Kenyon_December2013_Slides

Regulatory Challenges
to Mathematical Finance
Chris Kenyon
12.12.2013
London Quantitative Finance Seminar
Contact: [email protected]
Acknowledgments & Disclaimers
This presentation is based on joint work with Andrew Green.
The views expressed in this presentation are the personal views of the
speaker and do not necessarily reflect the views or policies of current or
previous employers.
Not guaranteed fit for any purpose. Use at your own risk.
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Contents
Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Step 1. Risky Markets are Incomplete
Step 2. Desks are Inherently Risky
Step 3. Desks’ Risk Quantification
Step 4. Funding is a Separate Risk from Capital
Step 5. Costs Set by Desk Risk
Summary
Regulatory-Optimal Funding
Regulations
Funding Optimization
Results
Summary
Conclusions
Bibliography
Appendix
Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Regulatory-Optimal Funding
Conclusions
Bibliography
Appendix
Introduction
I
Regulators clearly believe that derivatives can never be risk free
I
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Burst of regulation after the 2008 financial crisis slowing?
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,
Already: Basel III officially starting Jan 1, 2014 (EU, US)
Soon: Leverage Ratio; Liquidity Coverage Ratio
Prudent Valuation (EBA 2013),
Non-IMM proposal (BCBS-254 2013)
Potential replacement of VaR by Expected Shortfall (BCBS-219
2012) now uncertain because not elicitable.
Direct effect on bottom line, what effect on theory?
5/62
Steps
I
Desks always risky ⇒ Strictly positive Capital cost
I
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Holding costs for long positions 6= holding costs for short positions
Incomplete-markets (Cerný 2009; Kaido and White 2009)
Holding costs (Tuckman 1992), not transaction costs (Kabanov and
Safarian 2010)
Idiosyncratic effects ⇒ no Risk-Neutral Measures
I
I
,
Have to recover Institutional Costs (facilities, personnel)
Regulations ⇒ Holding Costs ⇒ Incomplete Market
Trading difficulties, potentially empty markets (seen before (Jouini,
Koehl, and Touzi 1997))
Also implied by arbitrage (Shreve 2004)
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Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Regulatory-Optimal Funding
Conclusions
Bibliography
Appendix
Risk-Neutral Measure
Definition
Let P be the physical measure, then a probability measure Q is said to
be risk-neutral if:
(i) Q and P are equivalent;
(ii) under Q discounted stock prices are martingales.
,
I
(Shreve 2004) shows that if the market price of risk equations
cannot be solved then there is arbitrage assuming that the cost
of 1 unit of stock is exactly the negative of -1 units of stock.
I
Not true here because holding costs are present whether the
position is short or long.
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Theorem 1: No Risk-Neutral Measure
Theorem
If each market participant has different idiosyncratic continuous
dividends when holding the same stock then there is no risk-neutral
measure.
Proof.
Obvious. Let the stock price, from the point of view of market participant i, be:
P
dSi (t) = (µi + ai )Si (t)dt + σSi (t)dW i (t)
where ai is the objective dividend received by market participant i, and µi is the P drift believed by
market participant i. This implies that in the idiosyncratic risk-neutral measure of i, the evolution of
the stock price is:
Q
dSi (t) = (r + ai )Si (t)dt + σSi (t)dW i (t)
where r is the riskless rate. The P drifts of the market participants have been replaced by the
riskless rate, but dividends are unchanged because they are objective although idiosyncratic.
Hence there is no risk neutral measure because the rates of return are different for each participant
(under each participants’ risk neutral measures).
