Tài chính doanh nghiệp - Finance 407: Multinational financial management - Topic 10: Currency options and hedging

Topic #10: Currency options and hedgingL. GattisThe Pennsylvania State University1Finance 407: Multinational Financial ManagementPoll2What is your profit if you take a short position in 5 euro futures contracts at a price of $1.2501 and the euro is selling for $1.2651 at maturity? Each contract was for €100,000. $7,500-$7,500$1,500,-$1,500None of the aboveHow much was initial margin if the initial margin is 6%?$7,590$7,500$37,503$37,953None of the aboveLearning Objectives3Learning ObjectivesStudents can use compute the costs, payoff and profits of options and understand how options are used to hedge fx positions Foreign Currency Options4A foreign currency option is a contract giving the option purchaserthe right, but not the obligation, to buy (Call Option) or sell (Put Option) a given amount of foreign exchange at a fixed price per unit for a specified time period (until the expiration date). Exercise Type:American Option; buyer has the right to exercise the option at any time between the date of writing and the expirationEuropean Option: can be exercised only on the expiration dateThe option buyer pays the Seller (a.k.a. writer or grantor) a premium for the optionPrice Elements of an Option5Every option has three different price elements: The exercise or strike price, which is the exchange rate at which foreign currency can be purchased (call) or sold (put). The premium, cost, price, or value of the option itself (paid in advance by the buyer to the seller).The underlying or actual spot exchange rate in the market. Mony-ness6An option whose exercise price is the same as the spot price of the underlying currency is said to be at the money (ATM). Strike = SpotAn option that would be profitable if exercised immediately is said to be in the money (ITM). ITM Call: Strike Spot “Can sell at a premium”An option that would not be profitable if exercised immediately is referred to as out of the money (OTM). OTM Call: Strike > Spot “cheaper to buy in the spot market”OTM Put: Strike =X) =0ITM: buy in spot and sell@strike; Profit = Max(0,X-St)QOption Profit = Payoff – CostPoll11You buy 5 $1.30 strike calls on 125,000 euros for 5 cents per euro. What is your profit is the euro is selling for $1.15 at maturity?A. $-31,250 B. $0 C. $31,250 D. $62,500 E. None of the abovePoll12You buy 5 $1.30 strike puts on 125,000 euros for 4 cents per euro. What is your profit is the euro is selling for $1.25 at maturity?A. -$6,250 B. $6,250 C. -$25,000 D. -$87,500E. None of the aboveHedging with Currency Puts13Suppose Dell has a €500,000 December receivable. If unhedged, what is the US$ receivable value if the spot price is $1.3115 or $1.1225?$1.3115: $1.3115* €500,000=$655,750$1.1225: $1.1225* €500,000=$561,250If the position is hedged using a short $1.2228 forward, the hedged value of the receivable is: $1.3115: Sell using forward price: $1.2228* €500,000=$611,400$1.1225: Sell using forward price: $1.2228* €500,000=$611,400 The Forward contract is the obligation is sell at the forward price.Suppose Dell buys Phlx Euro Dec Puts at the strike price of $1.2228. Assuming physical delivery, what is the US$ receivable value if the spot price is $1.3115 or $1.1225?$1.3115: Do not exercise, sell A/R at spot: $1.3115 €500,000=$655,750$1.1225: Sell using forward price: $1.2228* €500,000=$611,400 The option contract is the right, but not obligation,to sell at the forward price.What is the initial cost of the options if the premium is 1.25 cents.Option Cost =€500,000*$.0125=$6,250“Unwinding Options”14Options can be unwound prior to delivery by selling the option at the new market price. Your profit is then P1-P0.Problem: Suppose you buy three June PHLX call options (Size:€62,500) with a $.90 strike price at a price of 2.3 (¢/€).What would be your total dollar cost for these calls, ignoring broker fees? After holding these calls for 60 days, you sell them for 3.8 (¢/€). What is your net profit on the contracts assuming that brokerage fees on both entry and exit were $5 per contract? Options vs. Forwards/FuturesOptionsForward/FuturesCostsPremiumNone(but, Margin for futures)PayoffsOnly positive for call or put buyerPositive or negativeExercise DateFlexible if American StyleOne