Collateral consistent derivatives pricing
FRIC Practitioner Seminar, CBS
Martin D. Linderstrøm, [email protected]
Counterparty Credit & Funding Risk
www.danskeresearch.com
Agenda
• The intuition behind collateral consistent pricing.
− A benchmark case: A multi-currency calibration under EUR cash collateral.
• The complexities of a multi CSA book
− Which collateral assumptions hold for calibration instruments?
− The ISDA Standardized CSA approach
− Market fragmentation between CCP cleared and bilateral trades?
• Case studies in curve calibration
− What are reasonable bounds for forward curves?
− Arbitrages in fragmented markets?
• Pricing and hedging discounting risks under different CSA regimes?
− The collateral valuation adjustment.
− The cheapest-to-deliver optionality in CSAs
− Hedge ratios with and without optionality?
www.danskeresearch.com
2
Swaps in the old way
• In the “old” days (until Aug’07) many
market participants had just one swap
curve for each currency.
− Forward rates – irrespective of tenor – were
calculated on this.
− Discount factors were also derived from this
curve.
• This implicitly assumes:
5Y 3M-6M Basis
70
60
50
40
30
20
10
0
2005
2006
2007
− No money market basis (e.g. 3s6s basis is
zero).
− No cross currency basis (e.g. EUR/USD basis
is (close to) zero).
− Traders can fund themselves at xIBOR.
− Note that on a single curve, a Floating Rate
Note trades at par at fixing time.
• These assumptions are no longer valid.
5Y EONIA-3M Basis
2008
2009
2010
2011
2012
2011
2012
5Y EUR/USD X-CCY
10
0
-10
-20
-30
-40
-50
-60
-70
-80
2005
2006
2007
2008
2009
2010
www.danskeresearch.com
3
Swaps in the new way
• Need for multiple projection
Forward LIBOR Surface
curves for each currency.
− This should reflect CCS spreads.
− But what should be my anchor in terms
of currency and credit premium?
− If your trade is collateralised, you should
discount with the collateral rate.
− What is your collateral rate?
1.2
15-May-13
21-Aug-13
curve for each currency.
23-Oct-12
• Need for a single discounting
1-Feb-13
− We cannot compute 3M xIBOR and 6M
xIBOR forwards on the same curve.
10M
5M
1B
23-Aug-10
29-Nov-10
7-Mar-11
15-Jun-11
21-Sep-11
29-Dec-11
5-Apr-12
17-Jul-12
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
Discount Factors
1.0
0.8
0.6
0.4
0.2
0.0
www.danskeresearch.com
4
The institutional setting
• The ISDA Master agreement
− The legal umbrella underpinning netting.
− Default and early termination provisions.
• ISDA Definitions
− Sets standards for methodologies such as settlement of options, application of floating
rates etc.
• ISDA Credit Support Annex (Credit Support Deed)
− Defines the terms for collateralisation.
− Sets Thresholds, Independent Amounts, Mininmum Transfer Amounts and valuation
frequency.
− Eligible collateral and specifies interest earned.
www.danskeresearch.com
5
The intuition behind collateral consistent pricing
Flow analysis: EUR Derivative - EUR Cash collateral
Bank
T0: Payment (=+100 EUR)
T0: Payment (=+100 EUR)
Counter Party
T0: Contract
(PV=-100 EUR)
Trading Desk
T1: Interest= RIntern*(1/360)*100 EUR
T1: Contract
(PV=-100*(1+ RDisc/360) EUR)
Cash Desk
T1: Interest= REUR/OIS*(1/360)*100 EUR
T0: Payment (=+100 EUR)
T1: Interest= RIntern*(1/360)*100 EUR
Collateral
Management
•Cash desk is passing through the liquidity – no
haircuts or disagreement on valuation.
•Internal loop can be ”closed” if rIntern=rOIS
•See Piterbarg (2010).
T0: Payment (=+100 EUR)
•For the setup to be arbitrage free, the trader needs to
be discounted at the rate his cash position earns, i.e.
RDisc = ROIS.
•He could in principle hedge his cash exposure via an
EONIA swap.
www.danskeresearch.com
6
A benchmark case: A multi-currency calibration under EUR
cash collateral
• Stylised market:
EUR: 3M forward rates
− Only IRSs against 3M xIBOR.
