FIN 645: International Financial Management

FIN 645: International Financial Management
Lecture 4 Futures and Options on Foreign Exchange

Lecture Outline Forward Market: A Recap
Futures Contracts: Preliminaries Currency Futures Markets Basic Currency Futures Relationships Eurodollar Interest Rate Futures Contracts Options Contracts: Preliminaries Currency Options Markets Currency Futures Options Currency derivatives: classified as derivative or contingent claim securities because their values are derived from or contingent upon the value of the underlying security There are four (4) types of derivative products: Futures Forwards: already discussed Options Swap In futures/ forwards/swaps contracts, counterparties are under obligations to perform. In contrast, in options, it is the option of the buyer/holder to exercise or not depending upon the price of the underlying assets.

Forward Market: A Recap
A forward contract is an agreement between a firm and a commercial bank to exchange a specified amount of a currency at a specified exchange rate (called the forward rate) on a specified date in the future. Forward contracts are often valued at $1 million or more, and are not normally used by consumers or small firms.

When MNCs anticipate a future need for or future receipt of a foreign currency, they can set up forward contracts to lock in the exchange rate. The % by which the forward rate (F ) exceeds the spot rate (S ) at a given point in time is called the forward premium (p ). F = S (1 + p ) F exhibits a discount when p < 0. F/S -1 = p, If the euro’s one-year forward rate is $1.506 and the euro’s spot rate is $1.03, the euro forward premium is (1.506/1.03)-1= . = .02 or 2%, since p is positive, the forward rate contains a premium If the euro’s one-year forward rate is $1.00 and the euro’s spot rate is $1.03, the euro forward premium is (1.00/1.03)-1= . = or -2.91%, since p is negative, the forward rate contains a discount

Example: S = $1.681/£, 90-day F = $1.677/£ annualized p = F – S  360 S n = –  360 = –.95% The forward premium (discount) usually reflects the difference between the home and foreign interest rates, thus preventing arbitrage. From IRP, we know that, the forward premium (discount) usually reflects the difference between the home and foreign interest rates, thus preventing arbitrage.

Forward Market A swap transaction involves a spot transaction along with a corresponding forward contract that will reverse the spot transaction. A non-deliverable forward contract (NDF) does not result in an actual exchange of currencies. Instead, one party makes a net payment to the other based on a market exchange rate on the day of settlement. Pran group, needs to invest 100 million IRs. for its Indian subsidiary Pran India Limited. It wants the subsidiary to pay in IRs. in one year. Pran wants to lock in the rate at which IRs. can be converted back into dollars. Pran will request its bank for the following swap transactions. Today: The bank should withdraw dollars from Pran’s foreign currency account, convert the dollars to IRs. in the spot market, and transmit the IRs. to the Pran India Limited account. In one year: The bank should withdraw 100 million IRs. from Pran India Limited’s foreign currency account, convert them to dollars at today’s forward rate, and transmit them to Pran group’s account. If after one year, forward rate exhibits a discount, however, Pran group will receive fewer dollars in one year than it invested in the subsidiary today. But still avoids uncertainty.

Forward Market An NDF (Non-Deliverable Forward Contracts) can effectively hedge future foreign currency payments or receipts: Expect need for 100M IRs. Negotiate an NDF to buy 100M IRs. on Jul 1. Reference index (closing rate quoted by India’s central bank) = $.0020/IRs. April 1 Buy 100M IRs. from market. July 1 Index = $.0023/ IRs.  receive $30,000 from bank due to NDF. Like a regular forward contract, an NDF represents an agreement regarding a position in specified amount of a specified currency, a specified exchange rate, and a specified future settlement date. However, an NDF does not result in an actual exchange of currencies at a future date. Instead, one party to the agreement makes a payment to the other party based on the exchange rate at a future date. $.0020/IRs. $.0023/IRs. $.0018/IRs. Index = $.0018/ IRs.  pay $20,000 to bank.