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Idiosyncratic Effects
I
If dividends were not idiosyncratic then all participants would see
the same risk-neutral measure
I
Usually the Girsanov transformations are idiosyncratic but the
final measure is common
Capital requirements on derivative desks are different for
different banks, thus Theorem 1 is applicable
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Market Risk capital consists of a VaR part and a Stressed VaR part
where the stressed period is determined at the bank level
Expect different banks to have different stress periods, e.g. Greek
banks versus US banks
Systematically Important Banks have different capital requirements
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Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Step 1. Risky Markets are Incomplete
Step 2. Desks are Inherently Risky
Step 3. Desks’ Risk Quantification
Step 4. Funding is a Separate Risk from Capital
Step 5. Costs Set by Desk Risk
Summary
Regulatory-Optimal Funding
Conclusions
Bibliography
Appendix
Risk Transfers
DVA
FVA (c/p)
Capital (c/p)
Desk
Bank Risk
Desk Risk
Counterparty
Capital (desk)
FVA (desk)
CVA
Bank
Systematic Risks
Figure: Risk transfers between a trading desk and its parent bank, and
between the desk and its counterparties.
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Step 1. Risky Markets are Incomplete
Base case: back-to-back collateralized interest rate swaps (IRS).
Suppose IRS identical IRS except for opposite directions. The desk
will leak PnL due to the following.
I
Counterparty Credit Risk (CCR) capital on margin periods of risk
I
Institutional Costs (IC), i.e. facilities and personnel, etc.
I
Leverage Ratio (LR) capital
I
Initial Margins (IM) require funding (plus possible Default Fund
contributions)
Desk needs (small) arbitrage to cover costs, or close.
I
Desk requires competitive advantage, its business model.
I
With sufficient flow, swap terms may remain closely matched
(within 15bps) so no Market Risk capital requirement,
(BCBS-128 2006) paragraph 718(xiv).
Desk risk is from business model robustness for ongoing trading.
Market incomplete and capital costs strictly positive.
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Swap Edge Case
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Desk enters collateralized swap + uncollateralized swap
Enters collateralized CCDS on swap c/p at zero cost
Term repos uncollateralized swap+CCDS as package; puts extra into
riskless account
Effects
I Repo provides collateral for collateralized swap and vice versa
I Uncollateralized swap+extra pay CCDS premia and repo rate
I If CCDS spread >15bps, Market Risk capital on both swaps
I Initial Margin(s) requires funding
I Place extra funding from repo in riskless account (assume pays repo)
and pass back
I Collateralized CCDS, economic risk on CCDS jump-to-default
I Counterparty Credit Risk capital for margin period of risk
I Economic risk from uncollateralized swap default time
I Institutional Costs; Leverage Ratio capital
Outcome
I Desk leaks PnL
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Edge Case Details
Assumptions
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no bond CDS, or swap CCDS basis
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no capital relief priced into CDS, CCDS (Kenyon and Green
2013a)
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no repo haircuts
Notes
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Default times creates PnL volatility because different numbers of
protection coupons paid, and replacement swap not ATM
I
CDS/CCDS hedges not cashflow-replicating
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Economic capital is required by the bank covering PnL volatility
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Edge Cases: Consequences
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Market is incomplete from holding costs (non-zero cost capital,
IM, IC)
Holding costs idiosyncratic from Market Risk Stressed VaR
period, and capital portfolio effects (at least)
Market has no risk-neutral measure because holding costs
idiosyncratic
No funding yet → introduce haircuts on repos.
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Generalizing: Repo Haircuts
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Regulations (BCBS-189 2011; BCBS-193 2011) have
requirements before a repo has zero haircut
I
Double-default risk, and margin period of risk, mean non-zero
haircuts rational on packages
I
Funding buffers are costs. Basel III has the Liquidity Coverage
Ratio (30 days funding) and UK regulations have Individual
Liquidity Guidance (at least two weeks).
I
Funding buffer costs give a floor to the funding charge from the
bank to desks (if not seen as funding risk-reducing — possibly
repo desks).
