Risk Measurement for Callable Bonds Under Simplified Exercise Assumptions

# Risk measurement of multicallable bonds


# 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?

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

https://quant.stackexchange.com/a/61223

(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.