CURRENCY OPTIONS • An option is a contract in which the buyer of the option has the right to buy or sell a specified quantity of an asset, at a pre-specified price, on or upto a specified date if he chooses to do so; however, there is no obligation for him to do so • Options are available on a large variety of underlying assets including common stock, stock indices, currencies, debt instruments, and commodities. • Options are also available on financial prices such as interest rates. • Options on forward and futures contracts, options on swaps and finally options on options are also traded.
Options on Spot, Options of Futures and Futures Style Options • Option on Spot Currency: Right to buy or sell the underlying currency at a specified price; no obligation • Option on Currency Futures: Right to establish a long or a short position in a currency futures contract at a specified price; no obligation • Futures-Style Options: Represent a bet on the price of an option on spot foreign exchange. Margin payments and mark-to-market as in futures.
Options Terminology • The two parties to an option contract are the option buyer and the option seller also called option writer • Call Option: A call option on currency Y against currency X gives the option buyer the right to purchase currency Y against currency X at a stated price Y/X, on or any time upto a stated date. • Put Option:A put option on currency Y gives the option buyer the right to sell currency Y against currency X at a specified price on or any time upto a specified date.
Options Terminology (contd.) • Strike Price (also called Exercise Price)The price specified in the option contract at which the option buyer can purchase the currency (call) or sell the currency (put) Y against X. Maturity Date:The date on which the option contract expires. Exchange traded options have standardized maturity dates. • American Option: An option, that can be exercised by the buyer on any business day from trade date to expiry date. • European Option: An option that can be exercised only on the expiry date
Options Terminology (contd.) • Option Premium (Option Price, Option Value):The fee that the option buyer must pay the option writer “up-front”. Non-refundable. • Intrinsic Value of the Option: The intrinsic value of an option is the gain to the holder on immediate exercise. Strictly applies only to American options. • Time Value of the Option: The difference between the value of an option at any time and its intrinsic value at that time is called the time value of the option.
Options Terminology (contd.) • A call option is said to be at-the-money-spot if Current Spot Price (St ) = Strike Price (X), • in-the-money-spot if St > X and out-of-the-money-spot if St < X • A put option is said to be at-the-money-spot if • St = X, in-the-money-spot if St < X and out-of-the-money-spot if St > X • In the money options have positive intrinsic value; at-the-money and out-of-the money options have zero intrinsic value. • Practitioners compare the strike price with the forward rate for the same expiry date.
