RISK MANAGEMENTCVA Volatility - Minimizing the Aftershocks

BART PIRONprincipal risk consultant, SunGard

Anticipate.

Contents.1 Introduction

2 CVA Accuracy

2 CVA Volatility

3 Dynamic Date Grid

4 Daily CVA

5 Conclusion

Some CVA calculation methodologies can

produce undesired artefacts overstating the CVA P&L

volatility. This paper explains how this can happen and how it can be simply and

efficiently be rectified.

CVA Volatility - Minimizing the Aftershocks 01

Where does the problem lie?

Suppose for a moment that Figure 1 accurately describes the exposure profile for a given counterparty. This counterparty is assumed to have a master netting agreement, but not a collateral agreement. The graph may look a bit awkward at first glance. The spike in the exposure is caused by transactions being short or long a given risk factor, but with different maturities. As transactions mature of before others they reduce the overall netting effect and hence there is a sudden jumpin the exposure. This example has been chosen on purpose, not every portfolio will show such high spikes, but almost every portfolio will show peaks and troughs in the exposure profile when the latter is accurately calculated.

Now let us look at how a typical CVA calculation deals with an exposure profile like this. Calculating the exposure at every single business day in the future is prohibitively expensive so the exposure is usually only calculated for a number of ‘grid’ days, for example: 1 day, 2 days, 1 week, 2 weeks, 1 month, 3 months, 6 months and every 6 months beyond that. Figure 2 below shows what this looks like for our example exposure profile. The dots on the curve represent the grid dates.

As only a limited number of grid dates are used (in this case 39), some of the detail which was in Figure 1 went missing, but at least the essential shape is still there. Even the shape of the spike can be seen clearly, but notice it is much lower than in the first graph. There happened to be no grid point coinciding with the peak of the spike. Therein lies the problem. Too much detail is missed for the CVA to be calculated accurately.

0

500,000

1,200,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Figure 1 Expected Exposure Profile

INTRODUCTION

The purpose of CVA is, amongst others, to correct the

Mark-to-Market of the derivatives book for the effects of

credit risk. Hence any volatility of the CVA measure also

impacts the valuation of the derivatives on the balance

sheet and the P&L. P&L is influenced by a large number

of factors and these should be made as transparent as

possible. Unexplainable P&L volatility is not generally

welcomed. Some CVA calculation methodologies can

produce undesired artefacts overstating the CVA P&L

volatility. This paper explains how this can happen and

how it can be simply and efficiently be rectified.

02 CVA Volatility - Minimizing the Aftershocks

CVA Accuracy

The exposure profile in Figure 1 was generated by calculating the exposure for every single day for the next 15 years under every scenario and then averaging the values for each day. This is the most accurate calculation which is possible. Based on this profile the CVA1 turns out to be 27,884.

When calculating with a Fixed Date Grid as shown in Figure 2, the CVA comes out as 20,763. This is more than 25% less than the accurate calculation, a significant underestimate. But this lack of accuracy is not the only problem with the Fixed Date Grid. It also leads to more subtle problems.

CVA Volatility

We will look first at how CVA affects the quarterly P&L results and compare a Daily Date Grid to a Fixed Date Grid.

In Figure 3 below the portfolio is held constant to simulate a counterparty where no trading activity is taking place. To minimize the effects of other factors, we hold the market data2

constant and recalculate CVA at a number of points in time. The only effect on the CVA should be due to the portfolio aging and roll-off, and some small effects due to market data being held constant (rather than risk neutral drift). In theory, the CVA should change very slowly over time.

The see-saw pattern in the Fixed Date Grid line is caused by the grid calculation dates coinciding or not with particular peaks and troughs in the exposure profile. This volatility is hence entirely artificial.

Whereas the values in Daily Date Grid calculation are relatively smooth and decrease over time, the CVA under the Fixed Date Grid is far more volatile. Expressed as a percentage of the initial value, the CVA volatility of the Daily Date Grid column is 10% and for the Fixed Date Grid it is 31%.

As the Bilateral CVA feeds into the accounting P&L it will produce artificial P&L changes. This will make any attribution analysis of the P&L to its underlying causes particularly troublesome and difficult to explain to management.

1 BILATERAL CVA IS BEING USED IN THIS EXAMPLE. BUT THE SAME REASONING

APPLIES TO UNILATERAL CVA, DVA, FVA OR ANY OTHER XVA.

2 WE COULD ALSO EVOLVE THE MARKET DATA RISK NEUTRALLY OVER TIME,

BUT THAT DIFFERENCE WOULD BE VERY SMALL.

