International Master Economics and Finance

Transcription

1 International Master Economics and Finance Mario Bellia Pricing Derivatives using Bloomberg Professional Service 03/2013

2 IRS Summary FRA Plain vanilla swap Amortizing swap Cap, Floor, Digital Options and Dual Digital Options Example: a real contract OPTIONS Call Bull Spread Bear Spread Calendar Spread Straddle Strangle 2

3 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 OVME is Bloomberg main pricing application for options on equity, indexes, funds, bonds, bond futures and short term interest rate futures. 3

4 Part I INTEREST RATE SWAP 4

5 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. 5

6 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 3- month period, starting in 3 months. Principal: Rate: 0.18% Today: March 14, 2013 Effective: June 18, 2013 Maturity: Sept 18,

7 How to price a FRA Lender receives difference of 0.18% and reset rate in 3 Months 7

8 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 8

9 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 9

10 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: Notional ,00 Receive Fixed % Pay Float rate EURIBOR 6M Contract starts March 18, 2013 Maturity is March 18, 2016 (3Y) Payments are quarterly (in advance) 10

11 How to price a plain vanilla Swaps 11

12 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 FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar. 5, % Sept. 5, % Mar. 5, % Sept. 5, % Mar. 5, % Sept. 5, % Mar. 5, %

13 Example of the Book 13

14 Example of the Book 14

15 Amortizing swap Can be either Fixed-versus-Float or Float-versus- Float. Both counterparties make interest payments that either are declining (amortizing) or accreting (increasing) over the life of the deal. Example: Notional ,00 Pay Fixed 4. 75% Receive Float EURIBOR 3M Contract starts April 11, 2008 Maturity is April 11,, 2015 (7Y) Payments frequency: quarterly 15

16 Amortizing swap Amortization scheme: Notional Start End Days 75'000,00 11/04/ /07/ '322,00 11/07/ /10/ '644,00 13/10/ /01/ '966,00 12/01/ /04/ '288,00 14/04/ /07/ '610,00 13/07/ /10/ '932,00 12/10/ /01/ '254,00 11/01/ /04/ '576,00 12/04/ /07/ '898,00 12/07/ /10/ '220,00 11/10/ /01/ '542,00 11/01/ /04/ '864,00 11/04/ /07/ '186,00 11/07/ /10/ '508,00 11/10/ /01/ '830,00 11/01/ /04/ '152,00 11/04/ /07/ '474,00 11/07/ /10/ '796,00 11/10/ /01/ '118,00 11/01/ /04/ '440,00 11/04/ /07/ '762,00 11/07/ /10/ '084,00 11/10/ /01/ '406,00 13/01/ /04/ '728,00 11/04/ /07/ '050,00 11/07/ /10/ '372,00 13/10/ /01/ '694,00 12/01/ /04/

17 Amortizing swap 17

18 Amortizing swap 18

19 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>) 19

20 Caps and Floors Example: Notional ,00 Receive Fixed % Pay Float rate EURIBOR 6M Contract starts March 18, 2013 Maturity is March 18, 2016 (3Y) Payments are quarterly (in advance) 20

21 Caps and Floors 21

22 Caps and Floors In order to change from Cap to Floor, select the appropriate deal from the dropdown menu: 22

23 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. 23

24 Digital cap Digital options 0.5% when strike 2% <= the floating rate. 24

25 Digital floor Digital options 0.5% when strike 2% >= the floating rate. 25

26 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) If the index is above a pre-determined level (barrier), an A) payoff will be paid. b) 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. 26

27 Dual Digital options Example: Notional ,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 EUR6M + 0.5% b) If EUR6M < Barrier Fixed rate 0.32% 27

28 Dual Digital options 28

29 In Arrears Swap Rate is observed at time t i and paid at time t i rather than time t i+1 It is necessary to make a convexity adjustment to each forward rate underlying the swap Suppose that F i is the forward rate between time t i and t i+1 and i is its volatility We should increase F i by F 2 i 2 i ( ti 1 1 F i i t i ) t i when valuing a in-arrears swap 29

30 Example of a contract Company Alpha decide to join a IRS with Bank Beta. (Notional is ,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 - 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% 30

31 BANK PAYS: From March 28, 2006 to March 28, 2007 EURIBOR 6M Example of a contract 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 EURIBOR 6M if EURIBOR 6M is less than 3.85% 4.35% if EURIBOR 6M is greater or equal to 3.85% From March 28, 2007 to March 28, 2009 If EURIBOR 6M less than 3.85%, the rate will be 3,45%. If EURIBOR 6M greter or equal than 3.85%, rate will be EURIBOR 6M with a max of 6.75% Bank Flows (Period 1) Alpha Flows (Period 1) EURIBOR 6M EURIBOR 6M - 0,10% with a max of 6.75% EUR 6M Floating Rate EUR 6M Floating Rate -0.10% Spread max (EU-6.85%;0) - Cap Bank Flows (Period 2) Alpha Flows (Period 2) EUR 6M if EUR6M < Barrier 3,85% 3.45% if EUR6M < Barrier 3,85% 4,25% if EUR6M >= Barrier 3,85% EUR 6M if EUR6M >= Barrier 3,85% with a max of 6.75% EUR 6M Floating Rate EUR 6M Floating Rate 0.40% se EU>=3.85% + Digital Cap MAX(3.85%-EU;0) Floor MAX(EU-3.85%;0) - Cap 0.40% se EU<3.85% - Digital Floor MAX(EU-6.75%;0) - Cap 31

32 Example of a contract - Payoff 32

33 Example of a contract - Valuation 33

34 Example of a contract - Valuation Expected Flows (discounted) Bank Period Floating rate 1 45'996,75 Digital Cap ,76 -cap ,97 tot 43'684,54 Alpha Period Float rate - spread 1 44'510,69 -cap 1 0,00 Floor 2 14'481,42 -Digital Floor 2-7'858,61 -Cap 2-137,31 tot 50'996,19 Valuation -7'311,65 34

35 Example of a contract:multi Leg Deal Expected Flows (discounted) Bank Period Digital Cap ,76 -cap ,97 tot -2'312,21 Alpha Period Floor 2 14'481,42 -Digital Floor 2-7'858,61 -Cap 2-137,32 Valuation -8'797,70 tot 6'485,49 35

36 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.. 36

37 Part II OPTIONS 37

38 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 Stocks Foreign Currency Stock Indices Futures 38

39 Call and Put Options Profits Long Call Buy one European call option: price = $5 strike price = $100 Short Call Write one European call option: price = $5 strike price = $100 Long Put Buy one European put option: price = $7 strike price = $70 Short Put Write one European put option: price = $7 strike price = $70 39

40 OVME: basic settings 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 40

41 Methods used to price an option 41

42 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. Example Underlying: UNICREDIT Deal: EUROPEAN CALL OPTION Price Today: 3,806 Strike price: 4,4 Expire: May 14, 2013 (60 days) Position in shares:

43 Historical Line chart of underlying 43

44 Valuation of a European Call 44

45 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) 45

46 Spreads Options in Bloomberg Strategies involving spreads (i.e. same type of options) are available in: Products - Options Strategies - Call/Put Spread 46

47 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:

48 Bull Spread Using Calls 48

49 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:

50 Bear Spread Using Puts 50

51 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:

52 Calendar Spread using calls 52

53 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:

54 Straddle 54

55 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:

56 Strangle 56

57 Strategies 57

58 Styles 58

59 Structured notes 59