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Repo Haircut Effects
Bond
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Known finite limit on funding quantity
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Bank charges funding to desk at the funding risk of the desk’s
business model, floored by the price of funding risk
Swap: receive fixed on haircut fraction
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Known finite limit on funding quantity
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Bank charges funding to desk at the funding risk of the desk’s
business model, floored by the price of funding risk
Swap: receive floating, e.g. 3M EUR, on haircut fraction
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Potentially unlimited funding requirements
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No limit on potential funding costs
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Bank charges funding to desk at the funding risk of the desk’s
business model, including market impact of different funding
levels, floored by the price of funding risk
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Generalizing: Limited CDS and CCDS
I
Counterparty Credit Risk capital increases from the margin
period of risk to the maturity of the trades (regulatory details
important for caps)
I
Desk must now warehouse credit risk, hence require Economic
capital for increased PnL volatility
I
Increased repo haircuts (with usual credit risk on haircut amount)
Major qualitative difference is point on PnL volatility: “market can
remain irrational longer than you can remain solvent”.
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Edge Case Desk PnL
PROFIT
LOSS
Capital – known
Institutional Costs – known
Funding – sometimes unknown
I When there are no bond-CDS, or swap-CCDS bases, PnL is negative
I Default timing produces unfinessable PnL volatility requiring Economic capital
I Market Risk, CCR, IM, unavoidably costly
I Non-zero haircuts produce unfinessable losses conditional on survival1
1 Absent controllable recovery rates on own-issued bonds, which are problematic even in theory.
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Theorem 2: NMPwHC
Theorem (No Market Positions with Holding Costs)
If a market has assets with zero holding costs, and assets with strictly
positive holding costs, then there are no positions in assets with
positive holding costs.
Proof.
Trivial. Assuming economic agents are value maximizing, they will never hold positions that lose
money if there is an alternative.
I Markets with holding costs have familiar examples in commodity markets with storage costs
(e.g. gas). It is no accident that usual storage-cost-positive commodity strategies involve not
holding physical commodity positions, i.e. futures contracts.
I Here markets are different: participants can only hold physical positions.
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Corollaries
Corollary (No Complete Market with Holding Costs)
A complete market with holding costs is empty.
Corollary (Capital Market Empty)
Any market with mandatory capital requirements and positive capital costs is empty.
Corollary (Institutional Market Empty)
Any market with institutional costs is empty.
Corollary (Funding Market Empty)
Any market with funding requirements is empty.
Corollary (Risky Market Empty)
Any risky market with positive capital costs is empty.
These corollaries derive from Theorem 1 [NMPwHC] and our analysis of edge cases.
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Desks are Inherently Risky
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Risky markets with capital and institutional markets are
incomplete, and theoretically empty
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Therefore a desk can be a riskless portfolio only if it is empty
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Hence all existing desks are risky
This last statement will appear blindingly obvious to all practitioners2 .
However, it is necessary to provide the theoretical background in
order to place FVA on a sound academic footing.
2 Check
,
Dilbert.
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Trading Desks are Businesses
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If value-maximizing agents never trade how do desks exist?
Need additional assumptions about competitive advantages
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Skills
Barriers to entry: reputation; networks; systems; legal and
regulatory approvals
Rents, e.g. from monopoly position (only dealer in x)
Synergy with existing organization
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These competitive advantages form a business model
I
The business model will be more, or less, risky depending on the
robustness of the business model
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Counterparties do not Face Desk Risks
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Executives set up new desks, or close existing ones, with
changes in economic conditions
Many examples 2000-6 and 2008-onwards
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Structured credit desks post-2008; structured credit desks 2013
Fixed Income: “planned to eliminate most of its fixed-income
businesses because they had become unprofitable.”
