Foreign Exchange Exposure
• Cash flows of firm, ergo its market value, are affected by changes in the value of foreign currency, FX.
• Transactions Exposure – Explicit contractual amount denominated in FX.
• Operating Exposure – No contract exists yet FX exposure is present.
Two Methods of FX Quotation
• Direct Quotation• Number of home
(domestic, reference) currency units per unit of FX.
• Direct quote is inverse of indirect quote.
• Assumed in this course (intuitive).
• Indirect Quotation• Number of FX units
per unit of home (domestic, reference) currency.
• Indirect quote is inverse of direct quote.
• Not employed in this course (less intuitive).
Examples of Two Quotation Methods
• For Canadian firm.
• Direct quote on greenback, US$: C$1.053
• Indirect quote on greenback US$: US$0.95
• If FX appreciates (rises in value), the direct quote rises and the indirect quote falls.
• If FX depreciates (drops in value), the direct quote drops and the indirect quote rises.
Transactions Exposure
• First part of this four part course.
• Exporter - receives a contractually set amount of FX in future.
• Importer – pays a contractually set amount of FX in the future.
• Measure of FX exposure – the amount of FX involved.
Exporter’s Transactions Exposure
• Canadian beef exporter will receive US$1 million 3 months from now.
• S = direct quote on the greenback, i.e. C$/US$, 3 months hence. (Note: / means per.) S is plotted on horizontal axis.
• Exposed cash flow (ECF) = S x US$ 1 million. ECF is plotted on vertical axis.
Exporter’s Risk Profile
S(C$/US)
ECF(C$) US$1million
Exporter’s Risk Exposure
• Worried about depreciation in FX.
• Forward hedge: Sell FX forward. Arrange now to sell 3 months hence at price determined now, F (the forward rate).
• Option hedge: Buy right to sell FX, a put option on the FX.
Sell Forward Hedge
• Commit now to sell U$ 1 million 3 months from now at forward price, F, determined now.
• Price paid for Forward Contract = zero.
• Sell forward contract cash flow = (F – S) x U$ 1 million where S is the spot rate 3 months hence.
Sell Forward Contract
S(C$/U$)
Contract Cash Flow
F(C$/U$)
Hedge with Forward Contract
S(C$/U$)
F x U$1million
Hedged Cash Flow
Hedge with Put Option
• Put option is the right, not obligation like forward contract, to sell U$ 1 million 3 months hence at an exercise or strike price of X(C$/U$).
• P, put premium, price paid now for option.
• Put contract cash flow = X – S if S<X; 0 otherwise.
Put Contract Cash Flow
SX
Hedge with Put Option
SX
Hedged Cash Flow
Which is better? Sell forward or Buy put?
S
B
B = breakeven point
S<B, sell forward better
S>B, buy put better
Determination of B, breakeven FX Rate
• B is point of indifference between sell forward and buy put as hedges.
• S<B Forward is better ex-post• S>B Put is better ex-post• B = Forward rate + Future Value of Put
Premium; where interest rate is hedger’s borrowing rate.
• B = F + FV(P).
Hedging a U$ Receivable
• Canadian firm with U$ receivable due 6 months hence
• F (6 month forward rate) = C$ 1.35
• X (exercise price) = C$1.32
• P (put premium per U$) = C$0.05
• Borrowing rate = 6% quoted APR
• B (breakeven) = C$1.4015
3 Different Interest Rate Quotes
• Borrow $1 for 6 months at 6%:• APR, annual percentage rate, FV = $1.03 = $1 (1
+ .06/2 )• EAR, effective annual rate, FV = $1.02956 = $1
(1 + .06)^.5• CC, continuously compounded, FV = $1.03045 =
$1 exp(.06 x .5)• Default assumption: All interest (inflation,
appreciation) rates are annual.
Canadian Importer Problem
• Has U$ 5 M payable due 6 months hence.
• Two possible hedges: buy U$ forward or buy call on U$.
• Buy forward: Arrange now to buy U$5M 6 months from now at a rate set now, F.
• Buy call on U$ 5 M with exercise price X.
