1 Hedging with Foreign Currency Options Kris Kuthethur Murthy Vanapalli
2 Foreign Currency Option Financial instrument that gives the holder the right, but not the obligation, to sell or buy currencies at a set price called the strike price or exercise price before a specified maturity date. American Option European Option Bermudan Option
3 Why and When to use Options? Can be used to hedge potential transactions, or transactions that are contingent on something Can be used when we are uncertain about exchange rates in the future. May be useful whenever a firm wants to protect itself from the downside risk of exposure but reap some of the benefits on the upside
4 Call and Put Options Call Long position Option contains the right but not the obligation to buy currency at the exercise price Used to hedge foreign currency-outflows (payables) Put Short position Option contains the right but not the obligation to sell currency at the exercise price Used to hedge foreign currency-inflows (receivables)
5 Options Concept Call Option on the Dollar Put Option on the Yen Put Option on the Dollar Call Option on the Yen Concepts BUY the Option PAY PREMIUM Obtain the RIGHT to buy the dollars and to sell the yen. Risk is to a positive move in dollars. Obtain the RIGHT to sell the dollars and to buy the yen. Risk is to a negative move in dollars. Protection till maturity is a positive factor. However, there is a cost now, which is a negative factor. SELL the Option RECEIVE PREMIUM Assume the OBLIGATION to sell the dollars and to buy the yen. Risk is to a negative move in dollars. Assume the OBLIGATION to buy the dollars and to sell the yen. Risk is to a positive move in dollars. Reward now is a positive factor. However, there are risks till maturity, which is a negative factor.
6 Comparison of Hedging Alternatives Currency Option Right but not obligation to buy/sell options Premium payable Wide range of strike prices Retains unlimited profit potential while limiting downside risk Flexible delivery date of currency Foreign Exchange Forwards Obligation to buy/sell currency No premium payable Only one forward rate for a particular date Eliminates the upside potential as well as the downside risk Fixed delivery date of currency
7 Review of Hedging Techniques Hedging Technique To Hedge Payables To Hedge Receivables Forward/Futures hedge Money market hedge Currency option hedge Buy a currency futures/forward contract representing the currency and amount related to the payables. Borrow home currency and convert to currency denominating payables. Invest these funds until they are needed to cover the payables. Purchase a currency call option representing the currency and amount related to the payables. Sell a currency futures/forward contract representing the currency and amount related to the receivables. Borrow currency denominating receivables and convert to home currency. Invest these funds. The foreign loan is paid with the receivables. Purchase a currency put option representing the currency and amount related to the receivables.
8 Hedging Foreign Currency Outflows To protect against Pound appreciation, a firm has decided to purchase a 500,000 call option on British Pounds. The strike price written into the option is $1.55/ and the premium is 3 cents per pound. Premium = $0.03 X 500,000 = $15,000 Ceiling price = = $1.58/
9 Profit profile of Call Option Profit $/foreign currency
10 Hedging Foreign Currency Inflows A US company may have a cash inflow of 125,000 DM within the next quarter and decides to hedge this potential inflow using put options. The current spot rate is $0.60/DM and the company purchases options with a strike price of $0.56/DM for 0.5 cents per DM Premium = $0.05 X 125,000 = $6,250 Floor price = = $0.51/DM
11 Profit profile of Put Option Profit $/foreign currency
12 Hedging in an M & A scenario On Feb 1 st, Sundance Corp., a U.S. firm, agrees to buy Cogna Cola Inc., an Australian beverage manufacturer for AUD 100 million. The deal is set to close in late June (in five months) if it passes the vote of the Board of Directors of Cogna Cola Inc. The deal is priced in AUD, but Sundance s books and financing are in USD. The company is prepared for some variability in the USD cost of the deal, but has an internal break-even point beyond which the acquisition becomes unattractive. Therefore, Sundance faces a currency risk!!
13 Hedging in an M & A scenario Contd Sundance can easily hedge the currency risk by buying AUD forward. Today is February 1, The spot rate is USD/AUD; the June futures rate is USD/AUD. It would cost Sundance USD million to buy AUD 100 million forward at the June futures rate. This would be a perfect hedge if the future were certain!
14 Hedging in an M & A scenario Contd But what if the deal fails because of opposition of the Cogna Cola's Board of Directors and falls through? Sundance would have to buy AUD anyway and then convert them back to USD. If the USD strengthened in the interim to below USD/AUD, Sundance would lose money in the conversion. The stronger the USD, the greater the loss. If the USD/AUD were at USD/AUD, for instance, Sundance would spend USD million buying AUD at USD , but receive only USD million reconverting the AUD to USD.
15 Hedging in an M & A scenario Contd Sundance faces two risks: changes in exchange rates and the uncertainty of the deal's closure. Clearly, buying dollars forward covers one, but exacerbates the other. Sundance can choose At-the-money Option Zero-premium Collar
16 Hedging in an M & A scenario Contd At-the-money Option Buy: June USD/AUD American Call for AUD 100 million (2,000 contracts) Total Cost: USD 2,172,025 Premium USD per AUD = USD 2,170,000 Broker fee USD 25 + USD 1.00 per contract = USD 2,025 If the deal goes through, Sundance buys AUD at USD If it fails and the AUD has appreciated to, say, USD , it may still exercise the option and make a profit of USD 2 million If the deal fails and the AUD has depreciated, the call option is not exercised. The strategy's major drawback is its cost.