Commodities: “The bank is in the process of selling its physical
commodity arm in the face of rising regulatory pressure”
Wealth: “will stop offering wealth management services in about
130 countries by 2016”
Usually a desk can be closed without the bank failing
Desk risk 6= Bank risk
I
,
Desks must nevertheless pay the bank for the risks the desks
take on
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Aside: FVA vs DVA
I
When a desk is the whole bank then these have incomplete
overlap
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Incomplete because funding is a separate risk to credit (aka
capital) within business model — see later
Usual to analyze risky projects as stand-alone entities within firm
Paradoxical implication is that interaction effects dominate
stand-alone-within-firm calculation
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Desks’ Risk Quantification
DVA
FVA (c/p)
Capital (c/p)
Desk
Bank Risk
Desk Risk
Counterparty
Capital (desk)
FVA (desk)
CVA
Bank
Systematic Risks
I
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Desk risk comes from the robustness of their business models
Observable risk components (not comprehensive):
I
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Institutional costs
Funding requirements (create PnL leaks, and may be unlimited)
Capital requirements
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Funding is a Separate Risk to Capital: PRA
Liquidity Coverage Ratio coming soon.
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Contingent Forward Funding is a Tesseract
Dimensions
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Expiry — (up to) when the funding is required
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Tenor — for (up to) how long
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Rate — at what price
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Volume — (up to) how much
Data Sources
,
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Basis swaps give forward Libor funding for up to 12M
I
Longer forward maturities: issued callable bonds; forward CDS
spreads
29/62
Minimum funding costs
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Current work (Burgard and Kjaer 2011; Burgard and Kjaer 2012;
Morini and Prampolini 2011; Hull and White 2012) typically takes
funding as a curve, as an input, and constant. (Piterbarg 2012) is
one exception w.r.t. collateral and (Pallavicini, Perini, and Brigo
2012) another w.r.t liquidity.
Theoretical approaches unworkable because:
I
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market incompleteness
do not include tenor-specific funding optimization (PIDE)
do not include capital costs of funding
I
Practically set by an optimal funding strategy (Kenyon and Green
2013b) for the bank
I
If the desk is the same as the bank then this will set minimum on
desk funding costs, because counterparty trade creates at least
this cost (and hence risk) to the desk.
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Step 5. Costs Set by Desk Risk
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As a risky project a desk must pay for its risks
Because the desk counterparties create the desk risks, they
must pay for those risks — despite symmetry, this is a condition
for trading
I
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Like a CDS — protection buyer pays
I
A desk need not pay for non-desk risks
I
Like a desk, a bank must have competitive advantages to be
viable. The first of which is a banking license.
I
In as much as the bank and its counterparty face the same
systematic (correlation=1) risks these will not be priced in as
there is no risk transfer
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Marking to Market
“Uncollateralized Market Price” is an Oxymoron
,
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An uncollateralized trade builds in the risks of both
counterparties therefore it is not fungible
I
“uncollateralized market price” of a trade is an oxymoron,
because this market can only ever involve the two original
counterparties
I
There is no market price for such transactions because there is
no market
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Risky Markets Summary
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Theoretically Capital is a real cost to desks
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Theoretically Funding is a real cost to desks
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Capital is legally required
Desks are inherently risky because they depend on their business
model to recover PnL leaks
IM legally required (now or soon depending on setup)
Repos are usually required to have non-zero haircuts
Funding is a separate risk to those covered by capital, and this is
enforced via liquidity buffers
Funding risk of a desk >> default risk to counterparty; i.e.
interaction effects dominate stand-alone analysis
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Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Regulatory-Optimal Funding
Regulations
Funding Optimization
Results
Summary
Conclusions
Bibliography
Appendix
Regulatory-Optimal Funding
I
Gaps in funding theory for pricing — and between theory and
practice
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Regulatory limits on funding strategies
Practical funding to address data and market issues
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Methodology evaluation using standard machine learning statistical
machinery
Optimizing funding parameters using P and Q
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,
Current work (Burgard and Kjaer 2011; Burgard and Kjaer 2012;
Morini and Prampolini 2011; Hull and White 2012) typically takes
funding as a curve, as an input, and constant. (Piterbarg 2012) is
one exception w.r.t. collateral.