Options Terminology (contd.) Thus at time t a call (put) option expiring at time T is ATMF – at the money forward – if X = Ft,T (X = Ft,T) ITMF – in the money forward -if X < Ft,T (X > Ft,T) OTMF – out of the money forward - if X > Ft,T (X < Ft,T)
PHLX EUR/USD CALLS; EXPIRY: END DECEMBER 2008; QUOTES AS ON DECEMBER 4. SPOT RATE: 1.2764 Symbol Bid Ask Strike price (Cents per EUR) (Cents per EUR) ECDLR 8.43 8.79 119.50 ECDLV 7.52 7.85 120.50 ECDLC 6.70 6.95 121.50 ECDLG 5.83 6.10 122.50 ECDLK 5.01 5.24 123.50 XDELZ 4.61 4.85 124.00 ECDLO 4.20 4.40 124.50 XDELX 3.90 4.10 125.00 ECDLS 3.50 3.70 125.50 XDELY 3.20 3.40 126.00 ECDLW 2.92 3.10 126.50 XDELB 2.62 2.78 127.00 ECDLD 2.36 2.50 127.50 XDELF 2.08 2.22 128.00 ECDLH 1.81 2.00 128.50 XDELJ 1.63 1.79 129.00 EPALL 1.42 1.58 129.50 XDELN 1.24 1.41 130.00 EPALP 1.06 1.26 130.50
Symbol Bid Ask Strike Price ECDOK 3.80 3.95 123.50 XDEOZ 3.95 4.15 124.00 ECDOO 4.15 4.30 124.50 XDEOX 4.35 4.55 125.00 ECDOS 4.60 4.75 125.50 XDEOY 4.80 4.95 126.00 ECDOW 5.05 5.15 126.50 XDEOB 5.25 5.40 127.00 ECDOD 5.50 5.65 127.50 XDEOF 5.75 5.90 128.00 ECDOH 6.05 6.20 128.50 XDEOJ 6.30 6.40 129.00 EPAOL 6.55 6.70 129.50 XDEON 6.85 7.00 130.00 EPAOP 7.15 7.25 130.50 PHLX EUR/USD PUTS; EXPIRY: MARCH 2009; CENTS PER EUR, DEC 4, 2008
PHLX USD/CHF CALLS EXPIRING IN NOVEMBER 2008 (QUOTES AS ON SEPT 3, 2008) (STRIKES AND PREMIA QUOTED AS CENTS PER CHF) Symbol Bid Ask Strike Price XDSKG 3.55 3.79 88.00 SIQKI 3.23 3.44 88.50 XDSKK 2.91 3.12 89.00 SIQKM 2.60 2.82 89.50 XDSKO 2.32 2.55 90.00 SIQKQ 2.06 2.29 90.50 XDSKS 1.82 2.06 91.00 SIQKU 1.59 1.85 91.50 XDSKW 1.41 1.66 92.00 CHF/USD SPOT RATE : 90.85
PHLX GBP/USD PUTS EXPIRING IN NOVEMBER 2008 (QUOTES AS ON SEPT 3, 2008) (STRIKES AND PREMIA QUOTED AS CENTS PER GBP) STRIKE BID ASK 178.00 0.39 0.84 181.50 1.42 1.87 187.00 5.08 5.58 194.00 11.73 12.23 205.50 23.20 23.71 215.00 32.69 33.19 GBP/USD CLOSING SPOT : 1.8232
PHLX CURRENCY OPTION PRICE QUOTES (March 30, 2007, Cents per GBP) GBP/USD AMERICAN OPTIONS (CONTRACT SIZE: £31250) Strike CALLS PUTS Price Apr May Jun Apr May Jun 196.00 1.55 2.21 2.80 0.70 1.39 2.00 197.00 1.00 1.69 1.15 1.87 198.00 0.62 1.26 1.84 1.75 2.44 3.10 200.00 0.27 0.71 1.18 3.50 3.87 4.32
EUR/USD EUROPEAN OPTIONS (CONTRACT SIZE €62500) (Cents per EUR) Strike CALLS PUTS Price Apr May Jun Apr May Jun 131.00 2.13 2.44 2.75 0.05 0.22 0.43 133.00 1.13 1.66 2.16 0.32 0.71 1.00 135.00 0.25 0.72 1.13 1.43 1.73 1.99 137.00 0.08 0.29 0.61
USD/YEN OPTIONS QUOTES (CME) Oct 10, 2005 Strike price CALLS PUTS Dec Mar Jun Dec Mar Jun 8600 2.77 - - 0.33 0.58 0.76 8700 2.02 3.15 4.29 0.57 0.84 1.02 8800 1.40 2.50 3.62 0.94 1.18 1.33 8900 0.94 - 3.04 1.48 1.64 1.73 Source: Reuters/CME.
