you deal with Inflation lag in a MC simulation?
# How do you deal with Inflation lag in a MC simulation?
Consider the UK RPI index. This index is published every month around the 15th (give or take a few days). The publication refers to the RPI index of the month before, so there is a lag of a few weeks between when the RPI is "set" and when it is published. How do I deal with this lag?
To be more specific, I'm performing a Monte Carlo simulation of the RPI index using the Jarrow-Yildirim model. The inflation process is determined through a geometric Brownian motion:
$$I(T) = I(t) \exp\left( \int_t^T(n(t) - r(t))dt - \frac{1}{2} \sigma^2 (T-t) + \sigma_I (W_I(T) -W_I(t))\right)$$
where $n(t)$ and $r(t)$ are the nominal and real rates. These follow a Hull-White process in the JY model.
So suppose I gather all my data on June 1st, i.e. discount curves and perhaps other data to calibrate the JY model. This sets the drift term of the real and nominal process. But on June 1st the "last known RPI" is that of April. How do I account for this lag?
My view: I simply perform a simulation starting from April. I interpret all data that I have as if it was gathered in April as well. In some sense I "roll back the clock" on my data, so I can make it match with the RPI index. Does that make sense?
My problem with this is is that 1) any valuations using this MC simulation give prices that are valid "in April", but I like to have a "June 1st" price. 2) I'm not sure if the data of June 1st can simply be rewind to April. Can prices of ZC inflation bonds, YoY swaps and caps be interpreted like that (i.e. simply shift all the paydates)?
## Answer by Gordon (score 3)
https://quant.stackexchange.com/a/18411
In inflation world, the deal payoff is always based on a certain lag convention. That is, the value $I(T)$ always refers to a published index level several months ago or is interpolated based on those published index levels.
For example, for a payoff on July 15, 2015, the indexed level referred is the published index level for May, 2015, based on the 2m lag convention, or April, 2015, based on the 3m lag convention, or interpolated from the index levels in April and May, 2015, based on the 2m-3m lag convention. See Section 4.3 in http://the.earth.li/~jon/junk/kerkhof.pdf for more details.
For your simulation, except for your model parameters, you also need the spot level $I(t_0)$ on the valuation date $t_0$, which can be referred or interpolated from the published index levels as above based on the respective lag convention.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.