Q is risk neutral measure (i.e. market implied)
P is physical measure
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Should you hedge funding costs?
Recall discussion on input costs in (Hull 2011):
1. Assume that different banks have different (funding) costs
2. Bank A hedges its (funding) costs
3. General market climate improves and the systematic part of
funding costs decreases for all banks
4. Treasurer of Bank A must now explain to the CEO and the Board
why Bank A is losing money relative to its competitors when
offering similar prices for similar products
Thus (funding) hedging decisions should always be at Board level
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Funding: Theory vs Practice
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Cost of funding? Ask Treasury.
I
Where does Treasury get the cost from?
Let’s assume that Treasury can borrow at Libor flat
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May be O/N + credit + liquidity, but this is sufficient for now as a
model for a ”typical major bank”
Some cash may be at repo, e.g. Gilts, but not for derivatives ...
unless these are repackaged into a repo’able security via internal
trades
Is this the cost of funding?
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PRA Liquidity Stress
,
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Model Setup
I
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Funding volume is always the same whatever the funding roll
39/62
I
In units of ∆ the number of times funding must be rolled to
horizon hn with roll length αn , nrolls (hn , αn ) is:
(
0
nrolls (hn , αn ) = l hn −αn m
αn −1
αn ≥ hn
otherwise
(1)
where: αn = α/∆; hn = h/∆.
I
Thus the gross excess funding Gef will be as a percentage:
Gef = 100 ×
,
nrolls
hn
(2)
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Average Expected Undiscounted Cost
Use the expected undiscounted funding cost C av as our primary metric because this is often used in
practice
C
av
t (α, h)
=

1 ‡
E min(α, h)Ft (t, t + min(α, h))
h t
+
nrolls
X
− ϕ∆Ft (t + i(α − ∆), t + ∆ + i(α − ∆))
i=1

+ min(α, h − i(α − ∆))Ft (t + i(α − ∆), t + min(i(α − ∆) + α, h))

(3)
Where:
Ft (t1 , t2 ) is the forward rate as seen from t between t1 and t2 ;
if nrolls < 1 then there are no terms in the summation;
‡ measure used in the expectaion (P, Q, or some combination).
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Optimization Problem
I
myopic version of our optimization problem based on Equation 3
is:
C av t,opt (h) = min C av t (α, h)
(4)
I
myopic as we are only permitted to chose α once, at the start.
I
Equation 4 is a non-linear, non-convex, optimization problem
because of the minimum terms in Equation 3.
I
To get some idea of solution character we assume a linear
(continuously compounding) yield curve y (T ) with constants a, b:
α
y (T ) = a + bT
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Optimal Q Funding
Proposition
Given a linear input yield curve (a > 0, b) the regulatory-optimal
Q-funding strategies with horizon h are:
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a > 0, ϕ = 1: all funding strategies are equivalent;
I
a > 0, a + bh > 0, ϕ < 1: Term funding;
I
a > 0, a + bh < 0, ϕ < 1: Shortest possible.
43/62
Optimal P Funding
Proposition
Given a linear input yield curve (a > 0, b) the regulatory-optimal
P-funding strategies where P=CONSTANT yield curve, with horizon h
are:
,
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a > 0, b > 0, ϕ = 1: Shortest possible;
I
a > 0, b > 0, ϕ < 1: Neither the shortest nor Term funding are
always optimal;
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a > 0, b < 0: Term funding;
44/62
P-optimal vs Q-optimal
,
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Strikingly, the Q-optimal and P-CONSTANT-optimal strategies are
almost opposite.
I
Most realistic case is perhaps where there is a bid-ask spread
and then the P-CONSTANT-optimal strategy is intermediate.
I
P-CONSTANT-optimal strategy is not even present within the
Q-optimal strategies.
I
CONSTANT case is not as restrictive as it may appear. Really
comparing baseline change with the differential of the yield curve.