Currency Futures Market
Currency futures contracts specify a standard volume of a particular currency to be exchanged on a specific settlement date. They are used by MNCs to hedge their currency positions, and by speculators who hope to capitalize on their expectations of exchange rate movements.

The contracts can be traded by firms or individuals through brokers on the trading floor of an exchange (e.g. Chicago Mercantile Exchange), automated trading systems (e.g. GLOBEX), or the over-the-counter market. Brokers who fulfill orders to buy or sell futures contracts typically charge a commission.

Futures Contracts: Preliminaries
A futures contract is like a forward contract: It specifies that a certain currency will be exchanged for another at a specified time in the future at prices specified today. A futures contract is different from a forward contract: Futures are standardized contracts trading on organized exchanges with daily resettlement through a clearinghouse. Both forward and future contracts are classified as derivative or contingent claim securities because their values are derived from or contingent upon the value of the underlying security Futures and forwards are same except: A forward exchange contract is tailor made for a client by an international bank F1 = (BDT/$) = 70 Futures are standardized and traded on exchange Forwards are customized and traded off-the-exchange

A major difference between a forward contract and a futures contract is the way the underlying asset is priced for future purchase or sale A forward contract states a price for the future transaction By contrast, a futures contract is settled-up or marked-to-market, daily at the settlement price The settlement price is a price representative of futures transaction prices at the close of daily trading on the exchange.

A buyer of a futures contract (one who holds a long position) in which the settlement price is higher (lower) than the previous day's settlement price has a positive (negative) settlement for the day. Buy long and sell short Since a long position entitles the owner to purchase the underlying asset, a higher (lower) settlement price means the futures price of the underlying asset has increased (decreased). Consequently, a long position in the contract is worth more (less).

The change in settlement prices from one day to the next determines the settlement amount Settlement amount is equal to the change in settlement prices per unit of the underlying asset, multiplied by the size of the contract, and equals the size of the daily settlement to be added or subtracted from the margin account Futures trading between the long and the short is a zero-sum game

Standardizing Features: Contract Size Delivery Month Daily resettlement Initial Margin (about 4% of contract value, cash or T-bills at your brokers). Contract size: the amount of underlying foreign currency for purchase/sell at a future time. Price quoted in USD Currency Units per contract British pound 62,500 Japanese Yen 12,500,000 Euro 125,000 USD Delivery month: the time during the year when contracts mature. e.g. March, June, September, December, etc. Daily Settlement: Is done through marking-to-market (discussed later in detail). A forward contract states a price for the future transaction. By contrast, a futures contract is settled up, or marked to the market, daily at settlement price. The settlement price is a price representative of futures transaction prices at the close of daily trading on the exchange. Discussed in detail later. An initial margin must be posted in to a collateral account to establish a futures position.

Daily Resettlement: An Example
Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate). Speculative purpose to profit from a change in the future price - Sell the currency expected to depreciate and buy the currency expected to appreciate. Hedging purpose to avoid price variation -Decision is driven from a risk management perspective Currently $1 = ¥140. The 3-month forward price is $1=¥150.

Currently $1 = ¥140 and it appears that the dollar is strengthening. If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will make money if the yen depreciates beyond $1 = ¥150. Let’s say the contract size is ¥12,500,000 Your initial margin in US dollars is 4% of the contract value: We sold the futures contract here. We are obligated here to deliver ¥ at contract expiry. You sell ¥ because you think it will depreciate.

If tomorrow, the futures rate closes at $1 = ¥149, then your position’s value drops. Your original agreement was to sell ¥12,500,000 and receive $83,333.33 But now ¥12,500,000 is worth $83,892.62 We are in speculation and we do not have ¥. You have to buy from the market. At $1=¥150, our position values at $83, However, if tomorrow, $1=¥149, we need more $ to buy same ¥12,500,000. Because from the contract, we are obligated to sell ¥, we are paying $ extra. You have lost $ overnight.