Figure 2 Exposure Profile with a Fixed Grid

0

200,000

400,000

800,000

600,000

1,000,000

1,200,000

0 1,000 2,000 3,000 4,000 5,000 6,000

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

0 3 6 9 12 15 18 21 24 27 30 33 36

Daily Date GridFixed Date Grid

Figure 3 CVA Comparison with a Fixed Grid as a graph

CVA Volatility - Minimizing the Aftershocks 03

Figure 4 Expected Exposure with Dynamic Dates

500,000

1,200,000

1,200,000

1,200,000

1,200,000

1,200,000

1,200,000

1,200,000

1,200,000

0 2 14 90 274

548

913

1,27

81,

643

1,85

32,

005

2,00

92,

067

2,25

02,

374

5,75

62,

432

2,61

72,

739

2,79

72,

981

3,10

43,

164

3,34

53,

470

3,52

83,

835

4,20

04,

565

4,93

15,

296

5,62

05,

661

5,75

6

0

Dynamic Date Grid

So how do we get rid of both the artificial volatility and the complications in P&L attribution analysis? One way would be to always calculate CVA using a Daily Date Grid. This is guaranteed to produce accurate and smooth results, but, as will be shown below, this can be prohibitively expensive.

Fortunately, there is a better solution. For most trades, credit exposure changes only slowly over time, except when there is a significant effect on the trade, such as a cash flow or an option exercise date. By dynamically inserting additional valuation dates per trade into the Fixed Date Grid, these shocks in the exposure are made explicit. This requires 2 additional valuation dates for each significant event, one before and one after the event, in order to see the shock.

For some portfolios adding another 2 valuation dates for every significant event would rapidly lead to valuing the portfolio at every business day, especially on the short end, resulting again to a prohibitively expensive calculation. But it is not necessary to value all trades at these additional event dates, if only the trades which have a significant event at that point are valued then the other ones can have their value interpolated between their adjacent dates, as they will be valued at their own significant event dates as well.

Figure 4 below shows the exposure from our example portfolio using a Dynamic Date Grid. Each dot corresponds to one date on the Fixed Date Grid or to a generated date. Note how closely it resembles the graph from Figure 1 which was done by simulating for every day for the next 15 years. Not only does it get the shape right, it also has almost exactly the same values for each date.

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

0 3 6 9 12 15 18 21 24 27 30 33 36

Daily Date GridDynamic Date Grid

Figure 5 CVA Comparison with a Dynamic Date Grid

04 CVA Volatility - Minimizing the Aftershocks

Let us now look at the CVA calculation with a Dynamic Date Grid. In the table below you can see the CVA calculated for the end of every quarter, again with all portfolio and market data held constant as described in CVA Volatility. The comparison between the simulation for the Daily Date Grid and the Dynamic Date Grid results in differences which are nowhere larger than 1%.

On Figure 5 above it becomes very hard to see the difference between the CVA calculated by both methods, and that is exactly the point.

The accuracy achieved through calculating with Dynamic Date Grid comes at a comparatively low price. The number of valuations necessary for this portfolio for the various cases is shown in the table below.

The increase in the number of valuations (and hence the resource consumption) from the Fixed Date Grid to Dynamic Date Grid is only 16%. Another increase of two orders of magnitude is needed to get to the accuracy of Daily Date Grid, which is barely different from the result reached by Dynamic Date Grid.

Daily CVA

Many banks have CVA desks managing the daily CVA P&L. When calculating daily CVA the effects are similar. On Figure 7 below you can see how daily CVA changes for a fixed portfolio using the various methods over a one month period. The sudden change in the Fixed Date Grid profile comes from a fixed date all of a sudden picking up a spike in the exposure.

Note that again it is hard to spot the difference between the Daily Date Grid and the Dynamic Data Grid whereas the Fixed Date Grid method produces an unwanted jump in CVA.

Fixed Date Grid 1,400,005

Dynamic Date Grid 1,630,005

Daily Date Grid 187,650,005

Figure 6 Number of valuations required

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 19 22 24 25

Fixed Date Grid

26

Daily Date GridDynamic Date Grid

Figure 7 Daily CVA over one Month

CVA Volatility - Minimizing the Aftershocks 05

Conclusion

Calculating CVA with a fixed grid of simulation dates, which is still being done by a large number of banks, leads to problems with the accuracy of the CVA result, but more importantly increases the volatility of the CVA artificially and makes P&L attribution to market factors difficult or even impossible. Similar effects occur for other xVA measures based on simulation through time.

This can be remedied by simulating the exposure on a Daily Date Grid, instead of just a Fixed Date Grid, but this method is computationally very expensive. Using a Dynamic Date Grid is fast and accurate giving most of the benefits of a Daily Date Grid in terms of P&L management with the performance of a Fixed Date Grid.

©2015 SunGard. Trademark Information: SunGard, and the SunGard logo are trademarks or registered trademarks of SunGard or its subsidiaries in the U.S. and other countries. All other trade names are trademarks or registered trademarks of their respective holders. CM4573

Enabling the Adaptive Enterprise

Sitting at the intersection of technology and finance, SunGard is focused on delivering fresh ideas and inventive solutions to help our customers adapt and thrive in an ever changing environment. With a blend of software solutions, cloud infrastructure, global service capabilities and deep domain expertise, SunGard is capable of supporting virtually every type of financial organization, including the largest and most complex institutions in the world. For more information, please visit www.sungard.com

getinfo@sungard.com

www.sungard.com twitter.com/sungard

linkedin.com/company/sungard