FX Payable
• Worried about the FX appreciating
S
-U$ 5 M
Exposed Cash Flow
Buy U$ Forward: Contract Cash Flow
F
U$5M
S
Buy Call on U$: Contract Cash Flow
X S
U$5M
Hedged Cash Flows
S
Forward Hedge-F x U$5M
B
Call Hedge
X
Buy forward versus buy call
B
S
Contract Cash Flows
B, breakeven FX rate between call and buy forward hedges
• B = forward rate - FV of call option premium
• FV (future value) uses the hedger’s borrowing rate.
• S<B call option better ex-post.
• S>B buy forward better ex-post.
Calculation of B
• Canadian firm with U$ 5 M payable due 6 months hence.
• F = C$1.35 ( 6 month forward rate)
• X = C$1.32 (exercise price of call)
• C = C$0.10 (call premium per U$)
• Borrowing rate = 6% quoted CC
• B = C$1.247
Significance of B = C$1.247
• If futureS > 1.247 better to buy forward ex-post.• If futureS < 1.247 better to buy call ex-post.• Define Pr( ) = probability of the event ( ).• If Pr(futureS>1.247) > Pr(futureS<1.247), better
to buy forward, rather than buy call, ex-ante.• Principle: The better ex-ante hedge is that which
maximizes the probability of choosing the correct hedge ex-post.
Forward vs. Option Hedges: Fundamental Trade-off
• Forward – no up-front outlay (at inception value of forward = 0) but potential opportunity cost later.
• Option – up-front outlay (option premium) but no opportunity cost later, ignoring option premium.
Option hedge vs. Forward hedge vs. Remain exposed
• Hedge FX liability.
• Ex-post analysis: S > F, buy forward is best; S < F, remain exposed is best.
• Option hedge is never best ex-post.
• Option hedge is an intermediate tactic, between extremes of buy forward and remain exposed.
Option hedge vs. Forward hedge vs. Remain exposed
F
Remain exposed
Writing options as hedges
• Zero sum game between buyer and writer.
• Writer’s diagram is mirror image of buyer’s about X-axis.
• Writer receives premium income.
• Write call to hedge a receivable, I.e., covered call writing.
• Write put to hedge a payable.
Basic problem with writing options as a hedge
• Viable if there is no significant adverse move in FX rate.
• FX receivable: viable if FX rate does not drop significantly.
• FX payable: viable is FX rate does not rise significantly.
• The original exposure remains albeit cushioned by the receipt of premium income.
A Lego set for FX hedging
• Six basic building blocks available for more complex hedges.
• Buy or sell forward.
• Buy or write a call.
• Buy or write a put.
Application of Lego set
• Option collar is an option portfolio comprised of long (short) call and short (long) put. Maturities are common but exercise prices may differ.
• What if there is a common exercise price = F, the forward rate pertaining to the common maturity of the options?
• Value of option collar must = zero.• Option collar replicates forward contract.
Option collar (buy call, sell put; common X = F) or Buy Forward
F S
F defines a critical value of X
• Another application of Lego set, option collars, and graphical reasoning.
• If X = F, C (call premium) = P (put premium).
• If X< F, C > P.
• If X> F, C < P.
Salomon’s Range Forward
• Another application of Lego set.• See Transactions Exposure Cases: Salomon
Contract to Aid in Hedging Currency Exposure.
• Buying a Range Forward is an option collar where a call, with X = upper limit of range, is purchased and a put, with X = lower limit of range, is written.
Salomon’s Range Forward (specific numbers)
• F = 1/DM 2.58 = U$0.3876• Range Upper limit, U= 1/DM2.50 = U$0.40• Range Lower limit, L = 1/DM2.65 = U$0.3774• If S(U$/DM) > U$0.40, US client buys DM at
U$0.40.• If S < U$0.3774, US client buys DM at U$0.3774.• If U$0.3774 < S <U$0.40, US buys DM at S.
Salomon’s Range Forward
SU=$0.4
L=$0.3774
Contract Cash Flow
Salomon’s Range Forward
SL UFX Liability Hedged Cash Flow
2 alternative ways of committing to buy (sell) FX in future
• Futures Contract• Traded anonymously
on an exchange.• “Marking to market” –
there are daily cash flow experienced.