The $ comes out of your $3, margin account, leaving $2,774.05 This is short of the $3, required for a new position. Your broker will let you slide until you run through your maintenance margin. Then you must post additional funds or your position will be closed out. This is usually done with a reversing trade. Maintenance Margin (usually 75% of initial margin or 3 percent of the contract value) that must be maintained as margin below which investors receive call for Variation Margin from the broker. Reversing trade is to enter into an identical contract but in OPPOSITE direction. Here enter into a future contract to sell $ ($1=¥150).

Enforced by potential arbitrage activities, the prices of currency futures are closely related to their corresponding forward rates and spot rates. Currency futures contracts are guaranteed by the exchange clearinghouse, which in turn minimizes its own credit risk by imposing margin requirements on those market participants who take a position.

Comparison of the Forward & Futures Contracts
Feature Forward Markets Futures Markets Operational mechanism Traded directly between contracting parties Traded on the exchanges Contract specification Varies from trade to trade Standardized Counterparty risk Exists, sometimes passed on to a guarantor Exists, But assumed by the clearing agency Liquidation profile Low, customized and not easily accessible High, exchange-traded Price discovery Not efficient, scattered markets Efficient centralized market Quality of information dissemination Poor, slow Good, fast

Comparison of the Forward & Futures Contracts
Forward Contracts Futures Contracts Participants Banks, brokers, Banks, brokers, MNCs. Public MNCs. Qualified speculation not public speculation encouraged. encouraged. Security Compensating Small security deposit bank balances or deposit required. credit lines needed. Clearing Handled by Handled by operation individual banks exchange & brokers. clearinghouse. Daily settlements to market prices. Marketplace Worldwide Central exchange telephone floor with worldwide network communications. Regulation Self-regulating Commodity Futures Trading Commission, National Futures Association. Transaction Bank’s bid/ask Negotiated Costs spread. brokerage fees.

Speculators often sell currency futures when they expect the underlying currency to depreciate, and vice versa. 1. Contract to sell 500,000 pesos @ $.09/peso ($45,000) on June 17. April 4 2. Buy 500,000 pesos @ $.08/peso ($40,000) from the spot market. June 17 3. Sell the pesos to fulfill contract. Gain $5,000.

MNCs may purchase currency futures to hedge their foreign currency payables, or sell currency futures to hedge their receivables. 1. Expect to receive 500,000 pesos. Contract to sell 500,000 pesos @ $.09/peso on June 17. April 4 2. Receive 500,000 pesos as expected. June 17 3. Sell the pesos at the locked-in rate.

Holders of futures contracts can close out their positions by selling similar futures contracts. Sellers may also close out their positions by purchasing similar contracts. 1. Contract to buy $.53/A$ ($53,000) on March 19. January 10 2. Contract to sell $.50/A$ ($50,000) on March 19. February 15 3. Incurs $3000 loss from offsetting positions in futures contracts. March 19 If a firm holding a currency futures contract decides before the settlement date that it no longer wants to maintain its position, it can close out the position by selling an identical futures contract. The gain or loss to the firm from its previous futures position is dependent on the price of purchasing futures versus selling futures. Why you might do so? If the spot rate increases substantially over one- month period, the futures price will likely increase by the same amount. In this case purchase and subsequent sale would be profitable. Conversely, a decline in the spot rate will correspond with a decline in the currency futures price, meaning that purchase and subsequent sale would result in a loss.

Currency Futures Markets
The Chicago Mercantile Exchange (CME) is by far the largest. Others include: The Philadelphia Board of Trade (PBOT) The MidAmerica commodities Exchange The Tokyo International Financial Futures Exchange The London International Financial Futures Exchange

The Chicago Mercantile Exchange
Expiry cycle: March, June, September, December. Delivery date 3rd Wednesday of delivery month. Last trading day is the second business day preceding the delivery day. CME hours 7:20 a.m. to 2:00 p.m. CST. Exchanges act as clearing houses for the futures market. Futures exchanges may have daily price limit.