45/62
1Y Spot Deposit Curves
BP
EU
0.10
0.05
0.08
0.04
0.06
0.03
0.04
0.02
0.02
0.01
1995
2000
2005
2010
0.00
1995
2000
JP
2010
2005
2010
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.05
0.04
0.03
0.02
0.01
0.00
2005
US
1995
2000
2005
2010
1995
2000
.
,
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Optimal Funding Costs? Theory and Practice
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Benchmark = expected value of perfect information (EVPI)
If you know the future what do you do?
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Compare with
I
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,
Still constrained by PRA liquidity rules
Can only trade on spot funding curve
Hedging
Assumptions (models) of future funding curve behavior
47/62
Machine Learning Statistical Machinery
Figure: Standard setup. We will identify the best funding curve predictor from
standard choices. Basically calibrate g() on next slide.
,
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Funding Curves
I Q : Risk Neutral
yRN (t0 , tf , τ )
=
yHistorical (t0 , τ )
dtRN (t0 , tf , τ )
=
τ
I EVPI
yEVPI (t0 , tf , τ )
=
yHistorical (tf , τ − (tf − t0 ))
dtEVPI (t0 , tf , τ )
=
τ − (tf − t0 )
I P : Constant
yConstant (t0 , tf , τ )
=
yHistorical (t0 , τ − (tf − t0 ))
dtConstant (t0 , tf , τ )
=
τ − (tf − t0 )
I P : Projected Base Rate
,
yPBR (t0 , tf , τ )
=
yHistorical (t0 , τ − (tf − t0 )) + g(t0 )(tf − t0 )
dtPBR (t0 , tf , τ )
=
τ − (tf − t0 )
49/62
Base Rate Predictors
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First model (almost) always Exponentially Weighted Moving
Average (EWMA): choose decay parameter λ
Refinements:
I
I
I
I
,
Limit gradient so that projected base rate does not go negative at
horizon
Apply threshold to calculated gradient: θ
Weight gradient between 0% and 100% of value: ω
Benchmark against EVPI
50/62
Setup
,
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Four major currencies analyzed together: BP, EU, JP, US
I
Minimum buffer ∆ = 1/12
I
Horizon h = 1
I
Bid-ask parameter ϕ = 0.75
51/62
Model Calibration & out-of-sample Performance
I
Best parameter set was: (λ, θ, ω) = (90days, 0.005, 0.3)
I
Average performance in bps funding cost over horizon h = 1Y
(bps)
Q vs EWMA
T-Test
EWMA vs EVPI
%-efficient
I
,
BP
13
E-25
16
44%
EU
22
E-27
15
59%
JP
10
E-45
4
71%
US
19
E-37
15
56%
Out-of-sample model test achieves significant gains versus
hedging over test period (series lifetime minus 5 years =
calibration/selection period).
52/62
Summary
I
Derivative funding requires forward funding surface, and forward
funding volatility tesseract: these pose practical issues
I
PRA and Basel III liquidity requirements change funding costs
Regulatory-optimal funding in can be run as a
machine-learning-type exercise to avoid practical market data
and completeness issues
I
I
I
,
Out-of-sample EWMA-based funding optimization achieved 44% to
71% of possible gains to EVPI from Q-hedging
T-Test levels of p < 0.00001 significance versus Q-hedging.
53/62
Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Regulatory-Optimal Funding
Conclusions
Bibliography
Appendix
Conclusions
,
I
Regulations have costly, asymmetric, and idiosyncratic effects:
this mean that market participants see no common risk-neutral
measure
I
Desks are risky and rely on competitive advantage to price in the
costs of their risks which include funding (buffers + options) and
capital
I
Funding, as an input cost, is a relatively unexplored area where
there is great potential
55/62
Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Regulatory-Optimal Funding
Conclusions
Bibliography
Appendix
BCBS-128 (2006, June). International Convergence of Capital Measurement and Capital Standards. Basel Committee for Bank
Supervision.
