# Risk measurement of multicallable bonds

Assume you have bought a multicallable bond where the issuer has the right to redeem the notional at various dates, e.g. a $$10$$ yr maturity, $$5$$% coupon yearly and each year one call date. Next, assume your risk management is not very sophisticated so that it is not able to measure the risk of such "exotic" bonds.

Is it deemed to be a conservative approach in terms of risk assessment if you take the first call date as maturity date (instead of the $$10$$ yrs) and only consider the coupon payment(s) you will receive until then?

(Bonds with more than 1 posisble call date are not very exotic. This answer applies to a bond with 1 European call date as well.)

That depends on what risk measures you want (or are required to) calculate.

For example, if you're trying to calculate sensitivities to 1bp change interest rate by tenor bucket, then the following simple approach may be good enough for you (although some people may say it's too simple to be acceptable even for this)

Find the option exercise date for yield to worst. (If the bond is putable, which is common in some emerging markets, then the best yield for the bond holder to exercise.) Assume that the bond issuer will exercise on the YTW date and disregard the optionality for the interest rate risk calculation.

But if your risk scenarios perturb the interest rates by hundreds of basis points (stress tests) then of course this would likely affect the moneyness of the option and the decision whether to exercise them.

However assuming that the first call date will be exercised, even if it is out of the money, will understate the interest rate risk. Numerical example. Suppose for concreteness that we calculate IR risk by calculating the option adjusted spread (OAS) from the observed bond price, then perturbing the interest rates one tenor at a time and repricing the bond keeping the OAS constant.

Suppose the bond is trading at 90, can be called at par in 1y, and otherwise matures in 10y. (European call, not "on or after"). Just making up some numbers, if you assume that the (far out of the money) call is exercised, then the interest rate sensitivity might be .1 to 1y interest rate and nothing after 1y; while if you assume that the call is not exercised, then the interest rate sensitivity might be 1, mostly to the 10y interest rate.

Vega of a callable bond is not useful, but sometimes you are required to calculate it.

A better (but harder to implement and compute) approach would be use a 2-dimensional tree (interest rates and credit spread) to get the probability of each call getting exercised. Use sums, weighted by exercise probabilities, of the risk measures under each exercise scenario.

• If we assume 1bp sensitivities, why would it understate the interest rate risk if we assume the bond to be called at the first call date? In fact, if bond prices quote above par then the exercise date based on YTC would be always the first call date. Or did I misunderstood something? – Philipp Feb 17 at 18:52
• I edited to add some details. It would be strange for a callable bond to trade much above the call price. The option is unlikely to be exercised if the bond is trading below the call price. – Dimitri Vulis Feb 17 at 19:43
• As long as we consider bonds trading below par I certainly agree with you. However, my watchlist comprises more than 2000 callable bonds and none of them trades below par (mostly they trade around 105) So why would we understate the risk of those above-par bonds if we take the first call date? – Philipp Feb 17 at 20:39
• Sry, maybe I misunderstood your question? I thought you wanted to make a blanket assumption that the first call would always be exercised, whether it's in the money or not. If you use small (like 1bp) rates bump, and assume that the call will be exercised if it makes economic sense, then it's (mostly) OK. But if the call is not in the money now, then you shouldn't just assume "exercise anyway". Also large (100s of bps) changes in rates would change the calls' moneyness, so you'd need something more complicated. – Dimitri Vulis Feb 17 at 21:00
• Also note that just comparing a coupon bond price to its call price (which is usually par but not always) doesn't quite tell you whether the call in in the money. Comparing the yields under different exercise scenarios considers (with some assumptions) the coupons accruing between now and the call date. – Dimitri Vulis Feb 18 at 5:49