A Quantitative Approach to Negative Rates | Numerix Video Blog

Jim: Hi welcome to the Numerix video blog I’m your host Jim Jockle. The bank of Japan announced in January and enacted in February negative interest rates for all of its banks; joining the Eurozone as well as the Nordics in terms of utilizing this new tool to stimulate the economy. Joining me today is Dan Li, SVP of the Global Financial Engineering Group here at Numerix to dive into this a little bit more. Welcome Dan. Dan: Hi Jim, how are you? And thanks for having me. Jim: Specific to derivati

ves, there are challenges in mispricing in terms of the models themselves. In addition, post Libor scandal we’ve introduced a dual curve environment especially as it relates to the termination of a risk free rate. Today, when you look at OIS in terms of having negative points on that curve – how is that changing the risk free rate under this dual curve methodology? Dan: From a risk free rate POV nothing has changed, so the fundamental risk neutral pricing framework would still use the risk free

rate. In this case, (the risk free rate curve) would still be the collateral curve, in term of the OIS, which would be the safest discounting curve. Also in collateralized trades, there could be CSA curve or CTD curve – so that hasn’t been changed. With negative rates in terms of what has changed: when we do the curve construction itself, typically via bootstrapping and corresponding discount factors are extracted from the available quotes – and the arbitrage free condition here is really the di

scount factor itself, which should fall between zero and one and be monotonically decreasing. So that makes the instantaneous forward rate positive always. So that’s the arbitrage free condition. When we push the rate to negative – theoretically this shouldn’t happen from an economic POV. This breaks the arbitrage free condition. So in terms of curve construction constraints this must be released. This is what we can observe in this economic phenomenon. On the other hand, in a negative rate envi

ronment, when you deposit money in to the bank or in to the reserves – you have to pay to deposit. This is counterintuitive. So that negative rate in terms of how low it will go is a big question, an unknown. Sometime the shift you can see, especially in Europe they keep cutting that interest rates lower and lower. So things are still unclear. If you go too far, money can go under the mattress not in a bank. Jim: In addition to the curve construction challenges, models themselves were not prepa

red to handle this kind of valuation change in the market, is that correct? Dan: This presents a big challenge for the current market – from three perspectives: 1. The curve construction perspective 2. Volatility (which would be the cap vol surface, or swaption surface or volatility cube;) Within that, there could be a quotation change and also an interpolation effect 3. Model calibration and pricing & risk To be more specific, in terms of curve construction (as mentioned) from the infrastructu

re POV you must release the constraints of the arbitrage free conditions so you can capture the negative rate. But usually, it is fairly common – such as cross currency basis swaps or cross currency basis curve you can see negative for years. But when you move to the volatility world – the standard quotation in the market is Black Scholes. This is seen as the (market standard) converter between the price and the implied volatility. That volatility is assumed log normal distributed. But if we hav

e a negative rate that means the strike would become negative. For that reason, given the log normal distribution then the standard Black Scholes would fail. So in other words in the market there would be two types of solutions for the quotation purpose: Instead of log normal, assume normal. It would allow the negative strike. On the other hand for those countries only quoted as log normal – you must do some tricks, meaning adding a shift. So you have a negative strike but add a flat shift to ma

ke a combined sum to positive. So in this case the (shifted) Black Scholes still works. This is referred to as Displaced Diffusion log normal process. This is on the quotation side, but what’s considered most tricky is on the interpolation side. You cannot just use what you observe from quotes to price all of your derivatives, say a seasoned swaption or another derivative (e.g. Bermudan swaption). So you really rely on constructing the cube; extract the dynamics from the cubes for implied volati

lities, then you can use those dynamics to calibrate to the model then price and get the corresponding risks. For this reason, the standard interpolation for the vol cube would be the classic SABR model (aka Stochastic, Alpha, Beta, Rho model). This model however, has similar constraints like Black Scholes – that if you have a negative rate then the model would fail. For this reason in the market we see today two prevailing approaches. One is similar to the quotation, you just add an arbitrary s

hift – referred to as Shifted SABR. Another more advanced, cutting edge approach, revolutionary approach would be the Free Boundary SABR. Jim: In terms of the various approaches – good enough? How much risk is left unaccounted for? Are we talking mispricing, hedges or ultimately millions in losses over next couple of quarters? Dan: Exactly. Here we just talked about the market data parts and your model – you need to capture all the negative strikes including calibration instrument elements – and

for the pricing, and for the risks. For example if you added a different shift – you would have a different price or different risk profile which would impact your daily PnL, daily risk management, portfolio and capital. That would have huge impacts as well. Jim: Stress testing has become a modern regulatory tool to understand stressed environments. But even now on the negative rates side there’s suggestions of looking at funds and portfolio performance and stressing against negative rates. How

important is it as you are looking at stress scenarios to be able to take into consideration these model choices as it relates to your entire portfolio? Dan: For some of the regulations there are requirements that all stressed scenarios and ESGs – for rates and all other quantities be positive. But now, because of this strange phenomena globally it’s not uncommon [to be negative]. Thus in my view from a regulatory perspective, along with a stressed scenario you must be able to state – whether y

ou can capture the negative rate, or whether you can capture all the different scenarios. It’s not only curve construction, the vol surface, and vol cube, the interpolation, the model calibration, then pricing – it’s everywhere in the derivatives pricing process, as well as risk assessment. So indeed this would have an impact. Jim: Well Dan, I want to thank you so much for your positive outlook on this negative issue. And of course on the Numerix video blog we want to talk about all the things y

ou want to talk about so feel free to follow up on LinkedIn or on Twitter @nxanalytics we’d love to hear from you and continue this conversation. Dan thank you so much.