BCBS-189 (2011). Basel III: A global regulatory framework for more resilient banks and banking systems. Basel Committee for Bank
Supervision.
BCBS-193 (2011, July). Revisions to the Basel II market risk framework: updated as of 31 December 2010. Basel Committee for Bank
Supervision.
BCBS-219 (2012). Fundamental review of the trading book — consultative document. Basel Committee for Bank Supervision.
BCBS-254 (2013). The non-internal model method for capitalising counterparty credit risk exposures - consultative document. Basel
Committee for Bank Supervision.
Burgard, C. and M. Kjaer (2011). Partial differential equation representations of derivatives with bilateral counterparty risk and funding
costs. The Journal of Credit Risk 7, 75–93.
Burgard, C. and M. Kjaer (2012). Generalised CVA with Funding and Collateral via Semi-Replication. SSRN.
Cerný, A. (2009). Mathematical Techniques in Finance: Tools for Incomplete Markets, (2nd edition). New York: Princeton University
Press.
EBA (2013). On prudent valuation under Article 105(14) of Regulation (EU) 575/2013. Technical report, European Banking Authority.
EBA-CP-2013-28.
Hull, J. (2011). Options, Futures and Other Derivatives, 8th Edition. New Jersey: Prentice Hall.
Hull, J. and A. White (2012). Is FVA a Cost for Derivatives Desks? Risk 25(9).
Jouini, E., P.-F. Koehl, and N. Touzi (1997). Incomplete markets, transaction costs and liquidity effects. European Journal of Finance 3,
325–347.
Kabanov, Y. and M. Safarian (2010). Markets with transaction costs. Springer.
,
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Kaido, H. and H. White (2009). Inference on Risk Neutral Measures for Incomplete Markets. Journal of Financial Econometrics 7(3),
199–246.
Kenyon, C. and A. Green (2013a). CDS pricing under Basel III: capital relief and default protection. Risk 26(10).
Kenyon, C. and A. Green (2013b). Regulatory-Optimal Funding. arXiv . http://arxiv.org/abs/1310.3386.
Morini, M. and A. Prampolini (2011). Risky Funding: A Unified Framework for Counterparty and Liquidity Charges. Risk 24(3).
Pallavicini, A., D. Perini, and D. Brigo (2012). Funding, Collateral and Hedging: uncovering the mechanics and subtleties of funding
valuation adjustments. SSRN. http://ssrn.com/=2161528.
Piterbarg, V. (2012). Cooking with collateral. Risk 25(8), 58–63.
Shreve, S. (2004). Stochastic Calculus for Finance, Volume II: Continuous-Time Models. Springer-Verlag.
Tuckman, B. (1992). Arbitrage with holding costs: a utility-based approach. Journal of Finance 47(4).
,
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Applied Quantitative Finance
The credit and sovereign debt crises have fundamentally changed the
way participants in the global financial markets perceive credit risk.
In market practice this is most directly visible from significant bases
throughout the interest rate world, especially tenor bases, crosscurrency bases, and bond-cds bases. This means that the curve used
for discounting is no longer the curve used for Libor (aka Fixing Curve
or Forwarding Curve). In the last two years a consensus has emerged
that this multi-curve pricing is now standard.
Discounting, Libor, CVA and Funding: Interest Rate and Credit Pricing is
the first book to illustrate new ways of pricing interest rate and credit
products in the post-crisis markets. Written by two seasoned practitioners, it will enable the readers to understand the many different
versions of credit and basis spreads, and to build the appropriate
discount curves that take the these spreads into account so that
collateralized derivatives will be priced correctly. The authors guide
the reader through the complexity added by OIS discounting and
multi-curve pricing as well as CVA, DVA and FVA.
Derivatives do not exist in a vacuum. Regulators world-wide have
reacted strongly to the crises with the introduction of Basel III.
