International Master Economics and Finance

International Master
Economics and Finance
Mario Bellia
bellia@unive.it
Pricing Derivatives using
Bloomberg Professional Service
03/2013
IMEF 2013
Bellia M.
IRS
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Summary
FRA
Plain vanilla swap
Amortizing swap
Cap, Floor, Digital Options and Dual Digital Options
Example: a real contract
OPTIONS
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Bellia M.
Call
Bull Spread
Bear Spread
Calendar Spread
Straddle
Strangle
Derivatives using Bloomberg
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Functions in Bloomberg
Two applications will be used in Bloomberg
to evaluate derivatives:
• SWPM <GO> Swap Manager
SWPM is the main interest rate derivatives pricing function in the
Bloomberg professional System, allowing users to price a wide
range of vanilla and exotic interest rate swaps, interest rate
options, swaptions and interest rate and hybrid structured notes.
• OVME <GO> Options Valuation
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Bellia M.
OVME is Bloomberg main pricing application for options on equity,
indexes, funds, bonds, bond futures and short term interest rate
futures.
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Part I
INTEREST RATE SWAP
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Forward Rate Agreement
A forward rate agreement (FRA) is an agreement that a
certain rate will apply to a certain principal during a certain
future time period
• FRAs are infinitely flexible over-the-counter instruments
(OTCs), as they can be structured to mature on any
date. In general, FRAs are traded on the future level of
3 or 6 month Libor (Euribor). An FRA is an Off Balance
Sheet instrument.
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How to price a FRA
FRAs can be valued in SWPM as:
• a Spot start
• IMM date (International Money Market) third Wednesday of
March, June, September and December
• Broken date (customized Start and end dates)
Example:
Suppose you enter in a FRA today, receiving a fixed rate for a 3month period, starting in 3 months.
Principal: 1.000.000 €
Rate: 0.18%
Today: March 14, 2013
Effective: June 18, 2013
Maturity: Sept 18, 2013
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How to price a FRA
Lender receives difference of 0.18% and reset rate in 3 Months
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Plain vanilla Swaps
A plain Vanilla interest rate swap is an agreement between
two counterparties to exchange cash flows (Fixed vs. Float)
in the same currency. The payments are made during the
life of the swap in the frequency that was pre-established.
In an interest rate swap the principal is not exchanged
Used to convert a liability from
– fixed rate to floating rate
– floating rate to fixed rate
With SWPM, one can configure many details of the deal,
such as Dates, amortization scheme, start and end of a
single payment…
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Valuation of Swaps
• The standard approach is to assume that
forward rates will be realized
• This works for plain vanilla interest rate and
plain vanilla currency swaps, but does not
necessarily work for non-standard swaps
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How to price a plain vanilla Swaps
Run SWPM EUR <GO>
In order to display SWPM in EURO currency.
Enter the details of the IRS, in our example:
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IMEF 2013
Bellia M.
Notional 1.000.000,00€
Receive Fixed 0.577075%
Pay Float rate EURIBOR 6M
Contract starts March 18, 2013
Maturity is March 18, 2016 (3Y)
Payments are quarterly (in advance)
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How to price a plain vanilla Swaps
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Example of the Book
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An agreement by Microsoft to receive 6-month LIBOR & pay a
fixed rate of 5% per annum every 6 months for 3 years on a
notional principal of $100 million
---------Millions of Dollars--------LIBOR FLOATING
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FIXED
Net
Date
Rate
Cash Flow Cash Flow Cash Flow
Mar. 5, 2007
4.2%
Sept. 5, 2007
4.8%
+2.10
–2.50
–0.40
Mar. 5, 2008
5.3%
+2.40
–2.50
–0.10
Sept. 5, 2008
5.5%
+2.65
–2.50
+0.15
Mar. 5, 2009
5.6%
+2.75
–2.50
+0.25
Sept. 5, 2009
5.9%
+2.80
–2.50
+0.30
Mar. 5, 2010
6.4%
+2.95
–2.50
+0.45
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Example of the Book
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Example of the Book
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Amortizing swap
• Can be either Fixed-versus-Float or Float-versusFloat.
• Both counterparties make interest payments that
either are declining (amortizing) or accreting
(increasing) over the life of the deal.
Example:
Notional 75.000,00€
Pay Fixed 4. 75%
Receive Float EURIBOR 3M
Contract starts April 11, 2008
Maturity is April 11, , 2015 (7Y)
Payments frequency: quarterly
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Amortizing swap
Amortization
scheme:
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Notional
Start
End
Days
75'000,00
72'322,00
69'644,00
66'966,00
64'288,00
61'610,00
58'932,00
56'254,00
53'576,00
50'898,00
48'220,00
45'542,00
42'864,00
40'186,00
37'508,00
34'830,00
32'152,00
29'474,00
26'796,00
24'118,00
21'440,00
18'762,00
16'084,00
13'406,00
10'728,00
8'050,00
5'372,00
2'694,00
11/04/2008
11/07/2008
13/10/2008
12/01/2009
14/04/2009
13/07/2009
12/10/2009
11/01/2010
12/04/2010
12/07/2010
11/10/2010
11/01/2011
11/04/2011
11/07/2011
11/10/2011
11/01/2012
11/04/2012
11/07/2012
11/10/2012
11/01/2013
11/04/2013
11/07/2013
11/10/2013
13/01/2014
11/04/2014
11/07/2014
13/10/2014
12/01/2015
11/07/2008
13/10/2008
12/01/2009
14/04/2009
13/07/2009
12/10/2009
11/01/2010
12/04/2010
12/07/2010
11/10/2010
11/01/2011
11/04/2011
11/07/2011
11/10/2011
11/01/2012
11/04/2012
11/07/2012
11/10/2012
11/01/2013
11/04/2013
11/07/2013
11/10/2013
13/01/2014
11/04/2014
11/07/2014
13/10/2014
12/01/2015
13/04/2015
91
94
91
92
90
91
91
91
91
91
92
90
91
92
92
91
91
92
92
90
91
92
94
88
91
94
91
91
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Amortizing swap
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Amortizing swap
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Caps and Floors
• A cap is a portfolio of call options on a reference
interest rate (i.e EURIBOR or LIBOR).
• It has the effect of guaranteeing that the interest rate
in each of a number of future periods will not rise
above a certain level
• Each call is called “caplet”, so a cap is a portfolio of
“caplets”
• A floor is similarly a portfolio of put options.
• For this (and others) derivatives, one of the input is
the volatility, that can be choose between flat
volatility (manual input) and VCUB volatilities.
(VCUB is available hitting VCUB <GO>)
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Derivatives using Bloomberg
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Caps and Floors
Example:
Notional 10.000.000,00€
Receive Fixed 0.577075%
Pay Float rate EURIBOR 6M
Contract starts March 18, 2013
Maturity is March 18, 2016 (3Y)
Payments are quarterly (in advance)
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Caps and Floors
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Caps and Floors
In order to change from Cap to Floor, select the
appropriate deal from the dropdown menu:
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Derivatives using Bloomberg
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Digital options
• An option whose payout is fixed after the underlying
exceeds the predetermined threshold or strike price. It is
also referred to as "binary" or "all-or-nothing option."
A digital cap is a cap option that provides a payoff of specified
coupon R% when strike K <= the floating rate.
A digital floor is a floor option that provides a payoff of specified
coupon R% when strike K >= the floating rate.
• Digitals provide the buyer with a fixed payout profile. This
means that the buyer receives the same payout
irrespective of how far above or below the Index reaches
in relation to the strike.
• Digitals are cheaper to buy than standard options.
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Derivatives using Bloomberg
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Digital options
Digital cap
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0.5% when strike 2% <= the floating rate.
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Digital options
Digital floor
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Bellia M.
0.5% when strike 2% >= the floating rate.
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Dual Digital options
• The receiver of this exotic payoff will obtain either of
2 alternative payoffs decided upfront.
• The payoff to be received at each coupon date will
depend from the level of the observation index
immediately before the coupon payment date:
a)
b)
If the index is above a pre-determined level (barrier), an “A)”
payoff will be paid.
If the index is below a pre-determined level, a “B)” payoff will
be paid
The two payoff can be either fixed rate, float rate, float rate minus
(or plus) a spread.