− 3M xIBOR-OIS basis swaps.
− X-CCY basis swaps against 3M XIBOR.
− Only swap instruments 1-30Y.
• Setup
EUROIS
3.5%
3.0%
2.5%
− Separate forward and discounting curves.
2.0%
− Single collateral assumption – all products
are EUR cash collateralised.
1.5%
− Want a CCS consistent valuation setup.
• Approach
− Calibrate jointly EUR3M and
EUROIS=EURDISC curves.
EUR3M
1.0%
0.5%
0.0%
0
60
120
180
240
Forward start (months)
300
www.danskeresearch.com
360
7
Benchmark case – cont’d
• Approach cont’d:
− Calibrate jointly USD3M, USDOIS and
USDDISC curves...
− ...requires EUR model as input since
X-CCY legs have initial PV...
− ...USDDISC curve is not dependent on
USDOIS.
• Pricing implication
− This creates a X-CCY dependence for
the pricing of every USD cashflow.
USD: 3M forward rates
3.5%
0.0%
3.0%
-0.1%
2.5%
-0.2%
2.0%
-0.3%
1.5%
USDOIS
− Hedging tool for USD net liquidity is to
trade USD fixed-EONIA float CCS…
0.5%
− …this delivers the required EONIA
floater to collateral mgmt.
0.0%
-0.4%
USD3M
1.0%
USDDISC
EUR/USD X-CCY 3M (rhs.)
0
60
120
180
240
Forward start (months)
300
-0.5%
-0.6%
360
www.danskeresearch.com
8
The intuition behind collateral consistent pricing (cont.)
Flow analysis: EUR Derivative - USD Cash collateral
Bank
T0: Payment (=+100 EUR)
T0: Payment (=+100 EUR)
Counter Party
T0: Contract
(PV=-100 EUR)
Trading Desk
T1: Interest= (REUR/OIS+s)(1/360)*100 EUR
T1: Interest= RIntern*(1/360)*100 EUR
T0: 100 EUR
T1: Contract
(PV=-100*(1+ RDisc/360) EUR)
Cash Desk
CCS Counter Party
T0: 126 USD
T1: Interest= RUSD/OIS*(1/360)*126 USD
T0: Payment (=+126USD)
T1: Interest= RIntern*(1/360)*126 USD
Collateral
Management
•To produce the collateral posting in USD an
Eonia/Fed-Funds CCS is entered.
•Notice that there is a spread s on the EUR leg!
•See Piterbarg (2012).
T1: Interest= RUSD/OIS*(1/360)*126 USD
T0: Payment (=+126 USD)
•The discount rate needs to reflect the spread in the
CCS.
•In reality there may be multiple currencies, and
hence a cheapest-to-deliver option for the collateral
poster!
www.danskeresearch.com
9
Calibration instrument assumptions
• Fundamentals
− What do we mean by calibration instruments?
− Our model tells where to price one product reletive to others…
− …so we should calibrate it market prices at which we can execute hedges.
• ”The Market”
− How is ”The Market” collateralised?
− No single answer…
− …CSAs are bilateral agreements – and they vary substantially.
− CCP collateralisation rules are however very clear.
• My calibration should depend carefully on the collateral assumptions that I will face
once I start using the calibration instruments for hedging.
− Each market segment offers one source of risk – but can be collateralised differently:
− On several CCPs EUR trades are EONIA collateralised, USD trades are FF collateralised…
− …the same goes for the ISDA Standardised CSA.
− But what holds true for FX products?
www.danskeresearch.com
10
Changing the assumptions
• Back to USD:
− Let us instead calibrate by using Fed Funds discounting…
− …most of ”The Market” for USD swaps clears via LCH…
− We are using the same market quotes for spot
instruments…
− …but see slight changes in the 3M Fwd curve for 3M USD
LIBOR.
• Intuition:
− A par-swap rate is a weighted average of xIBOR forward
rates.
− Changing the discounting assumption alters the weighting
of the individual fwd xIBOR rates.
− A typical swap market calibration has many degrees of
freedom.
• Conclusion:
− Depending on your assumptions, you can easily misprice
forward starting swaps with 1.0-1.5 bps.
