International Master Economics and Finance
Transcription
International Master Economics and Finance
International Master Economics and Finance Mario Bellia [email protected] Pricing Derivatives using Bloomberg Professional Service 03/2013 IMEF 2013 Bellia M. IRS • • • • • Summary FRA Plain vanilla swap Amortizing swap Cap, Floor, Digital Options and Dual Digital Options Example: a real contract OPTIONS • • • • • • IMEF 2013 Bellia M. Call Bull Spread Bear Spread Calendar Spread Straddle Strangle Derivatives using Bloomberg 2 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 IMEF 2013 Bellia M. OVME is Bloomberg main pricing application for options on equity, indexes, funds, bonds, bond futures and short term interest rate futures. Derivatives using Bloomberg 3 Part I INTEREST RATE SWAP IMEF 2013 Bellia M. Derivatives using Bloomberg 4 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. IMEF 2013 Bellia M. Derivatives using Bloomberg 5 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 6 How to price a FRA Lender receives difference of 0.18% and reset rate in 3 Months IMEF 2013 Bellia M. Derivatives using Bloomberg 7 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… IMEF 2013 Bellia M. Derivatives using Bloomberg 8 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 9 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: • • • • • • 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) Derivatives using Bloomberg 10 How to price a plain vanilla Swaps IMEF 2013 Bellia M. Derivatives using Bloomberg 11 Example of the Book • 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 IMEF 2013 Bellia M. 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 Derivatives using Bloomberg 12 Example of the Book IMEF 2013 Bellia M. Derivatives using Bloomberg 13 Example of the Book IMEF 2013 Bellia M. Derivatives using Bloomberg 14 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 15 Amortizing swap Amortization scheme: IMEF 2013 Bellia M. 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 Derivatives using Bloomberg 16 Amortizing swap IMEF 2013 Bellia M. Derivatives using Bloomberg 17 Amortizing swap IMEF 2013 Bellia M. Derivatives using Bloomberg 18 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>) IMEF 2013 Bellia M. Derivatives using Bloomberg 19 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) IMEF 2013 Bellia M. Derivatives using Bloomberg 20 Caps and Floors IMEF 2013 Bellia M. Derivatives using Bloomberg 21 Caps and Floors In order to change from Cap to Floor, select the appropriate deal from the dropdown menu: IMEF 2013 Bellia M. Derivatives using Bloomberg 22 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. IMEF 2013 Bellia M. Derivatives using Bloomberg 23 Digital options Digital cap IMEF 2013 Bellia M. 0.5% when strike 2% <= the floating rate. Derivatives using Bloomberg 24 Digital options Digital floor IMEF 2013 Bellia M. 0.5% when strike 2% >= the floating rate. Derivatives using Bloomberg 25 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. IMEF 2013 Bellia M. Derivatives using Bloomberg 26 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 IMEF 2013 Bellia M. EUR6M + 0.5% Fixed rate 0.32% Derivatives using Bloomberg 27 Dual Digital options IMEF 2013 Bellia M. Derivatives using Bloomberg 28 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 29 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 - IMEF 2013 Bellia M. 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% Derivatives using Bloomberg 30 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% IMEF 2013 Bellia M. 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 Derivatives using Bloomberg 31 Example of a contract - Payoff IMEF 2013 Bellia M. Derivatives using Bloomberg 32 Example of a contract - Valuation IMEF 2013 Bellia M. Derivatives using Bloomberg 33 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 IMEF 2013 Bellia M. 50'996,19 -7'311,65 Derivatives using Bloomberg 34 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 IMEF 2013 Bellia M. 6'485,49 Derivatives using Bloomberg Valuation -8'797,70 35 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…….. IMEF 2013 Bellia M. Derivatives using Bloomberg 36 Part II OPTIONS IMEF 2013 Bellia M. Derivatives using Bloomberg 37 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 • • • • IMEF 2013 Bellia M. Stocks Foreign Currency Stock Indices Futures Derivatives using Bloomberg 38 Call and Put Options Profits Long Call Buy one European call option: price = $5 strike price = $100 IMEF 2013 Bellia M. 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 39 OVME: basic settings • • • • • • • • • • IMEF 2013 Bellia M. 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 Derivatives using Bloomberg 40 Methods used to price an option IMEF 2013 Bellia M. Derivatives using Bloomberg 41 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. IMEF 2013 Bellia M. 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 Derivatives using Bloomberg 42 Historical Line chart of underlying IMEF 2013 Bellia M. Derivatives using Bloomberg 43 Valuation of a European Call IMEF 2013 Bellia M. Derivatives using Bloomberg 44 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) IMEF 2013 Bellia M. Derivatives using Bloomberg 45 Spreads Options in Bloomberg Strategies involving spreads (i.e. same type of options) are available in: Products - Options Strategies - Call/Put Spread IMEF 2013 Bellia M. Derivatives using Bloomberg 46 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 47 Bull Spread Using Calls IMEF 2013 Bellia M. Derivatives using Bloomberg 48 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 Bellia M. Derivatives using Bloomberg 49 Bear Spread Using Puts IMEF 2013 Bellia M. Derivatives using Bloomberg 50 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 Bellia M. Derivatives using Bloomberg 51 Calendar Spread using calls IMEF 2013 Bellia M. Derivatives using Bloomberg 52 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 53 Straddle IMEF 2013 Bellia M. Derivatives using Bloomberg 54 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 IMEF 2013 Bellia M. Derivatives using Bloomberg 55 Strangle IMEF 2013 Bellia M. Derivatives using Bloomberg 56 Strategies IMEF 2013 Bellia M. Derivatives using Bloomberg 57 Styles IMEF 2013 Bellia M. Derivatives using Bloomberg 58 Structured notes IMEF 2013 Bellia M. Derivatives using Bloomberg 59