CME After Hours Extended-hours trading on GLOBEX runs from 2:30 p.m. to 4:00 p.m dinner break and then back at it from 6:00 p.m. to 6:00 a.m. CST. Singapore International Monetary Exchange (SIMEX) offer interchangeable contracts. There’s other markets, but none are close to CME and SIMEX trading volume.

Basic Currency Futures Relationships
Open Interest refers to the number of contracts outstanding for a particular delivery month. Open Interest is a good proxy for demand for a contract. Some refer to open interest as the depth of the market. The breadth of the market would be how many different contracts (expiry month, currency) are outstanding. Deeper depth and wider breadth indicate more (price) efficiency and higher liquidity of the futures contract.

Reading a Futures Quote
Highest and lowest prices over the lifetime of the contract. Daily Change Closing price Exhibit 9.3, Canadian Dollar Opening Price: the price at opened for trade, say $0.6403/C$. Hi: the highest price traded throughout the day. Lo: the lowest price traded throughout the day. Settle: the settlement price (closing price) Change: Closing price of today – closing price of the previous day (not shown here). The opening price is not necessarily equal to closing price of the previous day. Please notice from your book that Open Interest is higher for nearby contract than for distant contracts. i.e. 8,427, 2051, 742 for Dec, March, and June respectively Lowest price that day Highest price that day Opening price Number of open contracts Expiry month

Eurodollar Interest Rate Futures Contracts
Widely used futures contract for hedging short-term U.S. dollar interest rate risk. The underlying asset is a hypothetical $1,000, day Eurodollar deposit—the contract is cash settled. Traded on the CME and the Singapore International Monetary Exchange. The contract trades in the March, June, September and December cycle. Futures contract are usually short-term in nature. However, they can be rolled over to achieve a long-term hedging horizon. Swaps by nature can be used to accomplish a hedged position for a longer term.

Reading Eurodollar Futures Quotes
EURODOLLAR (CME)—$1 million; pts of 100% Open High Low Settle Chg Yield Settle Change Open Interest June 97.58 97.65 97.59 97.64 .03 2.36 -0.3 425,705 Eurodollar futures prices are stated as an index number of three-month LIBOR calculated as F = 100-LIBOR. The closing price for the July contract is 97.64, thus the three-month LIBOR implied yield is 2.36 percent = 100 – 97.64 Exhibit 9.5 F = Settlement price Alternative to FRA-Forward Rate Agreement The minimum price change is one basis point. On $1 million of face value, one basis point represents $100 on an annual basis. Since it is a 3-month contract one basis point corresponds to a $25 price change.

Currency Options Market
Currency options provide the right to purchase or sell currencies at specified prices. They are classified as calls or puts. Standardized options are traded on exchanges through brokers. Customized options offered by brokerage firms and commercial banks are traded in the over-the-counter market. 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.

Options Contracts: Preliminaries
In-the-money The exercise price is less than the prevailing spot price of the underlying asset. At-the-money The exercise price is equal to the prevailing spot price of the underlying asset. Out-of-the-money The exercise price is more than the prevailing spot price of the underlying asset. Call OPTION In-the-money: Option buyer gains. At-the-money: Option buyer is at par. Out-the-money: Option buyer loses the premium (price paid to purchase the option). In an option, the buyer has the option to exercise if it is worthwhile. Otherwise, she does not exercise and only looses the premium. However, theoretically gains are unlimited.

Currency Call Options A currency call option grants the holder the right to buy a specific currency at a specific price (called the exercise or strike price) within a specific period of time. A call option is in the money if exchange rate > strike price, at the money if exchange rate = strike price, out of the money if exchange rate < strike price.

Currency Call Options Option owners can sell or exercise their options, or let their options expire. Call option premiums will be higher when: (spot price – strike price) is larger; the time to expiration date is longer; and the variability of the currency is greater. Firms may purchase currency call options to hedge payables, project bidding, or target bidding.

