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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. 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.
A 'beer mat' Black Scholes Merton approximation for at the money ATM options, with zero interest rates can be reduced to:. 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. 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.
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.
The consequences of an inaccurate volatility surface see box "How do I misprice thee? 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. Inaccurate volatility surfaces therefore result in weak risk management of option trading activity.
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:.
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. 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. 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 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.
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. 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. The red alert colouring on the difference surface in Figure 4 highlights three 'real world' volatility errors:. 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.
Like the longer dated options highlighted by Letter A, further out of the money strikes tend to trade less frequently. 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. 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. 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. 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. 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.
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. 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.
Therefore the factor for 30 days would be 1. 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. 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.
The profitability of a derivative business is based on the formula: Staying in line SuperDerivatives VolSurface is intended to prevent your options business from falling into this trap.
Risks The consequences of an inaccurate volatility surface see box "How do I misprice thee? VolSurface at a Glance Vendor: 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: The following method is therefore more accurate: A factor is then used, namely: