Titre de la prsentation sur 4 lignes maximum

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Master Finance ENPC
February 2006
Interest Rate Investment Products
Rédouane Guerouani redouane.guerouani_at_calyon.com
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Table of Contents

• About Calyon p3
• The Structured Notes Market p7
• The Client Perspective p9
• The Quantitative Research Perspective p11
• Products
• Models
• Numerical Methods
• Examples of Structured Notes p22
• Fixed rate structures
• Capped floaters
• Libor range accrual structures
• Reverse floaters
• Callable Spread Options
• Target redemption inverse floaters
• Next generation

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A
bout Calyon
4
Crédit Agricole Organization

• Calyon the investment and corporate banking arm
  of Crédit Agricole Group
• Calyon is the result of the April 2004 merger of
  Crédit Agricole and Crédit Lyonnais, two of
  Frances largest financial institutions.

CREDIT AGRICOLE GROUP
RETAIL BANKING ACTIVITIES
CORPORATE AND INVESTMENT BANKING ACTIVITIES
Crédit Agricole
Crédit Lyonnais
5
Crédit Agricole Group A banking giant with a
global footprint
6
A comprehensive and well-balanced International
network,covering over 60 countries
Europe Top 10 Corporate
Investment Banks in Euroland
500
4 300
4 700 (France)
Asia / Pacific Top 5 foreign banks with a
powerful network of 13 countries
Czech Republic Hungary Poland Russia Slovakia Ukra
ine
Americas A strong foothold
professionals 1 450
2 450
Canada

• China
• Beijing
• Shanghai
• Guangzhou
• Tianjin
• Xiamen
• Hong Kong
• India
• Mumbai
• Delhi
• Chennai
• Hamedabad
• Indonesia
• Korea
• Malaysia
• Philippines
• Singapore
• Taiwan
• Thailand

• Japan
• Tokyo
• Osaka

Capital Markets and Loan Syndication operate out
of a dual Paris/London platform

• United States
• New York
• Chicago
• Dallas
• Houston
• Los Angeles

Africa A full- range of services
600
Algeria Morocco Tunisia Cameroon Gabon Ivory
Coast Madagascar Republic of Congo Senegal South
Africa
Bahrain Djibouti Egypt Iran Israel Lebanon Saudi
Arabia BSF Turkey United Arab Emirates Yemen
Mexico
Venezuela
Brazil
Uruguay
Argentine
Australia
Chile
Three renowned and powerful brokers enhance
Calyons global reach
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T

• he Structured
• Notes Market

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Strong Growth in Structured Notes Market

• ? 2003 sets a new record in the
• Structured Investment Products
• Market ? 116Bn of Structured
• EMTN issued as of December 03
• (100 / 01 and 20 / 02)-Source mtn-I
• ? Various reasons behind the continuous growth of
  the market
• ? Yield enhancement in a low interest rate
  environment.
• ? Capital Protection in highly volatile
  environment (i.e. Capital Protected Notes)
• ? Risk diversification, access to new asset
  classes and regulatory constraints
• ? Products designed to satisfy needs of
  increasingly sophisticated investors

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How we do it
INVESTOR
Our main focus
Funds
Packaged EMTN
StructuredCoupon
CALYON,the arranger
Floating rateFunding Level
ISSUER
StructuredCoupon
Issue swap
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Issuer / Arranger Involvement

• The Issuer
• is the actual borrower
• provides the capital guarantee
• the Issuers rating does affect the coupon of
  the Notes ie the higher the Issuers ratings the
  lower the coupon
• some Issuers have preferences for Notes that are
  callable, hence making coupons on such Notes more
  attractive

• The Arranger
• provides the structured idea to the investor
• provides the structured coupon to the Issuer via
  a swap (the Issue Swap)
• manages the market risk linked to the structure

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How we do it
Our main focus
CLIENT
SALES
TRADING DESK
STRUCTURATION
Quantitative Research Team
CALYON
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Structured Products offered by Calyon

• FX Linked Notes / Yield Enhanced Deposits
• Products can be offered on most currencies (USD,
  EUR, JPY, GBP, )
• Dual-Currency Notes, Corridors, FX Range Accrual
  Notes,
• Interest-Rate Linked Notes
• Products can be offered in core currencies (USD,
  EUR, JPY, HKD, GBP)
• Callable, Capped Floaters, Reverse Floaters,
  Range Accruals, CMS-linked
• Structured Credit Products
• Credit Linked Notes (Single name,
  First-to-Default baskets)
• Cash and synthetic CDOs, Asset-backed securities.
• Equity Linked Notes
• Index Linked Notes, Notes linked to baskets of
  equities or single stocks
• Fund Linked Notes (Mutual or Hedge Funds)
• Commodity Linked Notes, Inflation, Weather Linked
  Notes

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Structured Products offered by Calyon

• Interest-Rate Linked Products
• European Options (vanillés, digitales , CMS,
  Corridors , )
• Bermudan Options
• Flexible (automatiques, triggers, chooser caps
  à  cartouches )
• Ratchet (path-dependent pay-off )
• Volatility Bond
• Spread Options
• Target Redemption Notes
• Snowball (Cancellable Ratchet)
• SnowRange (Cancellable Corridor Ratchet)
• PRDC, PRDKO
• Hybrids (Credit, FX, Equity, Commodities,
  Inflation, )

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M
odelisation
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Road Map
1. A model what for ? 2. Exotic
risk 3. Tutorial LGM 1 factor 4. Closed
Form Formulas and Numerical Methods 5. Other
Models
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What model for what product
PRODUCT
EXOTIC MODEL
NUMERICAL METHOD
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A Model what for?

• The client finances the purchase of ATM scenarios
  (or big coupons) by selling more complicated,
  out-of-the-money scenarios.
• Aside from certain free options in the book, we
  need in general to risk-manage all these options.
• The price of an exotic product depends on
• credit reserve
• model reserve
• trading margin
• sales margin (size, competitors, type of
  clients)
• The model computes the replication portfolio
  (swaps, caps, swaptions), i.e. the sensitivities
  each day.
• It projects the exotic product onto the vanilla
  world.
• Model calibration pricing risk engine

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Requirement for an Exotic Model

• Correct description of the risk (depends on the
  product)
• Digital risk
• Forward volatility risk
• Correlation risk
• Numerical efficiency for calibration (closed
  form)
• Pricing (PDE, trees, Monte-Carlo)
• Few meaningful parameters

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LGM 1 Factor

• LGM-1F properties
• Gaussian instantaneous forward rates
• ? The model is fully determined by the mean
  reversion ? and the deterministic volatility ?(t)
  (supposed piecewise constant)
• ? If the mean reversion is positive, forwards of
  long maturity will be less volatilile than
  forwards of short maturity.
• Lognormal discount factors

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LGM 1 Factor

• LGM-1F properties (continued)
• Gaussian short rate, mean reverting
• Forward Libors are shifted lognormal (constant
  1/coverage shift)
• structural skew of the model
• Thanks to the reconstruction formula, the whole
  dynamics of the curve can be summarized by a
  single gaussian state variable (e.g. the short
  rate)
• Analytical caplet and swaption prices
• PDE, Monte Carlo,

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Other Models

• HJM
• BGM
• Stochastic volatility models

22
E
xamples of Structured Notes
From the simple to the complex ...
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1
Simple Fixed Rate structures

• Description
• These structures allow an investor to earn a
  risk-less fixed rate coupon over the whole tenor
  of the investment.

• Risk / Reward profile
• low risk
• no enhanced return

• Attractive when
• steep yield curve

• Investor rationale
• simple structure
• coupon is known from beginning

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Simple Fixed Rate note

• Example a 5-year AAA note pays a fixed coupon
  of X.
• Assuming that the issuers funding level over 5y
  is Euribor-5bps, and that the 5y swap is trading
  at 2.66 at the time of closing, then the fixed
  rate paid by the note should be 2.61.
• The underlying swap will have the following form

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Multi-callable Fixed Rate note

• Example a 5-year AAA note pays a fixed coupon
  of 2.80. Moreover, the issuer can call note at
  par every 6 months.

• Underlying Swap
• In the underlying swap, the arranger has bought
  the right to cancel the swap at no cost every 6
  months, which enables him to give the investor a
  better rate.
• Stated differently, the arranger has bought an
  option to enter into the opposite swap where he
  pays Euribor - 0.05 and receives 2.80.
• The exercise dates for the option are every 6
  months (Bermudan option).

Multi-callable Payer swap Vanilla Payer Swap
Option to enter into Receiver Swap
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Multi-callable Fixed Rate note
Pricing Rationale Because the arranger is buying
the option, he should theoretically be paying a
premium. This premium will in fact be expressed
as an additional spread added on the Fixed Rate X
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2
Capped Floating Rate structures

• Description
• These structures allow investors to enjoy an
  extra spread above Pribor by agreeing to limit
  the overall coupons he receives to a pre-agreed
  Maximum Value.

• Risk / Reward profile
• low risk
• low enhanced return

• Investor rationale
• safe return
• opportunity cost if sharp rise in rates

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Capped Floating Rate structure
Example a 5-year AAA note pays a floating
coupon of Libor 0.50, subject to Max Cpn
3.50

• Underlying Swap
• In the underlying swap, the arranger receives
  LIBOR (funding) and pays LIBOR (coupon).
• The arranger also buys a Cap on the LIBOR which
  will guarantee that he will not pay above a
  certain level (the strike), thus the investor
  sells the cap.

Capped Floating Rate swap Floating/Floating
Swap Cap on the PRIBOR
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Capped Floating Rate structure

• Pricing Rationale
• Because the arranger is buying the Cap, he should
  theoretically be paying a premium.
• This premium will in fact be expressed as an
  additional spread added on the Floating Rate (in
  this case the 0.50) which the investor receives.

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Multi-callable Capped Floating Rate structure
Example a 5-year AAA note pays a floating
coupon of LIBOR 1, subject to a Maximum
Coupon of 4.50. Moreover, the issuer has the
right to call the note every 6 months.

• Underlying Swap
• As the capped floating rate structure, i.e. a
  swap with a cap
• Additionally, the arranger buys another option to
  enter into the opposite swap with a Cap.
• The option can only be exercised at specific
  times Bermudan

Multi-callable Capped Floating Rate swap
Floating/Floating Swap Interest Rate
Cap on PRIBOR Bermudan Option to
enter into the reverse swap
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Multi-callable Capped Floating Rate structure
Pricing Rationale Because of the additional call
option bought, the arranger should be paying an
additional premium. This premium will be
reflected in the higher spread compared to the
same non-callable version of the structure.
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Multi-callable Capped Floating Rate Structure

• Coupon 6m LIBOR 1
• Capped at 4.50
• NB 5y swap rate 2.66
• If the forward rates are achieved then the
  average rate paid would be 3.81, which is 1.15
  above the swap rate.
• This is compensated by the callability option
  that the arranger holds (and by the Cap price
  too).

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3
Libor Range Accrual structures

• Description
• These structures allow an investor to enjoy an
  enhanced fixed (or floating) return as long as
  the daily fixings of the reference index (eg.
  Libor) are within a pre-agreed range.

• Risk / Reward profile
• medium risk
• good enhanced return

• Investor rationale
• market forwards are over-valued
• index will stay within range

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5-Year Non-callable Range Accrual

• Issuer (A/A1) or better
• Amount EUR 10,000,000
• Maturity 5 Years
• Underlyings 6-month Libor
• Redemption100
• Re-offer 100

• Coupon SA, 30/360
• 1 (2.20 x n/N) with n number of days when
  6mL is within range.

Range     Y1 0 2.25               Y2 0
2.50               Y3 0 2.75              
Y4 0 3.00               Y5 0 3.25

This note is not callable.
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5-Year Callable Range Accrual

• Issuer (A/A1) or better
• Amount USD 10,000,000
• Maturity 5 Years
• Underlyings 6-month Libor
• Redemption100
• Re-offer 100

• Coupon SA, 30/360
• 3.30 x n/N with n number of days when 6mL is
  within range.
• Range    Y1 0 2.50
•               Y2 0 3.00
•               Y3 0 3.50
•               Y4 0 4.00
•               Y5 0 4.50
• CALL OPTION The notes are callable by the
  issuer after 6 months and every 6 months
  thereafter.

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4
Reverse Floater structures

• Description
• These structures allow investors to earn a coupon
  which increases with every drop in a given
  floating rate reference.