Currency Call Options Speculators may purchase call options on a currency that they expect to appreciate. Profit = selling (spot) price – option premium – buying (strike) price At breakeven, profit = 0. They may also sell (write) call options on a currency that they expect to depreciate. Profit = option premium – buying (spot) price + selling (strike) price

Currency Put Options A currency put option grants the holder the right to sell a specific currency at a specific price (the strike price) within a specific period of time. A put option is in the money if exchange rate < strike price, at the money if exchange rate = strike price, out of the money if exchange rate > strike price.

Currency Put Options Put option premiums will be higher when:
(strike price – spot rate) is larger; the time to expiration date is longer; and the variability of the currency is greater. Firms may purchase currency put options to hedge future receivables.

Currency Put Options Speculators may purchase put options on a currency that they expect to depreciate. Profit =selling (strike) price – buying price – option premium They may also sell (write) put options on a currency that they expect to appreciate. Profit = option premium + selling price – buying (strike) price

Combined Currency Put Option and Call Option
One possible speculative strategy for volatile currencies is to purchase both a put option and a call option at the same exercise price. This is called a straddle. By purchasing both options, the speculator may gain if the currency moves substantially in either direction, or if it moves in one direction followed by the other.

Efficiency of Currency Futures and Options
If foreign exchange markets are efficient, speculation in the currency futures and options markets should not consistently generate abnormally large profits.

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. European options are more widely used.

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 + =

Currency Options Markets
PHLX HKFE 20-hour trading day. OTC volume is much bigger than exchange volume. Trading is in seven major currencies plus the euro against the U.S. dollar. Philadelphia Stock Exchange

Contingency Graphs for Currency Options
+$.02 +$.04 – $.02 – $.04 $1.46 $1.50 $1.54 Net Profit per Unit Future Spot Rate For Buyer of £ Call Option Strike price = $1.50 Premium = $ .02 +$.02 +$.04 – $.02 – $.04 $1.46 $1.50 $1.54 Net Profit per Unit Future Spot Rate For Seller of £ Call Option Strike price = $1.50 Premium = $ .02 A British pound call option For Buyer of £ Call Option A contingency graph for a buyer of a call option compares the premium paid for the call option to potential the payoffs to be received for various exchange rate scenarios If the future spot rate is $1.50 or less per unit, the option would not be exercised. Net gain -$0.2 Break even point at $1.52 At any rate above $1.52, gain from exercising the option would more than offset the premium per unit, resulting in a positive net gain The maximum loss to the speculator is the premium paid for the option. For Seller of £ Call Option A contingency graph for a seller of a call option compares the premium received from selling a call option to the potential payoffs made to the buyer of the call option for various exchange rate scenarios At future spot rate less than $1.50 or less per unit, the net gain to the seller would be $0.2 per unit, as the option would not have been exercised. If the future spot rate is $1.51 the seller would lose $0.1 per unit (paying $1.51 for the pound in the spot market and selling for $1.5 to fulfill the exercise request). Yet the loss would be offset by the premium of $0.2 per unit, resulting in a net gain of $0.1 per unit. Break even point is at $1.52, and the net gain to the seller of a call option becomes negative at all future spot rates higher than $1.52. The maximum loss to the speculator is unlimited. Notice that contingency graphs for buyer and seller of this call options are mirror images of one another

