The Good, the Bad and the Ugly: FX Standard and Exotic Options

FIN 700 International Finance FXO: Foreign Exchange Options Professor Robert Hauswald Kogod School of Business, AU The Good, the Bad and the Ugly: FX Standard and Exotic Options The derivative with an attitude: FX Options opinion: upward potential, avoiding downward risk perspective: buying insurance vs. eliminating risk FX, FFX fixed commitment: obligation to buy/sell Grand tour of option theory as applied to FX options jargon and pricing recall peculiarities of FX options: split personality, FFX exotic options: FX is the primary incubator of ideas Hedging: FX, FFX, FXF, FXO 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald

Options: the Royal Derivative 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 3 CME: Open Interest 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 4

Having the Cake and Eat It, too Options confer contractual rights on holder: a right to buy (sell) a fixed amount of currency at (over) a specified time (period) in the future at a price specified today Insurance vs. fixed commitment: right to buy or sell at discretion of holder wait and see security: even over time have an opinion while cutting off catastrophes Right means choice: choice means value 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 5 Options Contracts: Definition An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset in the future, at prices agreed upon today. Calls vs. Puts Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today. Put options gives the holder the right, but not the obligation, to sell a given quantity of some asset at some time in the future, at prices agreed upon today. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 6

Options Contracts: Type European vs. American options European options can only be exercised on the expiration date. American options can be exercised at any time up to and including the expiration date. Since this option to exercise early generally has value, American options are usually worth more than European options, other things equal. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 7 Options Contracts: Intrinsic Value In-the-money The exercise price is less than the spot price of the underlying asset. At-the-money The exercise price is equal to the spot price of the underlying asset. Out-of-the-money The exercise price is more than the spot price of the underlying asset. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 8

A Short Options Menu: Review Flavor: OTC vs. exchange traded OTC: tailor made, no guarantee, negotiation priced exchange traded: standardized, clearing house, delivery guarantee and auction priced Style: European or American (not quote!) exercisable at maturity only (E) or any time (A) Type: the right to buy (call) or to sell (put) Underlying: spot or futures Parties: buyer (holder), seller (writer) 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 9 Currency and Interest Rate Options Currency options began trading on the Philadelphia Stock Exchange (PHLX) in 198, while interest rate options began trading on the Chicago Mercantile Exchange (CME) in 1985. Since then, the markets have expanded : more option exchanges around the world, more currencies and debt instruments on which options are traded, option contracts with longer maturities, more styles of option contracts, and greater volume of trading activity. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 10

PHLX (NASDAQ) Currency Options: Initial Specifications Currency Contract Size Australian dollar AUD50,000 British pound 31,50 Canadian dollar CAD50,000 Euro 6,500 Japanese yen 6,50,000 Swiss franc CHF6,500 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 11 PHLX (NASDAQ) Currency Options: Current Specifications Currency Contract Size Australian dollar AUD 10,000 British pound GBP 10,000 Canadian dollar CAD 10,000 Euro EUR 10,000 Japanese yen JPY 1,000,000 New Zealand dollar NZD 10,000 Swiss franc CHF 10,000 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 1

Types of Contracts A call option bestows on the owner the right, but not the obligation, to buy the underlying financial asset or commodity. A put option conveys to the owner the right, but not the obligation, to sell the underlying financial asset or commodity. A European option can be exercised once only at the maturity date of the option. An American option can be exercised at any time on or before the maturity date. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 13 Types of Contracts Examples An American call option on spot : The right to buy 1 million for $1.10 per from today until expiration on Dec 15, 001. This call on is also a put on US$. A European put option on Swiss franc futures : The right to sell SFr 10 million March 00 futures for $0.65 per SFr on (and only on) Mar 15, 00. This put on SFr is also a call on US$. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 14

Location and Scale of Trading Currency and interest rate options are traded by banks on an over-the-counter (OTC) basis and on organized futures and options exchanges. According to surveys conducted by the Bank for International Settlements, the volume of trading in terms of billions per day is: OTC Organized Exchanges 1995 1998 1995 1998 Currency Options $41.0 $87.1 $3.8 $1.8 Interest Rate Options $8.0 $45.9 $18.4 $193.1 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 15 Organized FX Options Markets Exchanges: standardized contracts size, strike, maturity, style, price, quoted in USD/? IMM (CME): options on futures PHLX (Philadelphia): options on spot Marked to Market: continuous resettlement margin calls for writer, clearing house guarantee Value dates: Friday before 3rd Wednesday in March, June, September, December; why? near term months (EOM): options are short term! settlement: 4 business days later; why? 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 16

