Chapter 5: Foreign Currency Options

1. Chapter 5: Foreign Currency Options • Options markets and uses for options • Terminology • Quotes • Option pricing • What affects option value? • The Greeks

2. Currency Options the right (not the obligation), to buy (a call) or sell (a put) specified amount specified date specified exchange rate the specified rate is called strike price (a.k.a. exercise price) the date the option contract ends is the option's expiration date the buyer (holder) betting against the seller (writer)

3. an American style option can be exercised anytime prior to its expiration • a European style option can only be exercised on its expiration date • both OTC options and exchange traded options exist • OTC of bank options are tailor-made like forwards • CME, CBOE, Philadelphia Exchange, Liffe • options have an up front cost, called a premium

4. Exchange traded options • Standardized by size and maturity dates • clearing house • brokerage commission • more liquid than an OTC option contract • only available for a limited number of currencies • no counterparty risk • Compared to futures, options provide a more flexible way of hedging • Allow limiting losses without sacrificing potential gains

5. payoff for option contracts - limited loss, almost unlimited potential gain • calls and puts • writer vs. holder • an option can be: • In-the-money • Out-of-the-money • At-the-money

6. Example: • Consider a Euro November put option with 0.980 strike price • If the exchange rate at expiration turns out to be 0.960 $/€, what is the gain/loss to holder of one contract? • Premium paid = 62500(.0119) = $743.75 • Profit at expiration = 62500(.02) = $1,250 • Overall profit = 1,250 – 743.75 = $506.25 • Breakeven point when (.98 - x) = .0119; x = .98 - .0119 = .9681

7. Types of currency options • Options on spot • Exchange traded • OTC • Options on currency futures • when exercised, one receives a foreign currency futures contract. • CME currency options are options on futures trading on the CME

8. FX Speculation • Speculation: taking an open position in expectation of profit • Assume: • $/€ spot currently 1.10 • 3-month “expectation” 1.05 • 3-month fwd rate 1.09 • € interest = $ interest • we have €110,000 = $100,000 for speculation

9. Spot speculation • “€ is expensive” • sell €, buy $ • @ current spot rate, €100,000 = $110,000 • in 3 months, exchange $110,000 @ 1.05 to €104,761.90 • Profit = €4,761.90 or 19.05% p.a. • note: does not have to be exercised on a certain date

10. Forward speculation • “€ forward rate is expensive” • sell € forward • enter a forward contract to sell € @ 1.09 in 3 months • no cash outlay • but, a binding commitment has been made • in 3 months: • with $110,000, buy €104,761.90 • sell €104,761.90 for $114,190.48 • % profit depends on collateral requirements

11. Speculating with options • “€ will depreciate” • need a right to sell € at a predetermined price • assume a put option with strike price of 1.10 has a premium of $0.0095 (contract size = €62,500) • @ expiration, spot =1.05 • exercise the put • profit ($0.05-$0.0095)/ € = $2,531.25 • $2,531.25/(0.0095 x 62,500) = 426% or 1,705% p.a. • break-even = 1.0905

12. Option Pricing and Valuation • Total value = Intrinsic value + time value • Intrinsic value • For call option = spot - exercise price • For put option = exercise price - spot • Time value • Affected by time to expiration and volatility (and by interest rate differential) • See exhibit 5.4, p. 134

14. Factors influencing option premiums: • strike price • assuming direct quotes ($/FC), higher strike price means a lower call premium - less likely the call will be in-the-money • the inverse is true for puts • Changes in spot rate (Delta) • assuming direct quotes ($/FC), higher spot means a higher premium • more likely the call will be in-the-money • again, opposite for puts • Changes in Delta (Gamma) • Changes in underlying price will cause delta hedge ratio to change • Gamma is the “second derivative” of the underlying price

15. volatility of the spot FX rate (Vega or Lambda) • stated in terms of daily std.dev. of the underlying • higher volatility means that the future spot rate might be much higher or much lower than it now is • the down side is limited • the up side (profits) are unlimited • higher volatility  greater probability that the spot rate will be above the strike price • term to maturity - i.e., time to expiration (Theta) • the longer the term to maturity, the longer the option has to move into the money • interest rate differential between the 2 currencies (Rho - Phi) • See exhibit 5.11, p. 145 for a summary

16. Implied volatility • Option pricing methods can be used to calculate the market’s expectation of future volatility • Volatility is the only component of option value that is not observable directly • See exhibit 5.8., p. 142 • Caution: Thin markets and time-varying volatility may cause deviations

17. Combinations of Options • With combinations of different options, we can create “more exotic” currency positions • Long straddle = combination of a long call and a long put on the same underlying asset with the same exercise price • A bet on volatility • Opposite of a naked straddle • Ask Nick Leeson how it works

18. Notice that a call option to buy pounds with dollars is equivalent to a put option to sell dollars. • If we buy a call option on pounds and sell a put option with the same expiration date and strike price, we have created a “synthetic forward” • Put-Call Parity: Long Call + Short Put + Exercise Price = Long Forward