17 Hedging in an M & A scenario Contd Zero-premium Collar Buy: June USD/AUD American Call for AUD 100 million (2,000 contracts). Sell: June USD/AUD American Put for AUD 100 million (2,000 contracts) with a Put Knock-in USD/AUD. Total Cost: USD 4,050 Premium paid: USD per AUD call = USD 900,000 Premium received: USD.009 per AUD put = USD 900,000 Broker fee USD 25 + USD 1.00 per contract = USD 4,050 If the deal goes through, Sundance knows it will pay no more than USD 70 million for Cogna Cola Inc. The strategy is relatively inexpensive, but its potential cost is that Sundance may have to cover its short position in USD if the USD appreciates against the mark below USD/AUD. The wrinkle here is that the AUD put is triggered only if the AUD depreciates below USD , a large decrease that would be unlikely to occur in the next five months.
18 DISCRETE & CONTINUOUS TIME OPTION PRICING EXAMPLES
19 Current stock price Want to find the current option price S, C (?) Binomial Option Pricing S C S, C S, C S S Stock price in the up state Stock price in the down state C M ax[s X, 0] C M ax[s X, 0] Two Period Binomial Model S S,C,C,C π is called risk-neutral probability S and so on Option payoff in the up state Option payoff in the down state Formulae: S Su. S S. u S. u. u S. u S S. d S S. d S. d. d S. d S S S. u. d S. d. u C Max(0, S X ) C Max(0, S X ) C Max(0, S X ) C Max(0, S X ) C C Max(0, S X ) C C C C 1 r d u d C C n n n C S C S C S (1 ) C 1 r (1 ) C 1 r (1 ) C 1 r C S C S C S 2 2
20 Example Two Period Binomial Model Put Option Pricing Discrete Time Consider a two-period binomial model in which the underlying is at 30 and can go up 14 percent or down 11 percent each period. The risk-free rate is 3 percent per period. A. Find the value of a European call option expiring in two periods with an exercise price of 30. B. Find the number of units of the underlying that would be required at each point in the binomial tree to construct a risk-free hedge using 10,000 calls. Solution: Given: X = 30 u = = 1.14 d = = 0.89 r = 0.03
21 Calculations S + = 30(1.14) = S ++ = 30(1.14)(1.14) =38.99 S - = 30(0.89) = S -- = 30(0.89)(0.89) = S +- = S -+ = Sud = 30(1.14)(0.89) = C ++ = Max(0, ) = 8.99 C +- = Max(0, ) = 0.44 C -- = Max(0, ) = 0 π = ( ) / ( ) = 0.56; 1 -π = = 0.44 C + = [0.56(8.99) (0.44)] / [ ] = 5.08 C - = [0.56(0.44) (0.0)] / [ ] = 0.24 C = [0.56(5.08) (0.24)] / [ ] = 2.86 n = [ ] / [ ] = Conclusions The number of units of the underlying required for 10,000 calls would thus be 6,453 today, 10,000 at time 1 if the underlying is at and 659 at time 1 if the underlying is at At price of 30 and time 0, the risk free hedge would consist of a short position in 10,000 calls and a long position in 6,453 shares of the underlying. At price of 34.20, the risk free hedge would consist of a short position of 10,000 calls and a long position in 10,000 shares of the underlying At price of 26.70, the risk free hedge would consist of a short position in 10,000 calls and a long position in 659 shares of the underlying n + = [ ] / [ ] = 1.00 n - = [0.44-0] / [ ] =
22 Example: Black Scholes Option Pricing Continuous Time Call and put options on an asset are available with an exercise price of $30. The options expire in 75 days, and the volatility is The continuously compounded risk-free rate is 3.5 percent, and there are no cash flows on the underlying. The precise Black-Scholes-Merton values of these options at different underlying prices are as follows. Asset Price Call Price Put Price $ $ $ A. From the Black-Scholes-Merton model, obtain the approximate values of the call delta and put delta if the underlying asset price is $28. B. Using the call delta and put delta obtained in Part A and the call and put prices given in the problem for the asset price of $28, calculate the approximate new call and put prices for a i. $1 increase in the price of the underlying asset ii. $5 increase in the price of the underlying asset C. Based on a comparison of your answers in Part B with the actual call and put prices given in the problem, what can you say about the approximations based on delta?
23 A. The value of N(d l ) is the approximate value of delta for calls and N(d l ) - 1 is the approximate value of delta for puts. So, first calculate the value of d l. The time to expiration is T = 75/365 = year. Using the normal probability table, N(-0.25) = 1 - N(0.25) = = = N(d l ) Or use =NORMSDIST(d l ) in Excel Therefore, the approximate value of delta for calls is and the approximate value of delta for puts is = B. Change in option price = Delta X Change in underlying asset price Call delta = Put delta = i. For a $1 change in the price of the underlying: Change in call price = (1) = $ Change in put price = (1) = -$ Approximate new call price = = $ Approximate new put price = = $ ii. For a $5 change in the price of the underlying: Change in call price = (5) = $ Change in put price = (5) = -$ Approximate new call price = = $ Approximate new put price = = $0.1059
24 C. For a $1 change in the price of the underlying, the approximate new call price of $ is different from but not too far off the actual call price of $ Similarly, the approximate new put price of $ is different from but not too far off the actual out rice of $ Therefore, the delta approximation is good but not perfect. For a $5 change in the price of the underlying, the approximate new call price of $ is fairly far off the actual call rice of $ Similarly the approximate new put price of $ is quite far off the actual put price of $ Therefore, the delta approximation is not particularly good. The above comparisons indicate that the approximations based on delta are worse for larger moves in the underlying price.
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