Elementary Option Strategies • Assumptions • Ignore brokerage commissions, margins etc • Dealing with European options • All exchange rates, strike prices, and premiums will be in terms of home currency per unit of some currency A and the option will be assumed to be on one unit of the currency A • Profit profiles shown at maturity
Elementary Option Strategies • Call Options • Current spot rate, St • Strike price X • Call option premium c • Spot rate at maturity ST • Call Option Buyer’s Profit = -c for ST X = ST - X - c for ST > X • Call Option Writer’s Profit = +c for ST X = -(ST - X - c) for ST > X
A CALL OPTION A trader buys a call option on US dollar with a strike price of Rs.49.50 and pays a premium of Rs.1.50. The current spot rate, St, is Rs.48.50. His gain/loss at time T when the option expires depends upon the value of the spot rate, ST, at that time USD/INRST AT EXPIRY Option Buyer’s Gain(+)/Loss(-) 48.2500 -Rs.1.50 48.5000 -Rs.1.50 48.7500 -Rs.1.50 49.0000 -Rs.1.50 49.2500 -Rs.1.50 49.5000 -Rs.1.50 49.7500 -Rs.1.25 50.0000 -Rs.1.00 51.0000 +Rs.0.00 52.0000 +Rs.1.00 54.5000 +Rs.3.50 56.0000 +Rs.5.00
Elementary Option Strategies Payoff Profile of a Call Option + c = 1.50 O ST c =1.50 - X=49.50 X+c=51.00 Breakeven Spot Rate Option Buyer ST : SPOT RATE AT EXPIRY Option Seller
Elementary Option Strategies • Put Options : Premium p • Put Option Buyer's Profit • = -p for ST X = X - ST – p for ST < X • Put Option Writer’s Profit • = +p for ST X = -(X - ST - p) for ST < X
A PUT OPTION A trader buys a put option on pound sterling at a strike price of $1.8500, for a premium of $0.07 per sterling. The spot rate at the time is $1.9465. At expiry, his gains/losses are as follows GBP/USD ST AT EXPIRY Option Buyer’s Gain(+)/Loss(-) 1.7000 +$0.0800 1.7300 +$0.0500 1.7500 +$0.0300 1.7600 +$0.0200 1.7800 $0.0000 1.7900 -$0.0100 1.8300 -$0.0500 1.8500 -$0.0700 1.8700 -$0.0700 1.9000 -$0.0700 1.9500 -$0.0700
Elementary Option Strategies Payoff Profile of a Put Option + p=0.07 O p=0.07ST X-p=1.78 - X=1.85 Option Buyer Breakeven Spot Rate at Option Expiry Option Seller
Elementary Option Strategies • Spread Strategies • Bullish Call Spread: Consists of selling the call with the higher strike price and buying the call with the lower strike price • Bearish Call spread:If the investor expects the foreign currency to depreciate, he can adopt the reverse strategy viz. buy the higher strike call and sell the lower strike call • Bullish Put Spread: Consists of selling puts with higher strike and buying puts with lower strike • Bearish Put Spread: Opposite of Bullish Put Spread These strategies, involving options with same maturity but different strike prices are called Vertical or Price Spreads
A Bullish Call Spread The CHF/USD spot rate is 0.75. April calls with strike 0.70 are trading at 0.07 and calls with strike 0.80 at 0.005. Sell the call with the higher strike price and buy the call with the lower strike price. Profits at expiration are as below : ST Gain/Loss Gain/Loss Net on Short on Long Gain/loss 0.6000 0.005 -0.070 -0.065 0.6500 0.005 -0.070 -0.065 0.7000 0.005 -0.070 -0.065 0.7500 0.005 -0.020 -0.015 0.7650 0.005 -0.005 0.000 0.7800 0.005 0.010 0.015 0.8000 0.005 0.030 0.035 0.8500 -0.045 0.080 0.035 0.9000 -0.095 0.130 0.035
Bull Spread Using CallsBuy Call Strike X1, Premium c1; Sell Call Strike X2, Premium c2 ; Profit c2 ST X1 • X2 c1 PROFIT PROFILE OF THE SPREAD STRATEGY :
Profit X1 X2 ST Bull Spread Using PutsBuy Put Strike X1, Premium p1; Sell Put Strike X2, Premium p2 p2 p1