USD3M Fwd: EONIA vs. Fed Funds based
3.5%
0.25
0.00
3.0%
-0.25
2.5%
-0.50
2.0%
-0.75
1.5%
-1.00
EONIA based
calibration
Fed Funds based
calibration
Diff (bps), rhs
1.0%
0.5%
-1.25
-1.50
-1.75
− This is huge in a market that trades with bid-offer spreads
in the 0.25-1 bps range.
0.0%
0
60
120
180
240
Forward start (months)
300
-2.00
360
www.danskeresearch.com
11
Changing the assumptions – cont’d
• Cross currency swaps:
− The same effect holds true for CCSs.
CCS 3M fwd breaks: EONIA vs. Fed Funds based
0.0%
0.10
− In most markets, the fwd curves for the CCS
breaks are less steep than xIBOR fwd curves…
− …this means that the discounting effect is
smaller.
• ISDA Standardised CSA:
− Is promoting USD cash collateral for FX products
incl. CCS…
− …so Fed Funds discounting must be right…
− …but what about the fwd curves needed to price
up this product?
This introduces a multi-step calibration
requirement…
…need to calibrate ”silo” models first and
subsequently introduce a new discounting curve.
0.05
-0.1%
0.00
-0.05
-0.2%
EONIA based calibration
-0.10
Fed Funds based calibration
-0.3%
-0.15
Diff (bps), rhs
-0.20
-0.4%
-0.25
-0.30
-0.5%
-0.35
-0.6%
0
60
120
180
240
Forward start (months)
300
-0.40
360
www.danskeresearch.com
12
Changing the assumptions – cont’d
• An aside on CCSs:
− The basic building block for CCSs is in
itself tricky…
CCS 3M fwd breaks: Difference to Fed
Funds (bps)
0.25
− …MtM FX resets or constant notionals?
− Should FX-Basis correlation be included?
− Does the market standard CCS product
rather warrant a full hybrid model?
0.00
• Conclusion:
− The full sequential calibration of the silobased model matters in certain curve
segments.
-0.25
− Is obviously dependent on interpolation
settings…
EONIA based calibration
− …but for plausible choices, the difference in
a 5Y5Y EUR/USD CCS can be up 0.25
bps.
Silo based calibration
-0.50
0
60
120
180
240
Forward start (months)
300
www.danskeresearch.com
360
13
The intuition behind collateral consistent pricing
Flow analysis: EUR Derivative - EUR security collateral
Bank
T0: Payment (=+100 EUR)
T0: Payment (=+100 EUR)
Counter Party
T0: Contract
(PV=-100 EUR)
Trading Desk
T1: Interest= RIntern*(1/360)*100 EUR
Cash
T1: Contract
(PV=-100*(1+ RDisc/360) EUR)
Cash Desk
Repo Cpty.
Bond
Bond
Collateral
Management
T1: Interest= RRepo *(1/360)*100 EUR
Bond
•Security collateral can be financed at their respective repo rate.
•Note the role of haircuts: Cash desk potentially receives one, but collateral management will have to
provide one in the CSA. Only differences in haircuts matter – and then becomes a question of
unsecured funding rates.
www.danskeresearch.com
14
Case study: Potential for market fragmentation in SEK
• CCP vs. Bilateral:
SEK3M: Fwd curve diffs (bps)
− Clearing is not standard in all markets – yet.
3.5
− In SEK, a large share of the IRS market is cleared
but much is still bilateral.
3.0
STINA-EONIA
− Among the market makers security collateral is
allegedly common place…
2.5
− …and some of this is closer to STIBOR funded.
2.0
• CCP valuation vs. cash accrual
− LCH.SwapClear uses STIBOR discounting for VM
calculation…
STINA-Fed Funds
STINA-STIBOR
1.5
1.0
− …but still pays T/N rate on SEK cash.
− First order (accrual rate) vs. second order
(accrual balance) effect.
• Conclusion:
− If there is still only one broker price, there should
be fragmentation in the forward swap market.
− Screen prices should be different.
0.5
0.0
-0.5
-1.0
0
60
120
180
240
Forward start (months)
300
360
www.danskeresearch.com
15
Collateral valuation adjustments
• CSA optionality:
3M forward EURDISC rates
− Many (older) CSAs contain long lists of eligible collateral.
− If collateral can be freely substituted, this creates a
cheapest-to-deliver option for the posting party.
− This creates a need for an effective discount curve –
created from more than one curve.
