# Keeping your vols on the straight and narrow

#### Published in Automated Trader Magazine Issue 12 Q1 2009

Automated option quoting engines are heavily dependent on someone or something inputting the correct volatilities behind the scenes. Get that wrong in these days of high frequency automated trading models and you’ll quickly be arbed off the face of the planet. Martin Gymer and Andy Webb take a look at a service designed to keep your vols in order – SuperDerivatives’ VolSurface.

The old 'rubbish in rubbish out' adage has always been particularly applicable to derivatives traders, who rely on automated pricing and risk management systems for their livelihood. That's because the core of any derivatives business is the data that the trading/quoting algorithms require. These are principally the volatility surface and interest rate curves.

The keystone to derivative trading is the quality, accuracy and reliability of these data across asset classes and markets, which has to be delivered electronically in real time (or as close to real time as possible) in order to allow distribution tools to be automated.

### Data that matters

A 'beer mat' Black Scholes Merton approximation for at the money (ATM) options, with zero interest rates can be reduced to:

#### Time x Constant x Volatility

With a volatility of zero and some time remaining, an option price will equal zero. Time value can therefore be considered volatility value. Consequently, the foundation of any derivatives business is volatility, or more accurately the volatility surface.

The profitability of a derivative business is based on the formula:

#### (Volume x Bid/Offer Spread) − (Risk Management Costs + Business Expenses)

Volume is the focus, as spreads have been in pretty consistent long term decline, so income growth can only happen through improved distribution. Combining this volume increase with today's automated distribution tools means that any errors or slow updates in volatility surfaces (which cause mispricing of options) only exacerbate the problem of market makers' liquidity (their main business asset) being given away at a loss.

### Staying in line

SuperDerivatives VolSurface is intended to prevent your options business from falling into this trap. The service combines SuperDerivatives' benchmark pricing model with market rates collected from a selection of active market participants.

The VolSurface function is to deliver an accurate, automated, and validated volatility feed for a range of both liquid and illiquid markets. (See sidebar "VolSurface at a Glance".)

Starting with the raw data, it is evident that VolSurface casts its net pretty wide; sources include interbank brokers, major market makers in the OTC markets, international and domestic brokers, exchanges and other market data sources including Reuters. A mixture of both traded and quoted vols are collected.

Obviously with such a range of raw data, initial data validation and cleaning are important. SuperDerivatives has a dedicated data management unit responsible for running a mixture of manual and automated data validations. Manual validations include checking for scenarios such as new data values differing by more than 20% from previous values, reversed bids/offers, zero values etc. Automated validations include raw data outside the current average bid/offer spread, stale data points, no negative forward volatility etc.

# Risks

The consequences of an inaccurate volatility surface (see box "How do I misprice thee?") are many and varied and in addition to outright mispricing that can be picked off include:

• Counterparty credit risk

If a bank's volatility surface is wrong, then by implication so
are its counterparty P & L numbers. A weak counterparty
might therefore have a liability to the bank that is being
understated, so the counterparty appears to be below its
assigned credit limit - when in reality it is above it.

• Reputation risk

Most corporate clients require an accurate end of month
valuation for all the products they have traded with their
banks. Inaccurate valuation of products due to an inaccurate
volatility surface can severely damage client relationships -
especially if mispricing subsequently results in
regulatory/accounting difficulties for the client.

• Trading limit risk

Trading limits assigned to individual traders and groups are
almost exclusively based on volatilities or Greeks. Inaccurate
volatility surfaces therefore result in weak risk management of
option trading activity.

• Risk management risk

Traders manage the risks in their options book using the
Greeks. These risk sensitivities change dramatically as the
volatility surface changes. Therefore even small discrepancies
in the volatility surface can result in the trader over or
under hedging their actual risk, with inevitably negative
consequences for profitability.

Once the data validation is completed, SuperDerivatives weights the data based upon a number of criteria, including:

• The level of the asset price, its tenor and the time the
value was contributed. (For example, some contributors may
deliver stronger/weaker data at certain times on certain days.)

• Contributor accuracy across various tenors - e.g. some
contributors may be accorded different weightings for different
tenors for the same asset.

• Dynamic distribution, with weightings adjusted based on a
value's position in the total distribution of values at a
particular point in time.

• The relationship among other tenors on the same
curve/surface.

This should hopefully be enough to satisfy even the most sceptical…

Despite the broad range of sources and the cleaning/weighting process used by SuperDerivatives, it is impossible to construct all nodes of a complete volatility surface with actual quoted or traded rates -especially when issues such as broken dates, fast markets and illiquid underlying markets are taken into account. Therefore the accuracy and realism of any method used for interpolating synthetic values between 'real' ones on the surface is critical. A variety of methods are currently in use in the market, some considerably less accurate than others. Often extensive manual tweaking is required to obtain a surface that is remotely realistic and safe to deploy.