Date (but can unwind futures contracts)# Positions(4) Buy or write, Calls or Puts(2) Long or short1515Option Valuation16Option valuation is a very difficult problem because the value depends on the option strike, option maturity, spot price, interest rates, and the volatility of the underlying exchange ratesAll of these factors are observable except volatility. Volatility is often estimated using the standard deviation of prior years exchange rate changesHigher fx rate volatility increases the value (and premium) of both puts and calls since the likelihood of large changes can only benefit option holdersBlack-Scholes and Binomial Models provide a benchmark to value options. These models assume exchange rates are normally distributedThese models also assume perfect, transaction free, continuous marketsClearly these assumptions are violated in the data, but the models still are used as the benchmark to price the options.Black-Scholes and Binomial Valuation Spreadsheet17$1.25 ATM call and putA Note of Option Delta18InterpretationsAn option’s delta is the change in the option price relative to a change in the underlying spot price.The likelihood that the option will be in the moneyAt-the-Options have a delta of about .5E.g, if the spot price of the ATM option on the prior slide increases $.10 (from 1.25 to 1.35). The call option price only increases by $.06 (about half)There is a 50% chance that the option will be ITMDelta and Money-ness and HedgeDeltas of OTM option aproach zero, Deltas ITM option approach 1 (in which case it looks like a forward, with 100% chance of exercise)Hedging policies may mandate a delta to ensure adequate coverage (i.e., cheap OTM options are not used to hedge the position)Option Pricing Model Implied Volatility19The spreadsheet valued the call at 5.09 cents using the assumptions (inputs) provided – 10% volatilityIf the option were actually selling at 4 cents you could either say the model is invalid or its inputs were wrongSince volatility is the only unobservable variable, we could find the volatility that ensures the models return a value of 4 cents – 7.78% in this caseThe volatility input that returns the market price is called the implied volatility (aka “implied vol”)The implied vol is used by traders to communicate prices – see WVOL in Bloomberg for a list of world implied volsPractice Problems20A six-month, $1.25 strike, put on the euro is selling for 2.15 (cents per euro). The contract quantity is for 125,000 euros. What is your profit (option payoff – premium) if you buy 5 puts and the euro at maturity is trading at $1.15 or 1.35?Profit (St=1.15)= (-.0215+(1.25-1.15))*125,000*5=$49,062.5Profit (St=1.35)= (-.0215)*125,000*5=-$13,437.50What is your profit if you buy 3 calls on the euro (quantity: 125,000 euros, strike price is $1.35) at a price (premium) of 1.50 cents per unit and sell them before maturity when the call bid-ask call price (premium) is 1.56-1.66 cents per unit? Profit = (-.015+.0156)*3*125,000=225Suppose you hedge a 125,000 Swiss franc payable which is expected to come due in 6 months. A six-month $.95 strike call is selling for 3.5 cents per franc. What is the USD cost of the option? What is the hedged USD cost of payable if the franc is selling for $.85 or $1.10?Cost = .035*125,000=$4,375.00 (Include the cost of option if problem states it)Hedged Value (.85) = No exercise, buy in spot , cost = .85*125,000=$106,250 Hedged Value (1.10) = Exercise, buy using call , cost = .95*125,000=$118,750 What is the cost of buying a ¥85 strike put on the yen that is selling for 3.5 100ths of a cent? Each contract is for 12,500,000 yen?.035/100*12,500,000=$4,375 Practice Problems21Suppose the pound is selling at $1.54 in the spot market. What range of strike prices are OTM calls and puts? What range of strike prices are ATM calls and puts?OTM Puts: X1.54OTM Calls: X>1.54 ITM Calls: X<1.54Suppose that black-Scholes value of a yen is 3 100ths of a cent and the market price is 4 100ths. Your BS input was 10%. Is the implied volatility higher of lower than 10%? Why?Higher than 105 since the market price is above the model price at 10%iClicker: Class Evaluation22How would you rate today’s class? Highest LowestTextbook23Shapiro and Sarin’s Foundation of Multinational Finance 6th Ed. Chapter 7 covers currency options