Tài chính doanh nghiệp - Topic 6: Currency forwards, futures, and options

Topic #6: Currency forwards, futures, and OptionsL. Gattis1Financial Risk ManagementLearning Objectives2Students understand and can recallPayoffs and profits of currency forwards, futures, and optionsForecasting spot and forward exchange rates with PPP, IRP, and UFRHow financial managers use forwards, futures, and options to hedge fx riskForwards3Forward contracts are negotiated between parties (OTC), the terms includeCurrency pair, Quantity, Price, Delivery date and locationPhysical delivery or cash settlementPhysical: Deliver or Take Delivery of Physical Currency. The majority of currency forwards are physical settlement.Cash Settlement: USD payment based on final spot exchange rate.Positions: Long (buyer of fx, takes delivery, gains if price increases, also called buyer) and Short party (seller of fx, make delivery, gains if price falls, also called seller)Usually requires no upfront payment if between two highly rated financial institutions A margin “Security deposit” may be required if your credit is worse than your counterpartyExample: 10% Initial Margin, Forward Price=$1.25, Q=100,000 euros: Margin = .1*1.25*100,000=$12,500 (USD Margin = IM% x F0 (Direct) x Qty of Forex)ProfitsLong Forward Payoff (and Profit) = (ST-F0,T)xQShort Forward Payoff (and Profit) = (F0,T-ST)xQF0,T= forward price at time 0, for delivery at time TST= Spot price at time T (Delivery of forward contract)EURUSD Forward Quotes (Bloomberg)4Positions and Hedging 5Hedging is the taking of a position that offsets an existing position. Asset ExamplesExpect to receive euros in 3-months (accounts receivable)Holding yen cashLondon real estate you expect to sell this yearOwn Shares of Novo Nordisk (Danish Stock)Is your exposure to an appreciating or depreciating dollar? How can you hedge?Liability ExamplesKroner accounts payableSwiss denominated bondPound line-of-credit balanceIs your exposure to an appreciating or depreciating foreign currency? How can you hedge?Reading WSJ Futures Prices6Size of contract:€125,000Futures Price of €1 at $1.2030Maturity monthFutures Price of ¥1 at $.008861 (or ¥ 112.85/$)Futures Problems7Suppose Dell has a €500,000 December receivableIf unhedged, the US$ receivable value if the spot price is $1.3115 or $1.1225 in December is?$1.3115: €500,000 x $1.3115 = $655,750$1.1225: €500,000 x $1.1225 = $561,250 Futures Problems8Dell has a €500,000 December receivable. Suppose they take a short position in four CME Euro Dec contracts (€125,000 each) at the settle price of $1.2228. Assuming physical delivery, what is the US$ receivable hedged value? If the margin requirement for hedgers is 5% of the USD contract value (FxQ). What is the USD margin requirement?Forwards vs. Futures9ForwardsFuturesTradingOTCExchangeDeliv. Date, QuantityNegotiated between partiesStandardized by exchangeQuotesUsually FX/$Usually $/FXTransaction CostsBid-Ask SpreadBroker FeesCredit RiskCounterparty (High)Exchange (low)Margin (Bond Req.)None UsuallyRequired, Paid upfrontClose Out90% Physical Delivery99% Offsetting TradeSettlementAt MaturityDaily mark-to-marketDaily Settlement(Mark-to-Market Process)10Futures contracts require a margin prior to taking a position. The margin requirement is Margin ($) = Initial Margin % x F0 x Quantity e.g. (8%, F=$1.25, Q=€125,000, 2 contracts) Margin =.08*1.25*125000*2 = $25,000The margin balance will change daily based on the change in the market price of the futures contract Daily Margin Change (if long) = ΔF x Quantity Daily Margin Change (if short) = -ΔF x Quantity e.g. (after going long at $1.25, the futures price goes to $1.26) You also get 1-day’s interest on your Margin balance (e.g., 4% APR, daily compounding) New Margin =25,000*(1+.04/365)+(1.26-1.25)*250,000 = $27,502.74Closing Out Position “Unwinding”1199% of futures contracts are “unwound” prior to settlement and delivery by taking an offsetting position (long/short) in the contract at the current contract price (FT).Long Unwound Payoff at t (t=X) =0ITM: buy in spot and sell@strike; Profit = Max(0,X-St)QOption Profit = Payoff – CostConcept Check25You 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 $1.15 at maturity?$-31,250$0$31,250$62,500None of the aboveYou 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?-$6,250$6,250-$25,000-$87,500None of the aboveHedging with Currency Puts26Suppose Dell has a €500,000 December receivable. If unhedged, what is the US$ 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: ??$1.1225: ??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 = ??“Unwinding Options”27Options 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 short2828Option Valuation29Option 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 Spreadsheet30$1.25 ATM call and putImplied Volatility31The 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 volsForward/Futures Problems 32What is your USD profit if you short 5 swissie forwards at $1.1245 and the swissie is selling for $1.2232 (per Sf) or $1.0833 at maturity. Each contract is for 125,000 Swiss francs. What is your USD profit if you long 3 yen forwards at 89.12 and the yen is selling for 87 or 95 at maturity? Each contract is for 12.5 million yen. What is the USD initial margin for buying 10 euro futures when the futures price is $1.3345, the quantity is 125,000 per contract, and the initial margin is 5%? 1. What is your margin balance after 2 days if the futures price falls to $1.3103 and interest is compounded at 6% discrete interest per year. Interest is compounded daily. You have an aussie payable of A$1,100,000 that you have hedged with futures contracts (each worth A$100,000). How many futures contracts do you need? What is the hedged USD value of the payable if the futures price is $0.88? You take a long position in 3 euro futures at 1.2523 (each is for 125,000 euros). The euro futures price rallies to $1.2856 when the ECB announces higher GDP growth. You decide to unwind by shorting 3 contracts at $1.2856. What was your USD profit? Forward/Futures Problems 33Suppose a Pepsi cost $1.75 in the U.S. and P787.50 (pesos) in Chile. What is the indirect PPP spot rate (Chilean Peso / USD)Suppose inflation in the Eurozone and the U.K. is 3% and 7%, and the spot rate is £1.40 per euro. What is the expected PPP spot rate in one year?What is the expected PPP spot rate in two years?What is the expected PPP spot rate in 6 months?Suppose interest rates in Denmark and China are 2% and 10% and the spot rate is ¥1.5 per Danish kroner.What is the IRP 1-year forward rate?What is the IRP 2-year forward rate?What is the IRP 3-momth forward rate?Option Problems34A 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? What 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? Suppose 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? The hedged cost of the payable is the total cost to make the payment including the derivative payoff and cost. 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? Suppose 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 ITM calls and puts? Suppose 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? Textbook35Shapiro and Sarin’s Foundation of Multinational Finance 6th Ed. Chapter 4 covers the use of purchasing power parity and interest rate parityChapter 7 covers the use of forwards, futures, and options