• Example:
− Can choose between placing EUR cash earning EONIA and
USD cash earning Fed Funds.
− This is effectively a series of call options on the EONIA-FF
CCS spread.
• Intrinsic value of CSA option:
Fed Funds based calibration
3.5%
3.0%
2.5%
2.0%
1.5%
− Find the upper convolution of the EONIA disc curve and
the Fed Funds adjusted curve (in fwd terms).
1.0%
− Use these forward rates to generate effective discount
curve.
0.5%
− In the specific example, it is expected to be cheapest to
deliver EUR for all 30Y years...
− …but there is a risk that USD will be cheaper.
EONIA based calibration
0.0%
-0.5%
-1.0%
0
60
120
180
240
Forward start (months)
300
www.danskeresearch.com
360
16
The intuition behind collateral consistent pricing (cont.)
Expected collateral flow – 100M EUR 20Y IRS Payer
• Net Flow
− Take forward Euribor rates and par
fixed rate as given, assume EUR OIS
discounting.
− Forward curve is upward sloping
− We pay out net the first 5 years, and
receive net the last 15 years.
Flow
1,000,000
800,000
600,000
400,000
200,000
0
-200,000
-400,000
-600,000
Flow Rec
Flow Pay
Flow Net
0Y
5Y
• Future Value as expected
collateral balance.
− Starts and ends at zero for the ATM
trade.
− Increses since we are owed more and
more.
− Decreases when we start to receive.
10Y
15Y
FV
40,000,000
35,000,000
30,000,000
25,000,000
20,000,000
15,000,000
10,000,000
5,000,000
0
FV Rec
FV Pay
FV Net
0Y
5Y
10Y
15Y
www.danskeresearch.com
17
The intuition behind collateral consistent pricing (cont.)
Forward Cross Currency Basis Spreads – 1Y Forward CCS next 20Y
• ColVA
− Consider the Collateral Valuation
Adjustment if collateral should be
posted in USD Cash rather than EUR
Cash.
− User the FV Net as the CCS notional
profile, compute the value of paying the
spread.
− The spread is determined through the
CCS with the Fed Funds rate flat on the
one leg and Eonia plus a spread on the
other.
Flow ColVA
0.000%
10,000
-0.100%
8,000
-0.200%
6,000
-0.300%
4,000
-0.400%
CCS Spread
Flow ColVA
2,000
-0.500%
-0.600%
0
0Y
5Y
10Y
15Y
FV ColVA
8,000,000
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
250,000
200,000
150,000
100,000
FV Net
FV ColVA
50,000
0
0Y
5Y
10Y
15Y
www.danskeresearch.com
18
The intuition behind collateral consistent pricing (cont.)
Discount Curve Risk wrt 1Y Forward CCS Spreads - 100M EUR 20Y IRS Payer
• Compute Discount Curve Risk
wrt. 1Y Fwd swaps to derive 1st
order ColVA impact estimate
from shifting collateral type.
Disc Risk
2,000
1,000
0
-1,000
-2,000
-3,000
• Example continued:
− ATM, ITM (ATM-100bp), OTM(ATM+100bp)
− Positive FV implies negative Fwd Disk
Risk.
− ITM/OTM have the extra disk risk from
an annuity.
− Result:
ATM
OTM
ITM
Impact
Impact
Impact
203k EUR
-356k EUR
761k EUR
0.00%
-0.20%
-0.40%
-0.60%
ATM Disc Risk
OTM Disc Risk
ITM Disc Risk
CCS Spread
1st Order ColVA: Disc Risk * CCS Spread
150,000
100,000
50,000
0
-50,000
-100,000
ATM Impact
OTM Impact
ITM Impact
www.danskeresearch.com
19
Option adjusted collateral consistent pricing
• Realised volatility on CCS spreads:
− Spot (normal) volatility is in the 20-50 bps
range on an annualised basis.
− Forward spreads are however less volatile.
• How to include volatility?
− Simple model, can only EUR or USD cash.
− Assume Gaussian model.
EONIA-FF CCS:
Rolling 30D realised volatility (annualised)
0.80%
5Y
0.40%
0.20%
0.00%
Feb-10
Aug-10
− Collateral poster is long a series of caplets
on CCS breaks, struck at 0 bps.
