Financial Engineering

Financial Engineering Lecture 10

Futures Options Overview • A Futures Contract on an Option • The underlying asset is not a stock • The underlying asset is a futures contract • Call Futures Option • Long Call = The right to long a futures contract • Short Call = The obligation to short a futures contract • Put Futures Option • Long Put = The right to short a futures contract • Short Put = The obligation to long a futures contract

Futures Options Option Specifications • Futures Options = FO • No delivery occurs • Commodities are Settled in Cash • Financials might take delivery • One option = one futures contract • Expiration • Financial options • Same date as futures contract expiration • Commodity Options • Expire the month prior to the futures contract expiration

Futures Options Pricing • FO prices are listed in “units” • Each “Unit” has a $ value Example (Corn FO) • Underlying asset = 5,000 bushels of corn • 1 unit = $6.25 (or 1/8 cents per bushel) • Dec300Call = 80 • 80 x $6.25 = $500 • The strike of 300 = $3.00 or 300 cents per bushel • CBOT lists details

Futures Options Example (Soybean FO) • March soybean futures are selling for 575 cents per bushel • The underlying asset is one futures contract on 5,000 bushels of soybeans as listed on the CBOT • The value of one futures contract • 5000 x $5.75 = $28,750 • The unit value is $50 • Determined 5000 x .01 = $50 • The futures option price is quoted in Units (which are cents per bushel) • But the total price is $50 x cents

Futures Options Example (Soybean FO) - continued • Mar525P = 5 (total cost = $50 x 5 = $250) • Mar550C = 35.50 ($1,775) • Mar600C = 8.25 ($ 412.50) • BE on March550C = 550 + 35.50 = 585.50

Futures Options Units • Vary depending on the underlying asset • Each asset has a unique relationship among • Asset price • Futures Contract specs • Option Basic Underlying Asset Categories • Commodity • Financial • Currency • others

Futures Options Example - gold is quoted in $ per ounce Example - Sugar is quoted in cents per pound CBOT web site Pricing – Same as regular options. Black Scholes Binomial

Futures Options FO Margin • Determined by volatility and risk of loss • Futures Options use unique margin accounting • SPAN= Standard Portfolio ANalysis of Risk Futures Options Uses Same as futures w/ flexibility Floors, ceilings, spreads, etc Employs all Option strategies Arbitrage (lots of mispricing)

SWAPS Birth 1981 Definition - An agreement between two firms, in which each firm agrees to exchange the “interest rate characteristics” of two different financial instruments of identical principal Key points Spread inefficiencies Same notation principal Only interest exchanged

SWAPS • “Plain Vanilla Swap” - (generic swap) • fixed rate payer • floating rate payer • counterparties • settlement date • trade date • effective date • terms • Swap Gain = fixed spread - floating spread

SWAPS Example (vanilla/annually settled) XYZ ABC fixed rate 10% 11.5% floating rate libor + .25 libor + .50 Q: if libor = 7%, what swap can be made 7 what is the profit (assume $1mil face value loans) A: XYZ borrows $1mil @ 10% fixed ABC borrows $1mil @ 7.5% floating XYZ pays floating @ 7.25% ABC pays fixed @ 10.50%

SWAPS Example - cont Benefit to XYZ Net position floating +7.25 -7.25 0 fixed +10.50 -10.00 +.50 Net gain +.50% Benefit ABC Net Position floating +7.25 - 7.50 -.25 fixed -10.50 + 11.50 +1.00 net gain +.75%

SWAPS Example - cont Settlement date ABC pmt 10.50 x 1mil = 105,000 XYZ pmt 7.25 x 1mil = 72,500 net cash pmt by ABC = 32,500 if libor rises to 9% settlement date ABC pmt 10.50 x 1mil = 105,000 XYZ pmt 9.25 x 1mil = 92,500 net cash pmt by ABC = 12,500

SWAPS • transactions • rarely done direct • banks = middleman • bank profit = part of “swap gain” example - same continued XYZ & ABC go to bank separately XYZ term = SWAP floating @ libor + .25 for fixed @ 10.50 ABC terms = swap floating libor + .25 for fixed 10.75

SWAPS Example - cont settlement date - XYZ Bank pmt 10.50 x 1mil = 105,000 XYZ pmt 7.25 x 1mil = 72,500 net Bank pmt to XYZ = 32,500 settlement date - ABC Bank pmt 7.25 x 1mil = 72,500 ABC pmt 10.75 x 1mil = 107,500 net ABC pmt to bank = 35,000 bank “swap gain” = +35,000 - 32,500 = +2,500

SWAPS Example - cont benefit to XYZ floating 7.25 - 7.25 = 0 fixed 10.50 - 10.00 = +.50 net gain .50 benefit to ABC floating 7.25 - 7.50 = - .25 fixed -10.75 + 11.50 = + .75 net gain .50 benefit to bank floating +7.25 - 7.25 = 0 fixed 10.75 - 10.50 = +.25 net gain +.25 total benefit = 12,500 (same as w/o bank)

Currency Swaps Similar to interest rate swaps Same type loan, just diff currency WHY? example: you have an investment in Japan Project is financed with US bonds You look for SWAP partner so you can emulate holding Japanese bonds Java Yahoo principal Yen loan 11% 12% $ 1 mil $ loan 8% 11.1% or Y120

Currency Swaps example - continued • Java borrows $1mil @ 8% • Yahoo borrows Y120mil @ 12% • Intl. Bank arranges swap • Java swaps 8% $ loan for 10.3% yen loan w/bank • Yahoo swaps 12% yen loan for 10.4% $ loan w/bank total available benefit = (11.1-8) - (12-11) = 2.1%

Currency Swaps example - continued benefit to Java $ loan +8 - 8 = 0 Yen loan +11 - 10.3 = .7 net gain = +.7% benefit to Yahoo $ loan 11.1 - 10.4 = +.7 yen loan -12 + 12 = 0 net gain = + .7% benefit to bank $ loan +10.4 - 8 = +2.4 yen loan - 12 + 10.3 = -1.7 net gain = + .7%

Financial Engineering