• Assume: futures rate = forward rate.
• Forward Contract• Deal directly with
bank.• No cash flows until
maturity• Empirical result: For
FX, futures rate = forward rate on average.
Conditional (contingent) exposure
• Whether or not you are exposed to the contractually specified FX depends on someone else’s decision.
• Situation where an option should be used, not a forward.
• Examples: cross-border merger, bidding on a foreign construction contract, selling with a dual currency price list.
Telus Case
• Dual currency prices: C$1,682 or Bh32,799.
• Customer decides on currency.
• Hedging the time span between sale and customer’s currency decision must be with a put option, not sell forward.
• Defined implied spot rate, S* = C$0.051= C$1,682/Bh32,799.
Telus’ Risk Exposure
C$0.051 S(C$/Bh)
C$1,682
Effect of dual currency prices
• Client chooses to pay currency adjusted amount.
• As if the following were true: Telus demands payment in C$’s but gives client a put option on Bh.
• Since Telus issues a put option to the client, it must buy the same option to hedge.
Danger in hedging conditional exposure with a forward
• Problem if Telus were to sell Bh forward: Telus may not receive Bh’s.
• Client will choose to pay in C$’s if the Bh appreciates beyond C$0.051.
• If Bh appreciates, Telus must satisfy the forward contract by buying the appreciated Bh on the spot market.
Telus’ hedged diagram if sell forward at F = C$0.051
C$0.051
C$1,682 Telus faces unlimited losses
Linkage between forward and options
• Forward contract is an option collar.
• Buy forward = buy call, sell put with X = F.
• Sell forward = sell call, buy put with X = F.
• Value of option collar = 0.
• What if X not = F?
• Put-Call-Forward Parity Theorem
Put Call Forward Parity (graph)
X F S
Put Call Forward Parity
C, P = Call and Put premiums
R = domestic risk-free rate
)()( XFePC RT
Put-Call Forward Parity Example
• 1-year contracts on sterling, PS.
• F = C$2.50; X = C$2.40; T = 1 year
• R (riskless Canadian rate) 5% quoted CC
• Via equation, C-P = C$0.095
• If P = C$0.05 then C = C$0.145.
• If C = C$0.20 then P = C$0.105.
Present value calculationsR
EAR
APR
CC
TR1
1
TR1
1
RTe
Value of buy forward contract post inception
)( ONRT FFe
F’s are forward rates, N – new versus O – original. R is domestic risk-free rate, T remaining maturity of forward at new date.
Another interpretation: FN is prevailing forward rate; Fo is desired contractual rate.
Value of buy forward post inception
FO FN
Post inception buy forward example
• Bought 13-month sterling forward a month ago at then prevailing forward rate, F13 = C$2.40.
• Now prevailing F12 = C$2.50; T = 1year; R (riskless Canadian rate) = 5% CC.
• Value of Forward contract now = C$0.095 versus at contract inception of 0.
Contractual F vs. Prevailing F
• Contract. F: that specified in the contract• Prevail. F: that which renders the value of
the contract = zero.• Heretofore: Contract. F = Prevail. F ergo no
money changes hands at inception• If contract. F not = prevail. F, money
changes hands at inception• Who pays whom? How much is paid?
2nd interpretation: Buy PS 1-year forward
• Prevail. F = C$2.50 per PS
• Contract. F = C$2.40 per PS
• Canadian interest rate = 5% CC
• Firm must pay bank upfront $0.095 per PS
• The same formula has a different interpretation!
Value of sell forward post inception
)( NoRT FFe
ON FF , New versus original forward rates
T = time remaining until contract expiration at new date
R = domestic risk-free rate
Another interpretation: FN is prevailing forward rate; Fo is desired contractual rate.
Value of sell forward post inception
FN FOS
Post inception sell forward example
• Sold13-month sterling forward a month ago at then prevailing forward rate, F13 = C$2.40.
• Now prevailing F12 = C$2.50; T = 1year; R (riskless Canadian rate) = 5% CC.
• Value of Forward contract now = - C$0.095 versus at contract inception of 0.
2nd interpretation: Sell PS 1-year forward
• Prevail. F = C$2.50 per PS• Contract. F = C$2.40 per PS• Canadian interest rate = 5% CC• Firm must pay bank –C$0.095 per PS
upfront, i.e. bank must pay firm C$0.095 per PS upfront.
• The same formula has a different interpretation!
Coberturas Mexicanas
Forward contract on greenbacks denominated in Mexican pesos.
Price fixed in the contract is not the prevailing forward rate but the spot rate, So, at the contract’s inception.
Since usually F>So, an up-front fee, of PV(@Rm)(F-So) is imposed for compra de cobertura (buy) contract.
Compra (buy) de Cobertura
• Buy U$1,000 9-month cobertura.
• F (9-month) = MP10.
• So (at contract inception) = MP9.70.
• Mexican riskless rate (CETES) = 15%EAR.
• Up-front fee payable by firm to bank = MP270 = PV of U$1000 x (10-9.7).
Venta (sell) de Cobertura
• Sell U$1,000 9-month cobertura.• F (9-month) = MP10.• So (at contract inception) = MP9.70.• Mexican riskless rate (CETES) = 15%EAR.• Firm must pay the bank an up-front fee of
-MP270 = PV of U$1000 x (9.7-10).• Up-front fee of MP270 firm receives from
bank
Derivatives Pricing Problem
• Case in Transactions Exposure.
• Customer wants to sell DM125,000 5-month forward at rate of U$0.36 when prevailing forward is U$0.353.
• What price to charge customer? U$848.
• Price = U$(0.36-0.353)x125,000xPVfactor.
• Riskless rate,7.5%, is appropriate.
Derivatives Pricing Problem
• Customer also wants to buy a put on 125,000 DM’s 5 month maturity.
• Price of call with identical terms, C = U$0.01 x 125,000 = U$1,250
• Option collar (P-C), replicates previous forward contract.
• P – U$1,250 = U$848. Thus, P = U$2,098.
FX Bid-Ask Spread
• Bank is willing to buy FX at Bid.• Bank is willing to sell at (is asking) Ask.• Terms adopt bank’s perspective.• Hedging firm must buy FX at higher Ask
and sell FX at low Bid.• Buying one currency means selling the
other currency. Implies: Bid in one currency is the Ask of the other currency.
FX Bid-Ask Spread (transactions cost)
• % round trip cost = (1-(bid/ask)).• Bid on U$ = C$1.48; Ask = C$1.51.• Implies Bid on C$ = 1/C$1.51; Ask =
1/C$1.48.• (1 – (1.48/1.51) ) = 2% = (C$1,000-
C$980.13)/C$1,000.• C$1,000 to U$662.25 (=C$1,000/C$1.51)to
C$980.13 (=U$662.25xC$1.48).
Case: Options Trip Hiro Goto
• Japanese exporter wanted to hedge U$10M receivable via a put option.
• Finance put premium by issuing a call.• 3C=P; C<P as F<X=JY125/U$ I.e., market
expecting U$ to drop below JY125.• Zero cost option hedge is an option collar
with a twist due to different contractual amounts.
Hiro’s Hedge: Options Collar
S(JY/U$)JY125
Buy put on U$10M
Sell call on U$30M
Hiro’s “Hedged” Cash Flow
125 135
What eventuated!
Gomenasai! (Sooo sorry!)
• What Japanese exporter learned: By setting up an option collar, the up-front hedging outlay was reduced to zero, but the potential for a down-the-road opportunity cost was created.
• The potential opportunity cost eventuated! Pity!• Hiro insidiously shifted from an option hedge to a
type of forward hedge.
Black-Scholes Model for Valuing FX Options
• Applies only to European, not American, type.• Forward rate version: employs forward rate with
maturity same as that of option.• Spot rate version: employs spot rate at time option
is purchased. Also, foreign risk-free rate.• Variables common to both models: X, exercise
price; T, time to expiry; RD, domestic risk-free rate; volatility (standard deviation) of the continuously compounded rate of appreciation.