• Conclusion
− Given the shape of the CCS fwd break
curve, the short expiries are deep OTM…
10Y
0.60%
Feb-11
Aug-11
Feb-12
Aug-12
3M forward EURDISC rates
Intrinsic
20 bps vol
50 bps vol
4.0%
3.0%
2.0%
− …little effect on effective discounting curve.
1.0%
− But significant increases for long dated
expiries (closer to ATM and higher vega).
0.0%
0
60
120
180
240
Forward start (months)
300
www.danskeresearch.com
360
20
Option adjusted collateral consistent pricing – cont’d
• Theory:
Intrinsic (0 bps): CCS Dv01 (EUR)
− Fujii & Takahashi (2011) and Piterbarg (2012)
• Example:
Base
+10 bps
+20 bps
30,000
− 30Y EUR Payer, 100m 250 bps OTM.
25,000
• Risk:
− Using the intrinsic approach, not CCS hedge
is required (EUR trade, EUR cash is CTD with
certainty).
− But this will change as basis spreads
increase  Risk will ”jump”.
− Stability in hedges is an important argument
for developing CTD models…
− …especially in ”naive” bump-and-re-run” mode.
Model
Intrinsic CTD
Option adj. CTD, 20 bps
Option adj. CTD, 50 bps
PV Initial
-46.67m
-45,80m
-43.92m
Difference
878k
2.756k
Note, this is a typical pension fund trade – a difference
of 6% of the PV of derivatives can mean insolvency.
20,000
15,000
10,000
5,000
0
-5,000
-10,000
-15,000
1Y 2Y 3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
www.danskeresearch.com
21
Option adjusted collateral consistent pricing – cont’d
Option adj (20 bps): CCS risk (EUR)
Base case
+10 bps
Option adj (50bps): CCS risk (EUR)
+20 bps
Base case
15,000
15,000
10,000
10,000
5,000
5,000
0
0
-5,000
+10 bps
+20 bps
-5,000
1Y 2Y 3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
1Y 2Y 3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
• Option adjusted discount deltas:
− Results in stable hedges.
− Intuition fits well against USD cashonly benchmark case.
USD cash only: CCS risk (EUR)
Base case
+10 bps
+20 bps
25,000
20,000
15,000
10,000
5,000
0
1Y 2Y 3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
www.danskeresearch.com
22
Conclusion
• There is a direct link between collateral terms and discount factors.
• This is important – it is not just for market makers in derivatives.
• It is not trivial to construct collateral consistent swap curves – and
arbitrages are sometimes not far away.
• The ”poor man’s” collateral consistent approach can bring most market
participants far.
• While the value of CTD options embedded in CSAs is debatable – the
risk implications are clear.
www.danskeresearch.com
23
References
• Piterbarg, V. (2010), ”Funding beyond discounting: Collateral
agreements and derivatives pricing”, Risk Magazine February, pp.97102
• Fujii, M. & Takahashi, A. (2011), ”Choice of collateral currency”, Risk
Magazine January, pp. 120-125
• Piterbarg, V. (2012), ”Cooking with collateral”, Risk Magazine, pp. 58-63
www.danskeresearch.com
24
Disclosure
This presentaitonhas been prepared by Danske Research, a division of Danske Bank A/S ("Danske Bank").
Analyst certification
Each research analyst responsible for the content of this research report certifies that the views expressed in the research report accurately reflect the research
analyst’s personal view about the financial instruments and issuers covered by the research report. Each responsible research analyst further certifies that no part of
the compensation of the research analyst was, is or will be, directly or indirectly, related to the specific recommendations expressed in the research report.
Regulation
Danske Bank is authorized and subject to regulation by the Danish Financial Supervisory Authority and is subject to the rules and regulation of the relevant regulators
in all other jurisdictions where it conducts business. Danske Bank is subject to limited regulation by the Financial Services Authority (UK). Details on the extent of the
regulation by the Financial Services Authority are available from Danske Bank upon request.
The research reports of Danske Bank are prepared in accordance with the Danish Society of Financial Analysts’ rules of ethics and the recommendations of the
Danish Securities Dealers Association.
