Under 21.2 of the BCBS text, FRTB creates the requirement to capture Vega and Curvature risk for instruments with optionality under the sensitivities based approach:
The sensitivity based approach in FRTB tries to much more realistic in it’s capture of risk and more aligned to how models would look at this. In doing this, it also tries to look through securities which have embedded optionality and forces capitalisation of unhedged Vega and Curvature risk. Unfortunately, it specifically captures callable bonds into this process which creates the problems we will discuss later.
Instruments subject to each component of the sensitivities-based method
21.2 In applying the sensitivities-based method, all instruments held in trading desks as set out in [MAR12] and subject to the sensitivities-based method (i.e. excluding instruments where the value at any point in time is purely driven by an exotic underlying as set out in [MAR23.3]), are subject to delta risk capital requirements. Additionally, the instruments specified in (1) to (4) are subject to Vega and curvature risk capital requirements:
(1) Any instrument with optionality [1].
(2) Any instrument with an embedded prepayment option [2] – this is considered an instrument with optionality according to above (1). The embedded option is subject to Vega and curvature risk with respect to interest rate risk and CSR (non-securitisation and securitisation) risk classes. When the prepayment option is a behavioural option the instrument may also be subject to the residual risk add-on (RRAO) as per [MAR23]. The pricing model of the bank must reflect such behavioural patterns where relevant. For securitisation tranches, instruments in the securitised portfolio may have embedded prepayment options as well. In this case the securitisation tranche may be subject to the RRAO.
(3) Instruments whose cash flows cannot be written as a linear function of underlying notional. For example, the cash flows generated by a plain-vanilla option cannot be written as a linear function (as they are the maximum of the spot and the strike). Therefore, all options are subject to Vega risk and curvature risk. Instruments whose cash flows can be written as a linear function of underlying notional are instruments without optionality (e.g. cash flows generated by a coupon bearing bond can be written as a linear function) and are not subject to Vega risk nor curvature risk capital requirements.
(4) Curvature risks may be calculated for all instruments subject to delta risk, not limited to those subject to Vega risk as specified in (1) to (3) above. For example, where a bank manages the non-linear risk of instruments with optionality and other instruments holistically, the bank may choose to include instruments without optionality in the calculation of curvature risk. This treatment is allowed subject to all of the following restrictions: (a) Use of this approach shall be applied consistently through time.
(b) Curvature risk must be calculated for all instruments subject to the sensitivities-based method.
Footnotes
[1] For example, each instrument that is an option or that includes an option (e.g. an embedded option such as convertibility or rate dependent prepayment and that is subject to the capital requirements for market risk). A non-exhaustive list of example instruments with optionality includes: calls, puts, caps, floors, swaptions, barrier options and exotic options.
[2] An instrument with a prepayment option is a debt instrument which grants the debtor the right to repay part of or the entire principal amount before the contractual maturity without having to compensate for any foregone interest. The debtor can exercise this option with a financial gain to obtain funding over the remaining maturity of the instrument at a lower rate in other ways in the market.
Given that for callable bonds, the debtor that has the right to repay the principal amount without compensating for loss of interest, these products are covered by footnote [2].
Callable bonds introduced…
Callable bonds (bonds where the issuer has a right to redeem the instrument prior to maturity) exist for a number of reasons, and it is important to understand these before we enter into the discussion of FRTB.
Economics:
The ability to call bonds when it has become possible to refinance at cheaper levels can be one driver for issuance. These bonds are typically redeemed when spreads are tighter or market conditions are conducive to new issuance. The reverse of this was made very clear to the market in 2008, (where it had pretty much become market practice to redeem on call dates) when Deutsche Bank bucked the trend and did not redeem its hybrid capital bonds.
Capital treatment:
Basel II LT2 securities had their capital benefit amortised when there was less than 5 years of remaining maturity and hence these would typically be called and replaced with new issuance.
Capital Optionality:
Regulations change and evolve, as do bank business models, and having expensive issuance in the market that is not capital efficient (or no longer required) is not a great place to be. Having call options allow the issuer to redeem these securities when they no longer serve their original purpose.
Attracting investors:
The additional yield in these instruments that arise from the issuer purchasing optionality from its investors attracts some investors with minimum yield targets
Why are callable bonds special?
As we have seen, the reasons to exercise the option to call a bond are numerous, and very different to vanilla options found or embedded in other asset classes.
In a typical single underlying instrument with optionality (e.g. interest rate option or FX option) the decision to call an option is whether the option is “in-the-money”, which is simply a function of the strike of the option and the underlying spot/forward rate/price, both of which are either known or observable.