#### Figure 1

A key requirement is the smoothness of the interpolation method through time. Older systems using a manual update of twelve or so volatility nodes will be subject to errors (see Figure 1). A portfolio moving one day through time (blue line in Figure 1) can cause one of these fixed buckets to fall into a new volatility band (green line in Figure 1).

This causes the three month bucket to be valued on the eleventh node on one day and with the same surface be valued on the tenth node the next! This step change causes large swings in P and L and Greeks, to say nothing of pricing accuracy on quotes. A smooth surface is therefore a must for any derivatives operation.

Rather than any of the traditional methods (such as linear or cubic spline interpolation), SuperDerivatives uses a proprietary model for obtaining VolSurface synthetic values where market-sourced values are not available. The model requires three volatility data points per tenor, so for example in the FX market it uses three standard inputs - the ATM volatility, 25 delta risk reversal and 25 delta butterfly. The limited number of inputs required and their inherently liquid and available nature represents a significant advantage.

#### Figure 2

When calculating the tenor (timeline) interpolation for missing data points in low liquidity time horizons, SuperDerivatives' proprietary interpolation methodology allows for all currency-specific day count issues, such as public holidays, weekends and the number of days in the year.

### In the real world

In order to illustrate one possible use of VolSurface, we put together some simple VBA code that would run in a middle office risk manager's spreadsheet and compare EURUSD VolSurface values with those in a volatility surface maintained by a trader in Excel on a remote machine. The VBA code would then automatically highlight any important discrepancies in the trader's surface.

The starting point is a spreadsheet maintained in the middle
office that automatically downloads the VolSurface

from the SuperDerivatives FTP site, using some of the VBA time
functions. (For the purposes of this review we are only
downloading data once a day at set times for three major markets
- Tokyo, New York and London - but the code could be easily
modified to perform hourly or other time interval downloads.)

The VolSurface data is imported into the risk management spreadsheet, which also contains a link to the volatility surface in the trader's spreadsheet on a separate machine (in real life on the trading floor). The difference between the values in the trader's EURUSD volatility surface and the EURUSD VolSurface (trader's surface minus VolSurface) are then calculated in the middle office spreadsheet, as can be seen in Figure 2.

As can be seen from Figures 3a and 3b, there are very significant differences between the SuperDerivatives VolSurface (Figure 3a) and the trader's volatility surface (Figure 3b).

The differenced values between these two underlying data sets in the middle office EURUSD worksheet in Figure 2 are the data source for an Excel surface chart residing within the trader's EURUSD worksheet. The trader has no direct access to the VolSurface data but has an automatically updated view of the discrepancies between his/her volatility surface and the SuperDerivatives VolSurface.

#### Figure 3a

This can be seen in Figure 4, which also shows a warning alert that automatically pops up when certain levels of deviation between the two surfaces are exceeded. In addition, so as to provide an audit trail, a further segment of VBA code writes a record to a log file every time a deviation alert is triggered.

This is just a very simple example for a single currency pair. Obviously, the risk management team could write a complete rule set for every instrument that would trigger alerts when certain points on any trader's volatility surface exceeded or undershot the corresponding VolSurface values by a specific margin. Furthermore, rather than merely flagging these with certain colours on a surface chart, it would also be possible to colour flag individual cells containing errant values in the trader's volatility surface table by using Excel's conditional formatting feature.

#### Figure 3b

The red alert colouring on the difference surface in Figure 4 highlights three 'real world' volatility errors:

• Letter A in Figure 4 flags up that many of the trader's
longer dated vols (5 years and above) are set too high. Because
these longer dates are usually less frequently traded, it is not
uncommon for traders to take the nearest active period and assume
a flat volatility surface beyond that point. Nevertheless, given
the greater sensitivity of long dated options to volatility
changes, the risks of this approach are significant. Small
differences here have a large impact on a portfolio's value and
validation should continue until these differences are zero.
(Especially since the combination of interest rate and spot rate
volatility has such a major impact on these longer dates.)

• Letter B highlights the fact that the trader's low delta
wings on his/her volatility surface are a mile below the
VolSurface benchmark. Like the longer dated options highlighted
by Letter A, further out of the money strikes tend to trade less
frequently. It is therefore likely that the trader has simply
done a straight line interpolation of his/her volatility, working
outwards from the 10 delta calls and puts on the surface. Not
uncommon, but still bad practice that could prove expensive.

A particular problem is that the low vols on the trader's surface
would have meant that any trades outstanding at these low deltas
would probably have failed to appear on any conventional risk
management radar.

• Letter C points to a slightly less serious problem. While the trader clearly has his/her short term vols set too high, the worst offenders are very short dated options, which are about to roll off the book anyway and will soon be apparent in realised P & L. Therefore, as a single instance this is not likely to prove a massive issue. However, the risk manager might be well advised to keep an eye on the alert log to make sure the trader isn't doing this all the time.

#### Figure 4

### Conclusion

The whole approach to risk management of option desks has changed in recent years. Given the scale of their operations, at least one large bank has already acknowledged to regulators that the days of risk managing traders through micromanaged policing are effectively over. Their alternative is to adopt a joint responsibility approach involving both traders and risk managers that includes regular and detailed communication, which is then circulated in a condensed form to senior management.