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Dual Digital options
Example:
• Notional 75.000,00€
• Barrier 0.5%
• Reference rate: EURIBOR 6M
• Contract starts March 18, 2013
• Maturity March 18, 2016 (3Y)
• Payments are quarterly (in advance)
Payoff
a) If EUR6M >= Barrier
b) If EUR6M < Barrier
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EUR6M + 0.5%
Fixed rate 0.32%
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Dual Digital options
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In Arrears Swap
• Rate is observed at time ti and paid at time ti rather
than time ti+1
• It is necessary to make a convexity adjustment to
each forward rate underlying the swap
• Suppose that Fi is the forward rate between time ti
and ti+1 and i is its volatility
• We should increase Fi by
Fi 2
2
i
(ti 1 ti )ti
1 Fi i
when valuing a in-arrears swap
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Example of a contract
Company Alpha decide to join a IRS with Bank Beta.
(Notional is 1.500.000,00€)
BANK PAYS:
-
From March 28, 2006 to March 28, 2007
EURIBOR 6M
From March 28, 2007 to March 28, 2009
EURIBOR 6M if EURIBOR 6M is less than 3.85%
4.35% if EURIBOR 6M is greater or equal to 3.85%
ALPHA PAYS
-
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From March 28, 2006 to March 28, 2007
EURIBOR 6M minus spread 0,1% with a max of 6,75%.
From March 28, 2007 to March 28, 2009
If EURIBOR 6M will be less than 3.85%, the rate will be 3,45%.
If EURIBOR 6M will be greter or equal than 3.85%, rate will be
EURIBOR 6M with a max of 6.75%
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Example of a contract
BANK PAYS:
From March 28, 2006 to March 28, 2007
EURIBOR 6M
ALPHA PAYS
From March 28, 2006 to March 28, 2007
EURIBOR 6M minus spread 0,1% with max of 6,75%.
From March 28, 2007 to March 28, 2009
From March 28, 2007 to March 28, 2009
EURIBOR 6M if EURIBOR 6M is less than 3.85%
If EURIBOR 6M less than 3.85%, the rate will be 3,45%.
4.35% if EURIBOR 6M is greater or equal to 3.85% If EURIBOR 6M greter or equal than 3.85%, rate will be
EURIBOR 6M with a max of 6.75%
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Bank Flows (Period 1)
EURIBOR 6M
Alpha Flows (Period 1)
EURIBOR 6M - 0,10%
with a max of 6.75%
EUR 6M
EUR 6M
-0.10%
max (EU-6.85%;0)
Floating Rate
Floating Rate
Spread
- Cap
Bank Flows (Period 2)
EUR 6M if EUR6M < Barrier 3,85%
4,25% if EUR6M >= Barrier 3,85%
Alpha Flows (Period 2)
3.45% if EUR6M < Barrier 3,85%
EUR 6M if EUR6M >= Barrier 3,85%
with a max of 6.75%
EUR 6M
0.40% se EU>=3.85%
MAX(EU-3.85%;0)
EUR 6M
MAX(3.85%-EU;0)
0.40% se EU<3.85%
MAX(EU-6.75%;0)
Floating Rate
+ Digital Cap
- Cap
Floating Rate
Floor
- Digital Floor
- Cap
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Example of a contract - Payoff
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Example of a contract - Valuation
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Example of a contract - Valuation
Expected Flows (discounted)
Bank
Floating rate
Period
1
45'996,75
Digital Cap
-cap
2
2
3468,76
-5780,97
tot
Alpha
Float rate - spread
-cap
Floor
-Digital Floor
-Cap
43'684,54
Period
1
1
2
2
2
44'510,69
0,00
14'481,42
-7'858,61
-137,31
tot
Valuation
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50'996,19
-7'311,65
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Example of a contract:Multi Leg Deal
Expected Flows (discounted)
Bank
Digital Cap
-cap
Period
2
2
3468,76
-5780,97
tot
Alpha
Floor
-Digital Floor
-Cap
-2'312,21
Period
2
2
2
14'481,42
-7'858,61
-137,32
tot
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6'485,49
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Valuation
-8'797,70
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Other swaps
Floating-for-floating interest rate swaps,
step up swaps, forward swaps, constant
maturity swaps, compounding swaps,,
accrual swaps, diff swaps, cross currency
interest rate swaps, equity swaps,
extendable swaps, puttable swaps,
swaptions, commodity swaps, volatility
swaps……..