Currency Underlying Asset CME : C$ FXO Contract Specifications futures futures C$ futures futures PHLX : spot spot C$ C$ spot spot Contract Size 15,000 1,500,000 C$ 100,000 6,500 C$ 10,000 1,000,000 10,000 10,000 Strike Price Interval $0.01 $0.0001 $0.005 $0.0 $0.0 $0.005 $0.005 $0.001 Minimum Price Change $0.01 $0.0001 $0.01 $0.0 $0.01 $0.0001 $0.01 $0.01 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 17 Value of One Point $1.50 $1.50 $10.00 $6.5 $1.00 $1.00 $1.00 $1.00 PHILADELPHIA SE EURO/$ OPTIONS 6,500 (cents per ) Strike Price 0.940 0.960 0.980 Contract Specifications Financial Times, June 1, 000 CALLS PUTS Jul Aug Sep Jul Aug Sep.44 3.04 3.6 1.3 1.89.49 0.53 1.15 1.6 0.46 0.86 1.6 1.19 1.67.07.38.78 3.19 Previous day s vol., Calls 65 Puts 8. Prev. day s open int., Calls 4,111 Puts 888 Consider the August 000 /$ call option with a strike price of $0.96. The closing price was $0.0189 per. The buyer of this call option would expect to pay 6,500 $0.0189 = $1,181.5 plus commission charges. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 18

Pricing Terminology Three price elements: current price of underlying asset: FFX outright strike (exercise): price at which transaction occurs (option) premium: the option s price itself Price location: at/in/out-of-the-money options at: current spot = strike in: option profitable if exercised immediately out: option could not be profitably exercised Intrinsic value: extent to which an option is in-themoney (profit of immediate exercise) 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 19 Intrinsic vs. Speculative Value Intrinsic Value The difference between the exercise price of the option and the spot price of the underlying asset. Speculative Value The difference between the option premium and the intrinsic value of the option. Option Premium = Intrinsic Value + Speculative Value 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 0

If the call is inthe-money, it is worth S T E. If the call is outof-the-money, it is worthless and the buyer of the call loses his entire investment of c 0. Profit Long Call c 0 E + c0 E loss C at = C et = Max[S T -E, 0] Out-of-the-money In-the-money Long 1 call 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 1 S T If the call is in-themoney, the writer loses S T E. If the call is out-ofthe-money, the writer keeps the option premium. Profit c 0 Short Call -C at = -C et = -Max[S T -E, 0] S T E + c 0 E short 1 loss Out-of-the-money In-the-money call 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald

If the put is inthe-money, it is worth E S T. The maximum gain is E p 0 If the put is outof-the-money, it is worthless and the buyer of the put loses his entire investment of p 0. Profit E p 0 loss Long Put P at = P et = Max[E - S T, 0] p 0 E p 0 long 1 put In-the-money 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 3 E Out-of-the-money S T If the put is inthe-money, it is worth E S T. The maximum loss is E + p 0 Profit p 0 If the put is outof-the-money, it is worthless and the seller of the put keeps the option premium of p E + p 0. 0 loss Short Put -P at = -P et = -Max[S T -E, 0] E p 0 E 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 4 S T short 1 put

Market Value, Time Value and Intrinsic Value for an American Call The red line shows the payoff at maturity, not profit, of a call option. Note that even an out-of-the-money option has value time value. Profit loss Out-of-the-money 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 5 E Long 1 call Intrinsic value Time value In-the-money S T Price Determinants Current spot FX, domestic and foreign interest rate St, rd, rf rd rf T t FFX by IRP from spot FX and interest rates FtT, Ste Exercise price E, X, K Time to maturity: length of period to expiration T t Underlying FX rate process: volatility Type: European or American A right: use probability theory to evaluate contingencies Prerequisite: a model of the underlying asset, i.e., FX rate Distributional assumption: the spot (forward) FX rate s logarithmic change is normally distributed 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 6

European Option Pricing Formula: Black-Scholes-Merton The model is $ C F N( d ) E N( d )] e [ 1 Where 0 C 0 = the value of a European option at time t = 0 F S t e ( r r ) T $ r $ = the interest rate available in the U.S. r = the interest rate available in the foreign country in this case the U.K. d 1 ln( F / E).5 T, T d d 1 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 7 T r T ( r$ r ) T (.055.06)0.50 F Ste (1/100) e 1/100.503 1/100.503 ln.5(0.5).5 ln( F / E).5 T 1/100.005 0.156 d1 0.07446 T.5.5 0.1768 d d1 T 0.07446.5.5 0.1053 r$ T Ce [ F N( d1) E N( d )] e 0.055 0.5 Ce [1/100.503 N(0.07446) (1/100) N( 0.1053)] e C $0.006137 e 6M Call on JPY Use the European option pricing formula to find the value of a six-month at-the-money call option on Japanese yen. The strike price is $1 = 100. The volatility is 5 percent per annum; r $ = 5.5% and r = 6%.

