Scenario-Based Measures of Interest Rate Risk

# Metrics to assess Interest rate risk (other than Duration and Convexity)


# Metrics to assess Interest rate risk (other than Duration and Convexity)












I am currently expanding the risk methodology of different risks and curious about ways to measure interest rate risk: the most obvious are duration and convexity. However, what are other metrics to consider that do not require a super-computer to be realized?

Thanks!

PS: in liquidity risk there are metrics such as Liquidity-index, Ahimud illiquidity measure and Roll measure. I am looking for sth like that.

## Answer by Dimitri Vulis (score 0, accepted)

https://quant.stackexchange.com/a/85347

There are many different metrics better suited for different kinds of applications - banking book versus trading book, long a few bonds versus a complicated non-linear book...

As an example, BCBS standard "Interest rate risk in the banking book" https://www.bis.org/bcbs/publ/d368.pdf

> the impact of interest rate shocks on their change in economic value of equity (∆EVE) and net interest income (∆NII), computed based on a set of prescribed interest rate shock scenarios

As you see, as with most market risk factors, the measures are either of the form of impact of some market shock scenarios on some figures, such as fair value, EVE, NII, etc; or "reverse stress" - solve for a scenario that would cause an unacceptable impact.

Interest rates have term structure, but for simplicity we often pay more attention on scenarios where rates move in parallel.

IR01/dv01/pv01/pvbp conveys the same information as duration, but is calculated as the change in fair value when interest rates move basis point (bp) in parallel. 1bp move is an example of a risk scenario.

IR01 by tenor bucket conveys the same information as key rate (partial) duration - the impact on fair value from key rates in one tenor bucket moving 1 bp. In most situations, the sum of IR01s by tenor bucket is close to the IR01 from a parallel shift.

An example of a simple reverse stress test measure would be the number of basis points that the rates need to move in parallel to cause unacceptable impact to fair value, EVE, etc. The larger this number, the further away we are from this impact.

Convexity indicates that your factor sensitivities are non-linear, i.e. that $n\times$ the impact of 1bp move does not exactly equal the impact of a $n$bp move. However approximating the impact of a large move from a small move and convexity is often not accurate enough; rather, you need a full revaluation under a comprehensive collection of stress scenarios.

Typically, a book is revalued under some hypothetical stress scenarios (e.g. all rates parallel move 100, 200, ... 400 bps up and down; short end up whole long end down; etc) and some historical stress scenarios (what if the market moves now like it did in March 2020 or in August 1998 etc). You can use each scenario separately, or you can assign some likelihoods to different scenarios, and take the worst impact across all scenarios weighted by likelihood, and use that as risk measure.

If you're working with currencies where interest rates are much higher than in developed markets - e.g. order of 100% a year, and fluctuating a few % every day - then the 1bp risk scenario is too small.

Edit: the "change in fair value" is sometimes the P&L, but sometimes accountants don't recognize it until it gets realized, so I used this language.

Some people like to see their (first order) IR delta in terms of how much hedge (number of IR futures contracts and/or IR swaps notionals) would be needed to completely flatten it.

In addition to the ubiquitous 1bp bump, some people like risk scenarios expressed in terms of historical principal components of the curve, particularly when sensitivities are non-linear. For example, for the first few PCs - what would be the impact of the PC moving up or down 1, 2,.. historical standard deviations? In reverse, how much historical standard deviations would the PC need to move in order to cause some undesirable impacts?

In addition to interest rates, a book may have sensitivities to various basis / spreads, which can similarly be measured in terms of 1bp bumps, or historical standard deviations.

If multiple currencies are involved, e.g. a bond is denominated in $C_1$, and your accounting is in $C_2$, then it may be helpful to monitor the "cross gamma" terms - how much with the $C_1$ IR risk, expressed in terms of $C_2$, change if the $C_1/C_2$ exchange rate changes, and equivalently how much will the sensitivity to the $C_1/C_2$ exchange rate change if the $C_1$ IR changes.