Hitherto quants could ignore capital costs and charges, but as of
January 2013 this world is gone. Discounting, Libor, CVA and Funding
explains details of Basel III that are important for pricing, especially
around the CVA VaR and default exposure capital charges.
90101
9 781137 268518
www.palgrave.com
Printed in Great Britain
ISBN 978-1-137-26851-8
DISCOUNTING,
LIBOR, CVA
AND FUNDING
Interest Rate and Credit Pricing
Chris Kenyon
Roland Stamm
This book will be required reading for quantitative practitioners who
need to keep up-to-date with the latest developments in derivatives
pricing, and will also be of interest to academic researchers and students
interested in how instruments are priced in practice.
DISCOUNTING, LIBOR, CVA AND FUNDING
The crises have also altered the perception of banks and governments
– they are no longer regarded as zero-risk counterparties. Now both
sides of an uncollateralized trade need to consider, and price in, the
risk that the other defaults: my CVA is your DVA. Even collateralization does not remove pricing problems: when you post collateral how
much do you have to pay for it? This FVA is not symmetric in many
ways: whatever it costs you to source it, your counterparty will only
pay you OIS. Even worse is that your funding costs are unlikely to be
the same as those of all your counterparties.
Dr. Chris Kenyon (London, UK) is a Director
at Lloyds Banking Group in the front office
Quantitative Research ñ CVA / FVA group.
Previously he was head quant for counterparty
risk at Credit Suisse, and at DEPFA Bank PLC he
was Head of Structured Credit Valuation (post
crisis), working on pricing model development
and validation, and market risk. He has also held
positions at IBM Research, and Schlumberger
where he applied real options pricing to everything from offshore rig lease extension options
to variable volume outsourcing contracts.
Chris holds a PhD in Applied Mathematics from
Cambridge University where he was a Research
Fellow (Computer Modeling), and an MSc in
Operations Research from the University of
Austin, Texas. He is a regular writer and conference speaker, his papers have appeared in
Quantitative Finance, Risk Magazine, Operations
Research, IEEE Computer amongst others, and
presented at academic conferences and industry
meetings including those organized by Bachelier
Finance Society, WBS, Marcus Evans, Risk
Magazine, and many more.
Dr. Roland Stamm is Head of Risk Methods and
Valuation at HRE Group (formerly DEPFA Bank),
where he is responsible (among other things) for
the development of new pricing models, model
set up, validation and calibration, CVA adjustments and market risk methodology. He was
previously Head of Valuation at HRE Group, and
has also held positions as Head of Market Risk
Products, Head of IT Development and Project
Manager, all at DEPFA Bank. He holds a PhD in
Mathematics (Algebraic Topology) from the
Westfälische Wilhelms-Universität, Münster
where he was awarded a magna cum laude
for his thesis The K- and L- Theory of Certain
Discrete Groups, and received a master’s degree
in Mathematics from the Johannes-GutenbergUniversität, Mainz.
Chris Kenyon
Roland Stamm
20/06/2012 11:01
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Thanks for your attention — questions?
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Introduction
No Risk-Neutral Measure
Risky Markets and Derivative Holding Costs
Regulatory-Optimal Funding
Conclusions
Bibliography
Appendix
Appendix: Bond Edge Case
Desk purchases single Z-rated floating-rate bond (rate includes
CDS cost)
I Enters collateralized CDS on bond at zero cost
I Term repos bond plus CDS as package; pays for bond; puts
extra into riskless account
Effects
I Bond coupons+extra pay CDS premia and repo rate
I Bond+CDS repo has no Market Risk, no CVA Risk
I Collateralized CDS (designated CVA hedge so no Market Risk)
has economic risk from jump-to-default of CDS c/p
I Counterparty Credit Risk capital for margin period of risk on
collateralized trades and repo
I Economic risk from bond default time
I Institutional Costs; Leverage Ratio capital
Outcome
I With no bond CDS basis, desk leaks PnL
I
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