V@R and minimal tick value

A Value-at-Risk (VaR) methodology is a technique to estimate the maximum loss at a given time horizon that is exceeded only at a certain probability level.

Several methodologies are used to obtain those estimations and a lot of them are based on “scenarios”. They can be historical data inspired, stress tests or Monte Carlo.

Those methodologies are often used to compute Initial Margin (IM) related to exchange traded portfolios.

The instruments in exchange trades setup have standardized terms and conditions, including a “tick value” or “minimal increment” which indicates the precision of the price quotation mechanism. This is often one cent on prices and one basis point for interest rates.

I have been involved in many VaR and IM methodologies over the past years: development, replication, validation. One question that I have been asked several times with different flavours is: How should the methodology account for tick value in the scenarios? Should the price generated by the scenarios be rounded to the nearest tick value?

My simple answer is: Scenarios valuation should not take into account the tick value.

This may sound counterintuitive as one would in general try to have a valuation system that represents the reality as closely as possible. But let me explain the reason behind my opinion.

First in general cases, this is not very important. Take crude oil, trading at 87.65 USD/barrel, a scenario of +10% in price gives a new price of 96.415 USD. This is a P/L of 8.745 USD. Given a trading unit of 1,000 barrels, for VaR purposes you can have 8,745, 8,750 or 8,740 USD per contract, depending on your tick value rule. This is not very important.

Now take three-month SOFR contracts down the curve, with maturities around 5 years and a spread position between two consecutive contracts. The tick value is 0.5 bp. Typically, the scenarios for the interest rate contracts are obtained through scenarios for the interest rate curve from which the specific contracts scenarios are generated. To get a 0.5 bp change in the spread between two consecutive three-month contracts, a slope change of roughly 2 bps is needed between two yearly forward rates. If a rounding to the nearest tick is used and the data is misaligned in some way, the scenario generated may create for most scenarios a P/L of 0 USD!

The usage of tick value may also have a serious impact for out-of-the-money (OTM) options. Previously traded options may be now far OTM with a theoretical value lower than the tick value. The settlement value is then reported as one tick, e.g. 1 cent. Again this will cause many scenarios to have a P/L of 0. But other issues may arise, for example an implied volatility may be backed from that price and used as it was a real market parameter. One important issue for exchange users is to estimate the potential future IM related to new positions or market movements. Starting from an almost meaningless OTM value may lead to “strange” estimates when the same instrument gets in the money in a stress-test.

Some exchanges are trying to work around the issue of the tick value rounding providing 0 P/L in some scenarios by rounding up the losses instead of rounding to the nearest tick. This is conservative on its face value, but may lead to meaningless numbers, for example with an option valued at 1 cent losing 2 cents! In a large portfolio, those 2 cents may be invisible and appear innocuous, but anybody trying to attribute the IM or reverse stress the losses will get “interesting” results.

In my opinion, the scenarios used should not be viewed as a perfect representation of a known future, but be the representative of a class of possible futures. In assemblies, an elected representative is not representing himself, but the opinion of a set of people he represents and should work for the good of “The People”, not for himself. One computed scenario represents a subset of the possible futures, the computed P/L is not an exact one scenario P/L, but some “average” representative of that class of scenarios. Moreover, those scenarios P/L are further manipulated to compute an IM, e.g. a given probability level VaR with some kind of interpolator and maybe that result is itself rescaled to obtain a different period or different probability level risk measure. Should a further tick rounding be used at each level? How do you split the total P/L “tick rounding” when several contracts are involved, potentially with different tick values?

All those issues appear only due to an attempt to incorporate a feature (tick value) that is not really meaningful when assessing risks. The feature generates many (smallish) issues with no clear benefits.

Hence my general opinion on that question: For risk measure purposes, scenario valuation should not take into account the tick value.