• Investor rationale
• hedge against stagnating or dropping rates
• rates will not rise very much

• Risk / Reward profile
• medium risk
• low enhanced return

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5-Year Non-callable Reverse Floater

• Issuer (A/A1) or better
• Amount USD 10,000,000
• Maturity 5 Years
• Underlyings 6-month Libor
• Redemption100
• Re-offer 100

• Coupon SA, 30/360
• Y1 Max 0 4.50 - 6mL
• Y2 Max 0 4.75 - 6mL
• Y3 Max 0 5.00 - 6mL
• Y4 Max 0 5.25 - 6mL
• Y5 Max 0 5.50 - 6mL
• This note is not callable

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5-Year Callable Reverse Floater

• Issuer (A/A1) or better
• Amount USD 10,000,000
• Maturity 5 Years
• Underlyings 6-month Libor
• Redemption100
• Re-offer 100

• Coupon SA, 30/360
• Y1 3.00
• Y2 Max 0 8.50 - 2 x 6mL fixings in arrears
• Y3 Max 0 9.00 - 2 x 6mL fixings in arrears
• Y4 Max 0 9.50 - 2 x 6mL fixings in arrears
• Y5 Max 0 10.00 - 2 x 6mL fixings in arrears
• CALL OPTION The notes are callable by the
  issuer after 6 months and every 6 months
  thereafter.

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Reverse Floater structures
Other variations
Step-up Reverse Floater Coupon Strike1 -
Libor for Y1, Strike2 - Libor for Y2, etc
... In this case the Floor that the arranger will
sell has variable strikes for each year.
Leveraged Reverse Floater Coupon Leverage
Factor x Strike - Libor In this case the
arranger will sell multiple Floors while still
only receiving one Libor funding.
Multi-callable Reverse Floater It is a Reverse
Floater structure where the arranger has the
right to cancel at no cost.
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5
Ladder Inverse Floating structures (Snowballs)

• Description
• These structures allow investors to earn a coupon
  which increases with every drop in a given
  floating rate reference. Moreover, each coupon
  will be a function of the previous coupon.
• The structure is usually callable by the issuer.

• Risk / Reward profile
• high risk
• high return

• Investor rationale
• rates will not rise as quickly as market thinks
• important to secure high coupon in beginning

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5-Year Snowball

• Issuer (A/A1) or better
• Amount USD 10,000,000
• Maturity 5 Years
• Underlyings 6-month Libor
• Redemption100
• Re-offer 100

• Coupon SA, 30/360
• Y1     3.25
• Y2     Max 0 Previous Coupon 2.25 - 6mL
  fixings in arrears
• Y3     Max 0 Previous Coupon 2.75 - 6mL
  fixings in arrears
• Y4     Max 0 Previous Coupon 3.25 - 6mL
  fixings in arrears
• Y5     Max 0 Previous Coupon 3.75 - 6mL
  fixings in arrears
• CALL OPTION The notes are callable by the
  issuer after 6 months and every 6 months
  thereafter.

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6
Target Redemption Inverse Floater notes

• Description
• These structures pay an inverse floater-type
  coupon. They redeem automatically once the total
  coupon paid reaches a Target value. They usually
  pay a very high first coupon.

• Risk / Reward profile
• very high risk
• very high return

• Investor rationale
• rates will not rise as quickly as market thinks
• important to secure high coupon in beginning

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Target Redemption Inverse Floater Notes
Example 7-year AAA Target Redemption Inverse
Floater pays a semi-annual coupon equal to Y1
8.00 Y2 to Y7 10.00 - 2 x LIBOR
6m Automatic Redemption if Total Coupon reaches
10.00

• Rationale
• If the coupon in the first semester of Year 2 is
  equal to 4.00 or more, then the note will redeem
  automatically and the investor would have made a
  10.00 return in 1.5 years.
• This means that the limit on the 6m PRIBOR is
• 10.00 - 2 x 6M PRIBOR 4.00 (which, when
  paid semi-annually, will give 2.00)
• hence solving for the W6M we get 6M PRIBOR
  3.00

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Target Redemption Inverse Floater Notes
Coupons Simulation using Market Forwards

• Y1 8.00
• Y2 to Y7 10.00 - 2 x LIBOR 6m
• Automatic Redemption if Total Coupon reaches
  10.00
• NB 2.5y swap rate 4.32 (interpolated)
• In the event that rates rise less than what the
  forwards are anticipating, then the coupon will
  fall.
• The investor could be locked in at a very low
  coupon for 7 years.