With this information, we can also calculate the Vega of such an instrument, which in the case of an interest rate option would be an interest rate Vega to the underlying rate, and for an FX option would be an FX Vega to the underlying currency pairs.
If such instruments trade in the market at observable prices, it is also then possible to imply the underlying “volatility” level used to price these using the calculated Vega, and if we have enough such prices, we can construct a volatility surface. If we have a history of such surfaces, we can build a time series.
For a callable bond however, the decision to call is a function of the following:
- The current funding rate (or the expected future funding rate) of the organisation that issued the debt, and the coupon the security was issued at
- The capital benefit the security provides to the organisation and the impact on any regulatory capital ratios that may arise from calling the instrument
- The impact of the action of “calling” on other liabilities the organisation has issued
A callable bond therefore is a multi-underlying instrument where a Vega would need to exist for each of the above.
Consider the two following callable contingent capital bonds:
| Issuer | Company A | Company B |
| Issue | Callable Bond 1 | Callable Bond 2 |
| Coupon | C1 | C2 |
| Capital Trigger | T1 | T2 |
| Company Funding rate | FA | FB |
| Current Capital Ratio | KA | KB |
| Current Price | PA | PB |
Even in this simplified example, we have created 2 Vega’s which are specific to each company:
VegaF : Sensitivity to the volatility of funding for the company, VolF
VegaK : Sensitivity to the volatility of capital for the company, VolK
We also have 2 moneyness parameters which are somehow dependent on each other:
- Bond Coupon, Ci relative to current funding rate Fi (based on bond yield)
- Capital Trigger Ti relative to current Capital Ratio Ki
The dependency exists because for example a bond cannot/is unlikely to be called even if there is a funding benefit if there is a materially adverse capital impact that may bring a company close to minimum capital ratios.
This brings about some significant issues. Firstly, we have two unknown Vega parameters we have to determine from the price and moneyness parameters. The moneyness parameters rely on being able to observe the funding rate of a company and also the current capital ratio.
The funding rate is not easily observable unless the company has issued recent non-callable unsecured debt of the same maturity, and the capital ratio is only observable when the company reports its earnings which is quarterly and in arrears.
Secondly, VegaF and VegaK are not aggregatable across different companies (to be more precise the portion of funding volatility specific to the company cannot be aggregated), and an observation of VolF and VolK for Company A is of little or no use for Company B
What has this got to do with the financial crisis?
We have managed to construct a risk factor that is very difficult (if not impossible in many cases) to observe and hedge that institutions may likely consider aggregating with and marking to an observable credit volatility level from products such as ITRAXX and CDX index options.
Any risk factor that is marked using an observable market instrument creates volatility to that market instrument, and hence will be hedged to that market instrument. The sensitivities based approach in FRTB is incentivising banks who are long inventory of callable bonds to write ITRAXX and CDX index options to become more “Vega neutral”. To be more precise, given that callable bonds tend to be out-of-the money, banks are being incentivised to write out-of-the money ITRAXX and CDX index options to become “Vega and Curvature neutral”.
This was a very similar approach used for bespoke CDO tranches being marked based on generic ITRAXX and CDS tranche correlations 15 years ago, and the source of many issues in the marketfinancial crisis. Bespoke CDO tranches again had no observable correlation in the market, but instead they were mapped to generic index tranches with very different constituents, diversification, and underlying characteristics, and again, once marked, these created PnL volatility and were hence hedged with the same generic tranches.
People may argue that these models did actually capture the idiosyncratic single name risk that would be created by owning say an equity tranche on a bespoke portfolio and selling an equity tranche on say an CDX index to “hedge” the correlation risk. This was then “hedged” by buying single name protection on some of the higher spread names, and selling index protection.
This is entirely correct; however, many traders will also remember what happened as spreads on Monoline Insurers (which were members of CDX IG at the time) started to spike during the crisis, and the models quickly started recognising long positions in Monoline CDS, perpetuating a viscous spiral in purchasing more and more Monoline protection as spreads widened.
Given our understanding of these issues today, is this really something that regulation should be encouraging? One could argue that this is a standardised model and seeking advanced model approval would help alleviate this, but i) given the likelihood of floors based on standardised capital charges, and ii) the fact that the quant models used to compute sensitivities are likely the same for both standardised and advanced models, once this box is opened, it will be very difficult to shut.
Whether or not this becomes a contributary factor in a future crisis event will remain to be seen…