Conflicts of interest
Danske Bank has established procedures to prevent conflicts of interest and to ensure the provision of high quality research based on research objectivity and
independence. These procedures are documented in the research policies of Danske Bank. Employees within the Danske Bank Research Departments have been
instructed that any request that might impair the objectivity and independence of research shall be referred to the Research Management and the Compliance
Department. Danske Bank Research Departments are organised independently from and do not report to other business areas within Danske Bank.
Research analysts are remunerated in part based on the over-all profitability of Danske Bank, which includes investment banking revenues, but do not receive bonuses
or other remuneration linked to specific corporate finance or debt capital transactions.
Financial models and/or methodology used in this research report
Calculations and presentations in this research report are based on standard econometric tools and methodology as well as publicly available statistics for each
individual security, issuer and/or country. Documentation can be obtained from the authors upon request.
Risk warning
Major risks connected with recommendations or opinions in this research report, including as sensitivity analysis of relevant assumptions, are stated throughout the
text.
First date of publication
Please see the front page of this research report for the first date of publication. Price-related data is calculated using the closing price from the day before publication.
www.danskeresearch.com
25
General disclaimer
This presentation has been prepared by Danske Markets (a division of Danske Bank A/S). It is provided for informational purposes only and
should be viewed solely in conjunction with the oral presentation provided by Danske Markets and/or Danske Markets Inc. It does not
constitute or form part of, and shall under no circumstances be considered as, an offer to sell or a solicitation of an offer to purchase or sell any
relevant financial instruments (i.e. financial instruments mentioned herein or other financial instruments of any issuer mentioned herein
and/or options, warrants, rights or other interests with respect to any such financial instruments) (“Relevant Financial Instruments”).
The presentation has been prepared independently and solely on the basis of publicly available information which Danske Bank considers to be
reliable. Whilst reasonable care has been taken to ensure that its contents are not untrue or misleading, no representation is made as to its
accuracy or completeness, and Danske Bank, its affiliates and subsidiaries accept no liability whatsoever for any direct or consequential loss,
including without limitation any loss of profits, arising from reliance on this presentation.
The opinions expressed herein are the opinions of the research analysts responsible for the presentation and reflect their judgment as of the
date hereof. These opinions are subject to change, and Danske Bank does not undertake to notify any recipient of this presentation of any such
change nor of any other changes related to the information provided in the presentation.
Danske Bank, its affiliates, subsidiaries and staff may perform services for or solicit business from any issuer mentioned herein and may hold
long or short positions in, or otherwise be interested in, the financial instruments mentioned herein. The Equity and Corporate Bonds analysts
of Danske Bank and undertakings with which the Equity and Corporate Bonds analysts have close links are, however, not permitted to invest in
financial instruments which are covered by the relevant Equity or Corporate Bonds analyst or the research sector to which the analyst is
linked.
Danske Bank is authorized and subject to regulation by the Danish Financial Supervisory Authority and is subject to the rules and regulation of
the relevant regulators in all other jurisdictions where it conducts business. Danske Bank is subject to limited regulation by the Financial
Services Authority (UK). Details on the extent of the regulation by the Financial Services Authority are available from Danske Bank upon
request.
This presentation is not intended for retail customers in the United Kingdom or the United States.
This presentation is protected by copyright and is intended solely for the designated addressee. It may not be reproduced or distributed, in
whole or in part, by any recipient for any purpose without Danske Bank’s prior written consent.
www.danskeresearch.com
26
Disclaimer related to presentations to U.S. customers
In the United States this presentation is presented by Danske Bank and/or Danske Markets Inc., a U.S. registered broker-dealer and subsidiary
of Danske Bank. In the United States the presentation is intended solely to "U.S. institutional investors" as defined in SEC Rule 15a-6.
Danske Bank is not subject to U.S. rules with regard to the preparation of research reports and the independence of research analysts. In
addition, the research analysts of Danske Bank who have prepared this presentation are not registered or qualified as research analysts with
the NYSE or FINRA, but satisfy the applicable requirements of a non-U.S. jurisdiction.
Any U.S. investor recipient of this presentation who wishes to purchase or sell any Relevant Financial Instrument may do so only by contacting
Danske Markets Inc. directly and should be aware that investing in non-U.S. financial instruments may entail certain risks. Financial
instruments of non-U.S. issuers may not be registered with the U.S. Securities and Exchange Commission and may not be subject to the
reporting and auditing standards of the U.S. Securities and Exchange Commission.
www.danskeresearch.com
27