Contingency Graphs for Currency Options
+$.02 +$.04 – $.02 – $.04 $1.46 $1.50 $1.54 Net Profit per Unit Future Spot Rate For Buyer of £ Put Option Strike price = $1.50 Premium = $ .03 +$.02 +$.04 – $.02 – $.04 $1.46 $1.50 $1.54 Net Profit per Unit Future Spot Rate For Seller of £ Put Option Strike price = $1.50 Premium = $ .03 A British pound put option For Buyer of £ Put Option A contingency graph for a buyer of a put option compares the premium paid for the put option to potential the payoffs to be received for various exchange rate scenarios If the future spot rate is above $1.50 per unit, the option would not be exercised. Net gain -$0.3 At a future spot rate of $1.48 of $1.48, the put option will be exercised. However considering the premium of $0.3 per unit, there will be a loss of $0.1 per unit Break even point at $1.47 At any future spot rates of less than $1.47, the buyer of the put option will earn a positive net gain. For Seller of £ Put Option A contingency graph for a seller of a put option compares the premium received from selling a put option to the possible payoffs made to the buyer of the put option for various exchange rate scenarios. It is a mirror image of the contingency graph for the buyer of a put option.

Conditional Currency Options
A currency option may be structured such that the premium is conditioned on the actual currency movement over the period of concern. Suppose a conditional put option on £ has an exercise price of $1.70, and a trigger of $1.74. The premium will have to be paid only if the £’s value exceeds the trigger value.

Option Type Exercise Price Trigger Premium basic put $ $0.02 conditional put $1.70 $1.74 $0.04 $1.66 $1.70 $1.74 $1.78 $1.82 $1.68 $1.72 $1.76 Net Amount Received Spot Rate Basic Put Conditional Put

Similarly, a conditional call option on £ may specify an exercise price of $1.70, and a trigger of $1.67. The premium will have to be paid only if the £’s value falls below the trigger value. In both cases, the payment of the premium is avoided conditionally at the cost of a higher premium.

Basic Option Pricing Relationships at Expiry
At expiry, an American call option is worth the same as a European option with the same characteristics. If the call is in-the-money, it is worth ST – E. If the call is out-of-the-money, it is worthless. CaT = CeT = Max[ST - E, 0] ST = Spot price of the underlying asset at time T. E = Exercise price of the option. CaT = Value of an American call option at expiry. CeT= Value of an European call option at expiry.

Currency Futures Options
Are an option on a currency futures contract. Exercise of a currency futures option results in a long futures position for the holder of a call or the writer of a put. Exercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put. If the futures position is not offset prior to its expiration, foreign currency will change hands. In a Currency Futures Option, the buyer has the right and option to enter into a futures contract (purchase/sell foreign currency at a pre-specified price).

Lecture Outline (continued)
Basic Option Pricing Relationships at Expiry American Option Pricing Relationships European Option Pricing Relationships Binomial Option Pricing Model European Option Pricing Model Empirical Tests of Currency Option Models

Basic Option Pricing Relationships at Expiry
At expiry, an American put option is worth the same as a European option with the same characteristics. If the put is in-the-money, it is worth E - ST. If the put is out-of-the-money, it is worthless. PaT = PeT = Max[E - ST, 0]

Basic Option Profit Profiles: Call Buyer
CaT = CeT = Max[ST - E, 0] profit Long 1 call ST Let say, we want to buy a call option on IBM stock. Suppose, currently IBM sells for $40 (S), and the price of the call (premium) is $5 and the strike/exercise price (E) is $40. At expiry, two things can happen: ST ≤ 40 (scenario 1) Or, ST > 40 (scenario 2) In scenario 1, we will let the option expire worthless and loose option premium, since we can buy the stock at a cheaper price from the spot market. However, in scenario 2, since ST > E, it is worthwhile to exercise. Our profit from exercise say if ST = 55 is: ST – E =55 – 40 = 15 The net profit is, ST – E - C=55 – = 15-5 =10 The break-even price therefore is E+C = $40+$5 =$45. For a buyer, gain is unlimited and loss is limited to the premium. $5 E+C E $40 $45 $55 loss