Bear Spread Using Calls BUY CALL STRIKE X2; SELL CALL STRIKE X1 PROFIT PROFILE: Profit X1 X2 ST
Elementary Option Strategies Butterfly Spreads This is an extension of the idea of vertical spreads. Suppose the current spot rate NZD/USD is 0.6000. The call options with same expiry date are available : Strike Premium 0.58 0.07 0.62 0.03 0.66 0.01 A Butterfly Spread is bought by buying two calls with the middle strike price of 0.62, and writing one call each with strike prices on either side, here, 0.58 and 0.66. The profit table is as follows :
A BUTTERFLY SPREAD(Contd.) STGain on Gain on Gain on Net 0.62 call 0.58 call 0.66 call Gain (long 2) (short 1) (short 1) 0.5000 -0.06 0.07 0.01 0.02 0.5200 -0.06 0.07 0.01 0.02 0.5600 -0.06 0.07 0.01 0.02 0.5800 -0.06 0.07 0.01 0.02 0.5900 -0.06 0.06 0.01 0.01 0.6000 -0.06 0.05 0.01 0.00 0.6100 -0.06 0.04 0.01 -0.01 0.6200 -0.06 0.03 0.01 -0.02 0.6400 -0.02 0.01 0.01 0.00 0.6500 0.00 0.00 0.01 0.01 0.6600 0.02 -0.01 0.01 0.02 0.6800 0.06 -0.03 -0.01 0.02
Elementary Option Strategies Butterfly Spread Payoff Profile of a Long Butterfly Spread : Payoff Profile of a Short Butterfly Spread :
Elementary Option Strategies • Horizontal or Time Spreads • Horizontal spreads consist of simultaneous purchase and sale of two options identical in all respects except the expiry date • The difference in premiums between the two options will be moderate at the time of initiation but will have widened at the time of expiry of the short term optionprovided the underlying exchange rate has not moved drastically
Elementary Option Strategies • Straddles and Strangles – Volatility Bets • A long straddle consists of buying a call and a put both with identical strikes and maturity. Usually both are at-the-money-spot. • A long strangle consists of buying an out-of-the- money call and an out-of-the-money put • Both are bets that the underlying price is going to make a strong move up or down I.e. market is going to be more volatile.
Straddles and Strangles A straddle consists of buying a call and a put both with identical strikes and maturity. As an example, suppose sterling December call and put options with a strike of $1.7250 are priced at 2.95 cents and 1.24 cents respectively. Profits for alternative values of ST are : ST Gain on Call Gain on Put Net Gain 1.6500 -2.95 6.26 3.31 1.6831 -2.95 +2.95 0.00 1.7000 -2.95 1.26 -1.69 1.7250 -2.95 -1.24 -4.19 1.7669 +1.24 -1.24 0.00 1.8000 4.55 -1.24 3.31
Elementary Option Strategies Payoff Profile of a Straddle + X 0 ST X-p-c X+p+c - X: Strike price in put and call; c : Call premium p : Put Premium ST: Spot rate at expiry
Elementary Option Strategies (X2 – p – c) (X1 + p + c) X1: Call strike X2: Put strike p: Put premium c: Call premium ST: Spot rate at Expiry + 0 ST - X2 X1 Payoff Profile of a Strangle
Elementary Option StrategiesStrip & Strap:CALLS + PUTS SAME STRIKE AND EXPIRY DATE Profit Profit + ST ST K K O - LONG STRIP LONG STRAP LONG (1 CALL+2 PUTS) LONG (2 CALLS+1 PUT)
Hedging with Currency Options • Hedge a Foreign Currency Payable with a Call. • Hedge a Receivable with a Put Option • Covered Call Writing. Earn a premium by writing a call against a receivable. • Options are a convenient hedge for contingent liabilities (Note however that the risk of the liability materialising or not cannot be hedged with the option) • Options allow hedger to bet on favorable currency movements with limited downside risk.