Exercise: Call on GBP Find the value of a six-month call option on the British pound with an exercise price of $1.50 = 1 The current value of a pound is $1.60 The interest rate available in the U.S. is r $ = 5%. The interest rate in the U.K. is r = 7%. The option maturity is 6 months (half of a year). The volatility of the $/ exchange rate is 30% p.a. Before you start, note that the intrinsic value of the option is $.10 our answer must be at least that. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 9 Pricing FX Options: Formulae Apply the classics: modify the seminal work of Black, Scholes and Merton to calculate theoretically fair prices Pricing formula (Garman, Kohlhagen; Grabbe): call ct exp rd T t FtN d1 KN d 1 d1 log Ft K T t, d d1 T t T t Put: pt exp rd T t FtN d1 KN d Interpretation: payoffs F - K and K - F weighted by discount factor: future strike and spot (IRP: FFX) probability of prices realizations: expected values PCP - put-call-parity: fundamental arbitrage equation 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 30

Option Value Determinants Call Put 1. Exchange rate +. Exercise price + 3. Interest rate in U.S. + 4. Interest rate in other country + 5. Variability in exchange rate + + 6. Expiration date + + The value of a call option C 0 must fall within max (S 0 E, 0) < C 0 < S 0. The precise position will depend on the above factors. 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 31 FX Options Are Different Split personality of FX Options: a call is a put EUR call = right to buy EUR for USD = USD put Close link to FFX by IRP : quoted in terms of? arbitrage against FXF: futures used to hedge FXOs General observations: Implied volatility quotes: BSM convention for price Fair prices: theoretical yardsticks for analysis American style options: solve lattice (tree) models Exotic options: numerical solutions only 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 3

Exotics: Path-Dependent Options Options are expensive: right, not obligation FFX: pay for downside risk with upside potential cheaper alternatives? exotic options OTC market: exotic options pioneered in FX lower cost of insurance by giving up unlikely events common theme: the price path determines pay-off Driven by hedging cost and accounting rules accounting hedge: can you spare an option? OTC: anything goes, mainly European style short menu of exotic options 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 33 Asian Options Pay-off rule: average spot FX rate over lifetime determines moniness (intrinsic value) at T in-the-money call: in-the-money put: Popular among corporates: accounting rules many companies translate or convert foreign cash flows by using average FX rate natural way to manage risk given corporate policy what do you hedge: economic or accounting risk? Short term European options 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 34

Look-Backs Pay-off rule: best/worst FX rate over life time determines moniness of option at expiration in-the-money call: in-the-money put: Corporates driven: accounting rules over short horizon, choice of FX rate for translation or conversion of foreign cash flows pick the most favorable one: valuable = expensive! Very short-term: time value explodes restaurant analogy 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 35 Barrier Options Underlying price movement triggers activation European options: activated or deactivated when a threshold is crossed by the underlying spot FX knock-ins: hitting barrier activates - birth knock-outs: crossing threshold deactivates - death Successor to cylinders: FX trading in a range Big success: less expensive option volatility bet holder surrenders part of the pay-off range less protection, especially against large movements 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 36

Down-and-out or Up-and-in? The two most common barrier options in FX: down-and-out call: EUR call struck at USD 0.90 and an out-barrier at USD 0.86 up-and-in put: JPY put struck at USD 0.70 with an inbarrier at USD 0.74 Put your money where your mouth is hit the barrier once and the option dies/comes alive give up small gains for reducing up-front price EUR U& O U& I EUR D& O D& I Pricing: pt pt pt, ct pt pt bargains on the missing leg and hedge conventional 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 37 Summary Grand tour of options in FX markets: pricing ingredients: the usual suspects the classics: BSM - of pedagogical value only the future: pricing FXO off yield curve models, IRP Split personality: every put a call and vice versa closeness to forward - IRP: hedging and arbitrage Exotic or Idiotic: proliferation of new options driven by accounting rules, greed and risk tolerance you be the judge: penny wise and pound foolish 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 38

GBP FXO Example: Parameters Let s try our hand at using the model. If you have a calculator handy, follow along. First calculate F S e Then, calculate d 1 and d t $ r T (.05.07)0.50 1.50e 1.485075 ( r ) d ln( F / E).5 T T ln(1.485075/1.50).5(0.4).4.5 1 d 0.106066.4.5 0.176878 0.106066 d1 T 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 39.5 GBP FXO Example: Premium F 1.485075 d 0.106066 1 d 0. 176878 N(d 1 ) = N(0.106066) =.54 N(d ) = N(-0.1768) = 0.498 $ C F N( d ) E N( d )] e 0 [ 1 r T.05*.5 C0 [1.485075.54 1.50.498] e $0.157 9/10/018 Exotic and Idiotic FX Options - Robert B.H. Hauswald 40