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Part II
OPTIONS
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Option Types
• A call is an option to buy
• A put is an option to sell
• A European option can be exercised only at the
end of its life
• An American option can be exercised at any time
Assets Underlying
Exchange-Traded Options
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Stocks
Foreign Currency
Stock Indices
Futures
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Call and Put Options Profits
Long Call
Buy one European call option:
price = $5
strike price = $100
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Short Call
Write one European call option:
price = $5
strike price = $100
Long Put
Short Put
Buy one European put option:
price = $7
strike price = $70
Write one European put option:
price = $7
strike price = $70
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OVME: basic settings
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Underlying: indicate the desired Equity ticker followed by the Equity
key, Index ticker followed by Index key, or Fund, ETFs and Hedge
Funds ticker followed by Equity key.
Direction: indicate 'B' for Buy, 'S' for Sell.
Style: specific kind of option
Exercise: indicate 'AM' for American, 'EU' for European.
Call/put and Strike Level: Indicate 'C' for Call, 'P' for Put
Strike Moneyness: Indicate Strike in % Moneyness.o A indicates At
the Moneyo nI indicates n% In the Moneyo nO indicates n% Out of
the Money
Expiry Date: Expiry date can be any date in the future.
Number of shares: The letter ‘N’ (number of shares) with a number
(you can abbreviate ‘K’ for thousand, ‘M’ for million.
Model: for standard vanilla contract, can be BS Continuous , BS
Discrete, Local Vol, Trinomial (see methods, next slide)
Volatility: BVOL (Bloomberg Surface) or Historical
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Methods used to price an option
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Single leg (or vanilla deal)
• First of all, select the underlying (Stocks, Stock
Indices, Foreign Currency, Futures..)
• Then, run OVME SL <GO> to a single leg deal.
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Example
Underlying: UNICREDIT
Deal: EUROPEAN CALL OPTION
Price Today: 3,806
Strike price: 4,4
Expire: May 14, 2013 (60 days)
Position in shares: 100
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Historical Line chart of underlying
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Valuation of a European Call
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Trading Strategies Involving Options:
Types of Strategies
• Take a position in the option and the
underlying
• Take a position in 2 or more options of the
same type (spread)
• Take a position in a mixture of calls & puts
(combination)
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Spreads Options in Bloomberg
Strategies involving spreads (i.e. same type of
options) are available in:
Products - Options Strategies - Call/Put Spread
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Bull Spread Using Calls
Buy a Call Option with a certain strike price and sell
a call option with a higher strike, on the same
underlying.
View: price increase
Example
Underlying: UNICREDIT
Deal: EUROPEAN CALL OPTIONS
Price Today: 3,806
Strike price BUY: 3,807
Strike price SELL: 4,400
Expire: May 14, 2013 (60 days)
Position in shares: 100
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Bull Spread Using Calls
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Bear Spread Using Puts
Buy a put with a certain strike price and sell a put
with a lower strike, on the same underlying.
View: price decline
Example
Underlying: UNICREDIT
Deal: EUROPEAN PUT OPTIONS
Price Today: 3,806
Strike price BUY: 4,400
Strike price SELL: 3,807
Expire: May 14, 2013 (60 days)
Position in shares: 100
IMEF 2013
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Bear Spread Using Puts
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Calendar Spread using calls
Options have the same strike price, but different
expiration dates.
Strategy is sell a call and buy
one with a longer maturity
Example
Underlying: UNICREDIT
Deal: Calendar Spread
Price Today: 3,806
Strike price : 4,000
Expire 1: May 14, 2013 (60 days)
Expire 2: July 14, 2013 (120 days)
Position in shares: 100
IMEF 2013
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Calendar Spread using calls
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Straddle
Buy a call and a put with the same strike price and
expiration date.
Appropriate if a large move of
the price is expected, but the
direction is unknow.
Example
Underlying: UNICREDIT
Deal: STRADDLE
Price Today: 3,806
Strike price : 4,000
Expire 1: May 14, 2013 (60 days)
Position in shares: 100
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Straddle
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Strangle
Buy a call and a put with the same expiration date
but different strike price.
Appropriate if a large move of
the price is expected, but the
direction is unknow. The call
strike is higher than the put
strike.
Example
Underlying: UNICREDIT
Deal: STRADDLE
Price Today: 3,806
Strike price CALL : 4,400
Strike price PUT: 3,870
Expire 1: May 14, 2013 (60 days)
Position in shares: 100
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Strangle
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Strategies
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Styles
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Structured notes
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