VolSurface fits well with this (or pretty much any other) approach to managing the risks of volatility surface errors. Having said that, many traders will also quickly appreciate that the service is not just a middle or back office tool, but something that will benefit their own trading profitability - especially where they are active in maintaining auto quoting vols.

There will always unfortunately be traders who deliberately
manipulate vols in order to create fictitious profits and
bonuses, and VolSurface would be a powerful means of preventing
this. However, the majority of traders will welcome anything that
gives them a clearer picture of where their vols are in relation
to the market. In addition to the modelling-related errors
outlined in the "The top four vol

suspects" sidebar, VolSurface will also be of value in saving
traders from the consequences of any 'fat finger' errors.

In automated options trading, where trade and data volumes flow ever faster and larger, VolSurface's widely sourced data, broad coverage and statistical rigour make it a strong contender.

# VolSurface at a Glance

**Vendor:** SuperDerivatives, 30 St Mary Axe, 33rd
Floor, London EC3A 8EP UK Tel: +44-20-7648-1050

**What it does:** provides objective volatility
pricing by collecting and normalising data from multiple
sources. Where raw data are not available, values are
calculated using a proprietary methodology intended to
replicate the logic used by the most active traders in the
market.

**Coverage:**

• **FX** - 130+ currency pairs including all
major (G7) and emerging markets.

• **Interest Rates** - wherever a currency
has an interest rate market; includes both major and emerging
market currencies.

• **Equities** - several thousand single
stocks and indices across all major global exchanges.

• **Commodities** - precious/base metals,
energy products, and agricultural commodities across all global
exchanges and markets.

**Delivery:** FTP, secure FTP, HTTPS and others by
arrangement

**Format:** Excel, XML, CSV and FpML and others by
arrangement

**Frequency:** various timeframes are available;
lowest current update frequency is hourly.

**Intended market:** middle to back office

# How do I misprice thee? Let me count the ways…

**The following are examples of some of the common ways
in which traders' vol surfaces go awry, and which products such
as SuperDerivatives' VolSurface are intended to
prevent:**

**Price trap**

A vanilla option is a commoditised product that is not
particularly onerous to price and distribute. By contrast
exotic options have added risks that require more than just
expiry date volatility to price. Basic exotic modelling
requires a replication portfolio (a butterfly, two at the money
options and a low delta call and put) to be priced in order to
calculate the additional hedging costs of these options.

This in turn requires a volatility surface that is accurate across its entire surface and not just the maturity. Just a small deviation on the surface can alter hedging costs and prices significantly. As automated trading of options by counterparties has moved from the vanilla into the exotic, the negative consequences of this sort of inaccuracy have increased near exponentially.

Aggregated trading platforms accessed by automated models can capture and arbitrage any pricing discrepancies in milliseconds. Therefore market makers providing liquidity (particularly in exotic options) have to ensure that they are not susceptible to this sort of arbitrage by maintaining accurate volatility surfaces. Unfortunately, by no means all do.

**Correlation/Beta**

Volatility surface errors can be problem enough when dealing
with liquid markets, but the consequences of getting the
surface wrong can become truly horrendous when rates have to be
extrapolated from other rates. For example, a common situation
is that directly quoted vols are usually unavailable on FX
cross rates between minor illiquid currencies. In those
situations, dealers or auto quoting platforms will derive
synthetic values for these minor pairs from the rates quoted
for each minor currency against a major one, for example EUR.

But what if both the volatility surfaces for EUR versus the
minor currencies are awry? Admittedly

there is a chance that the errors may cancel each other out,
but it is at least as likely that they will exacerbate the
mispricing for the synthetic pair. The net result is then a
potentially substantial loss.

**Weighted Volatility**

In portfolio risk management the measure of change in value of
an option/portfolio for a given change in volatility is its
vega, measured as the change in value for a 1% increase in
volatility.

It is therefore a natural assumption to look across all time frames and consider that because the risk numbers are based on a 1% move in volatility that these risk numbers will move in a linear fashion regardless of time. On that basis, if three month volatility moves from 10 to 11, then the assumption would be that one month and 12 month volatility would also rise by one.

In practice, when underlying markets move quickly, short dated volatilities react and move much faster than long dated ones. The following method is therefore more accurate:

Assume a flat 10 'at the money' term structure of volatility; to allow for a non-linear shift in volatility, traders simply weight the volatilities by time. They commonly use a base of 90 days and simply state that if volatility goes up by one point then the 90 day volatility will also go up by one point.

A factor is then used, namely:

**The square root of (Base day count (90)/time
period)**

Therefore the factor for 30 days would be 1.73 and for 360 days 0.50, which means that if the 90 day (base) volatility goes up by one then the 30 day volatility will rise by 1.73 and the 1 year by only 0.50. As existing volatilities are being multiplied by a factor, any error in the volatility surface is being compounded - yet again emphasising the key importance of an accurate surface.