Over-The-Counter (OTC) Market Practices • Like in the forex market, dealers trade directly with each other and through brokers • Unless a quote for a specific option - call or put - is requested, the market practice is to quote a two way-price in terms of implied volatility for an At-the-Money- Forward (ATMF) straddle for a given period
Futures Options • The underlying asset in this case is a futures contract • A call option on a futures contract, if exercised, entitles the holder to receive a long position in the underlying futures contract plus a cash amount equal to the price of the contract at that time minus the exercise price • A put option on being exercised gives the holder a short position in the futures contract plus cash equal to the exercise price minus the futures price
Options on Futures A call (put) on a futures contract with strike X gives you the right to establish a long (short) position in the futures contract at a futures price X. If you exercise, your position will be marked to market at the end of the day. A September EUR futures contract on EUR 125000 is currently trading at $1.2660; if you exercise a call with strike 1.1950, you become the owner of one September EUR futures contract with a price of $1.1950. You will open a margin account with a deposit of say 5% of the contract value. If the settlement price is $1.2560, your margin account will be credited with: $(1.2560-1.1950)(125000) = $7625.
Futures Style Options First consider a forward contract expiring at time T on an option with the same expiry date. The option is on the underlying currency. Essentially you pay the option premium at the time of expiry. A futures style option is like a forward-style option but with marking-to-market. Suppose you buy a futures style option on EUR 125000 at a price of $0.02 per EUR. You pay a margin as in futures. On the second day the option settles at $0.03. You can withdraw $(125000)(0.03-0.02) = $1250. Next day the option settles at $0.035 and expires. You gain a further $625 and now have to pay $0.035 premium per EUR. Ignoring time value you pay a net amount = $(4375-1250-625) = $2500. Whether you exercise the option or not depends upon (ST – X).
(1) A European call expiring at time T on a forward purchase contract also expiring at time T; strike price X How will it be priced relative to a call on spot forex? If it is an American option, under what conditions might it be exercised early? (2) Consider a European call expiring at time T, on a futures contract also expiring at time T. How will it be priced relative to an option on cash forex? Suppose it’s an American option; under what circumstances would it be rational to exercise it early? Assume that all future interest rates are known with certainty.
(3) Consider a European call expiring at time T on a forward purchase contract expiring at time T2 > T at strike X. If you exercise, at time T, you will own a forward contract expiring at T2, to buy one unit of forex at a price of X units of HC. Ignoring interest rate uncertainty, how would you value such an option? If the call is American, under what conditions might it be exercised early? (4) Suppose the option is on a futures contract expiring at T2 > T. How would you value a European option?, Ignoring interest rate uncertainty, would an American call be exercised early?
Innovations with Embedded Options • Range Forwards (Cylinder Option, Tunnel Option) • Participating Forwards • Conditional Forward (Forward Reversing Option) • Break Forwards • Many other combinations – structured products
Range Forwards Price Paid F2 F1 F1 F2 ST
A Participating Forward agreement is designed so that the buyer can reap part of the benefit of depreciation and the seller can reap part of the benefit of appreciation with no up-front fee. The contract thus guarantees a floor price to the seller, a ceiling price to the buyer and an opportunity of doing better than these. Consider first the sale of a participating forward. The seller is assured a minimum price F1 which is less than the current outright forward rate for the same maturity. If at maturity, the spot rate, ST, is greater than F1, the seller gets: [F1 + (ST - F1)]; 0 < < 1
DISSECTING A PARTICIPATING FORWARD…. With an outright forward, the seller is guaranteed a price of F (the current outright forward rate), the present value of which is Fe-r(T-t) where r is the risk-free interest rate, t is current time and T is maturity date. With a participating forward with sharing ratio , the seller gets F1+ max[0, (ST - F1)]. A European call option with strike of F1, maturing at T, also gives a payoff of max [0, (ST-F1)] at T. The current value of such an option is c (St,F1,T). The present value of the participating forward is thus [F1e-r(T-t) + c(St,F1,T)].