Basic Option Profit Profiles: Call Buyer
CaT = CeT = Max[ST - E, 0] profit Long 1 call E=67 ST Let say, the option has a current premium, Ca=0.30 per SF The exercise price is 67 cents per SF Suppose, at expiration the spot price is $ /SF The call option has an exercise value of =3.25 cents each SF62,500 of the contract or $ That is the call owner can buy SF62,500, worth $ (=SF62,500X$0.7025) in the spot market for $41,875(= SF62,500X$0.67) On the other hand if at expiration the spot rate is $0.6607/SF, the call option has a negative exercise value, =-.93 cents per SF. The call buyer is under no obligation to exercise the option if it is to his disadvantage, he should let it expire worthless, or with zero value. -Ca=-.30 ST=E+Ca 67.30 70.25 loss Out-of the Money At-the money In-the Money

Basic Option Profit Profiles: Call Seller
CaT = CeT = Max[ST - E, 0] profit -Ca=-.30 ST=E+ Ca E=67 ST For a seller, loss is unlimited and gain is limited to the premium. It is zero-sum game. short 1 call loss At-the Money

Options and Speculative Behavior
Anytime the speculator believes that ST will be in excess of the breakeven point, S/he will establish a long position in the call. The speculator who is correct realizes a profit. If the speculator is incorrect in the forecast, the loss will be limited to the call premium. Alternatively, if the speculator believes that ST will be less than the breakeven point, S/he will establish a short position in the call. The speculator who is correct realizes a profit, the largest amount being the call premium received from the buyer. If speculator is incorrect in the forecast, very large losses may result if ST is much larger than the breakeven point.

Basic Option Profit Profiles: Put Buyer
PaT = PeT = Max[E - ST, 0] E-Pa= =101.53 profit long 1 put ST A Put is opposite of a Call. A put is a right to sell at a pre-specified (E, strike/exercise) price. Pa = 2.47 cents E = 1.04 If ST=$1.0302/EUR, the put contract has exercise value of =.93 cents for each of the EUR 62,500 of the contract, or $581.25 ST= E - Pa -Pa=-2.47 E=104 = =101.53 loss

Basic Option Profit Profiles: Put Seller
CaT = CeT = Max[ST - E, 0] profit Pa=2.47 E=104 ST For a Put seller, gain is limited to the premium. However, the maximum loss is to have a zero-value stock and pay the strike price Short 1 put ST= E - Pa -E-Pa= =101.53 loss

Options and Speculative Behavior
Anytime the speculator believes that ST will be less than the breakeven point, S/he will establish a long position in the put. The speculator who is correct realizes a profit. If the speculator is incorrect in the forecast, the loss will be limited to the call premium. Alternatively, if the speculator believes that ST will in excess of the breakeven point, S/he will establish a short position in the put. The speculator who is correct realizes a profit, the largest amount being the put premium received from the buyer. If speculator is incorrect in the forecast, very large losses may result if ST is much smaller than the breakeven point.

American Option Pricing Relationships
With an American option, you can do everything that you can do with a European option—this option to exercise early has value. CaT > CeT = Max[ST - E, 0] PaT > PeT = Max[E - ST, 0] In contrast, European options can only be exercised at expiry.

Market Value, Time Value and Intrinsic Value for an American Call
CaT > Max[ST - E, 0] Profit Market Value Of the Option ST - E Time value When an option is written it is usually written out-of-the money, The option also has some in-built time value (time flexibility to see the price of the underlying changes/moves). As time passes, the time premium reduces. Intrinsic value = Stock price – Exercise price (for a call option). Please note that market value of option and intrinsic value converge at EXPIRY since there is no time value (or, time value reduces to zero at expiry as there is no time left). Intrinsic value ST E Out-of-the-money In-the-money loss

European Option Pricing Relationships
Consider two investments Buy a call option on the British pound futures contract. The cash flow today is -Ce Replicate the upside payoff of the call by Borrowing the present value of the exercise price of the call in the U.S. at i$ The cash flow today is E /(1 + i$) Lending the present value of ST at i£ The cash flow is ST /(1 + i£) Current Time Expiration ST ≤E ST >E Portfolio A: Buy Call -Ce ST-E Lend PV of E in US -E/(1+r$) E E __________________________________________________ Total -Ce-E/(1+r$) E ST Portfolio B: Lend PV of 1 unit of foreign currency I at rate ri -St/(1+ri) ST ST It follows that Portfolio A has an equal value as that of Portfolio B when ST >E . However, Portfolio A has a higher value when ST ≤E.

European Option Pricing Relationships Illustration
Current Time Expiration ST ≤E ST >E Portfolio A: Buy Call -Ce ST-E Lend PV of E in US -E/(1+r$) E E _________________________________________________________ Total -Ce-E/(1+r$) E ST Portfolio B: Lend PV of 1 unit of foreign currency i at rate ri -St/(1+ri) ST ST It follows that Portfolio A has an equal value as that of Portfolio B when ST >E However, Portfolio A has a higher value when ST ≤E.

When the option is in-the-money both strategies have the same payoff. When the option is out-of-the-money it has a higher payoff the borrowing and lending strategy. Thus: In-the-money means strike/exercise price is less than spot price (ST >E). Out-of-the-money means strike/exercise price is greater than the spot price (ST ≤E). Thus the equation sets the lower boundary of a n European call option payoff.

Using a similar portfolio to replicate the upside potential of a put, we can show that:

Binomial Option Pricing Model
Imagine a simple world where the dollar-euro exchange rate is S0($/ ) = $1 today and in the next year, S1($/ ) is either $1.1 or $.90. $1 $.90 $1.10 S0($/ ) S1($/ )

A call option on the euro with exercise price S0($/ ) = $1 will have the following payoffs. $1 $.90 $1.10 S0($/ ) S1($/ ) C1($/ ) $.10 C1 = Max (ST-E, 0) = Max($1.1 -$1.0, 0) = $0.10 Or, C1 = Max (ST-E, 0) = Max($0.9 -$1.0, 0) = $0 $0

The most important lesson from the binomial option pricing model is: the replicating portfolio intuition. Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities. We can replicate a portfolio’s (bond, stock, gold, etc.) payoff by investing in options that replicate/mimic the payoff.

European Option Pricing Formula
We can use the replicating portfolio intuition developed in the binomial option pricing formula to generate a faster-to-use model that addresses a much more realistic world.

The model is Where C0 = the value of a European option at time t = 0 r$ = the interest rate available in the U.S. r£ = the interest rate available in the foreign country—in this case the U.K.

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 40% p.a. Before we start, note that the intrinsic value of the option is $.10—our answer must be at least that.

Let’s try our hand at using the model. If you have a calculator handy, follow along. First calculate Then, calculate d1 and d2

N(d1) = N( ) = .5422 N(d2) = N( ) =

Option Value Determinants
Call Put 1. Exchange rate – 2. Exercise price – Interest rate in U.S – 4. Interest rate in other country + – 5. Variability in exchange rate Expiration date The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0. The precise position will depend on the above factors. The impact of determinants is opposite for call and put for the first four variables: Exchange rate Exercise price Interest rate in U.S. Interest rate in other country For call options If exchange rate (the underlying asset) rises, St-E rises. Therefore, call option value rises. Higher exercise means potential for lower profit. Therefore, call option value falls. Higher interest rate in the US means an US investor expect dollar to depreciate and foreign currency to appreciate (refer to Interest Rate Parity). This lead to a increase in call price (premium). The opposite is true when interest rate in other country is higher: call price falls. The interaction is same for both call and put for last two variables. Variability and expiration date (term to maturity) both positively affect both call and put options price.

Empirical Tests The European option pricing model works fairly well in pricing American currency options. It works best for out-of-the-money and at-the-money options. When options are in-the-money, the European option pricing model tends to underprice American options.

FIN 645: International Financial Management

Similar presentations

Presentation on theme: "FIN 645: International Financial Management"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

FIN 645: International Financial Management

Similar presentations

Presentation on theme: "FIN 645: International Financial Management"— Presentation transcript:

Similar presentations

About project

Feedback