BS Model, Forward Rate Version
C = Call premium; P = Put premium
)()(
)()(
21
21
dXNdFNeP
dXNdFNeCTR
TR
D
D
N(d2) – probability call exercised
N(-d2) – probability put exercised
Use numa.com or deltaquants.com calculator to implement Forward Rate Model
• Under calculators click options
• Stock price or spot = Forward rate
• Interest rate and Dividend yield both = Domestic risk-free rate.
• Exercise or strike price, Time to expiry, and Volatility defined as given.
Forward rate model example
• Value a call option on SFR (South African Rand) 1 M with X = C$0.65, 1-year F = C$0.70, Canadian risk-free rate = 10% CC, and volatility (standard deviation) = 24.8%.
• Numa: 0.084/SFR C = C$84,000.• Deltaquants: 0.086/SFR C = $86,000.• By selling SFR forward now can lock-in future
profit of $50,000 = (.70 - .65) 1M
BS Model, Spot Rate Version
C = Call premium; P = Put premium
)()(
)()(
21
21
dXNedSNeP
dXNedSNeCTRTR
TRTR
DF
DF
RF – foreign risk-free rate, plays role of dividend-yield of stock on which stock option is written.
Use numa.com or deltaquants.com calculator to implement Spot Rate Model
• Under calculators click options
• Stock price or spot = Spot rate
• Interest rate = Domestic risk-free rate
• Dividend yield = Foreign risk-free rate.
• Exercise or strike price, Time to expiry, and Volatility defined as given.
Spot rate model example
• Value a call option on SFR (South African Rand) 1 M with X = C$0.65, S = C$0.68, Canadian risk-free rate = 10% CC, SFR risk-free rate = 7% CC and volatility (standard deviation) = 24.8%.
• Numa: 0.084/SFR, C = C$84,000.• Deltaquants: 0.086/SFR, C = C$86,000.• Both BS models yield same value iff interest rate
parity (to be discussed) holds.
Adjusting for BS in the BS model (or
applying the model to the real world) • BS model assumes no transactions costs (no bid-
ask spread). • Thus, use average of bid and ask rates as the FX
rate. This applies to both spot and forward rates.• BS model assumes ability to borrow and lend at
the same interest rate.• Thus, use average of deposit and borrowing rates
as the interest rate. This applies to both domestic and foreign interest rates.
Interest Rate Parity Theorem
• Based on financial arbitrage.
• Assume 1 year period.
• Domestic investment/financing: (1+RD).
• Forward hedged foreign investment/financing: (1+RF)(F/S).
• Equality must hold.
Interest Rate Parity: Formulas
F
DT
TRRT
T
F
DT
TR
TR
S
FRsAPR
eS
FRsCC
R
R
S
FRsEAR
FD
1
1:
:
1
1:
0
0
0
Interest Rate Parity: Intuition
• IRP: a statement about what holds in equilibrium.• A high interest rate currency, FX, trades at a
forward discount. Why? Otherwise, if it traded at a forward premium it would be an attractive investment for everyone.
• A low interest rate currency trades at a forward premium. Why? Otherwise, if it traded at a forward discount it would be an attractive financing venue for everyone.
Interest Rate Parity: Numerical Example
• Current spot rate on greenback = C$1.35
• 2-year forward rate on greenback = C$1.41 (this is usually the unknown)
• R canadian = 7% CC
• R u.s. = 5% CC
• Greenback trades at a forward premium because it is the low interest rate currency.
Interest Rate Parity: How many variables?
• How many variables do you see?
• In reality, 8 not 4!
• Domestic borrowing, deposit rates.
• Foreign borrowing, deposit rates.
• Bid, ask spread on spot.
• Bid, ask spread on forward.
Money market hedging
• Application of interest rate parity theorem.
• Synthesize a forward contract with 3 transactions: buy (sell) FX in spot; borrow(lend) in domestic currency; lend(borrow) in FX.
• Why? May be able to enhance cash flows compared with outright forward contract.
Enhance cash flows?
• If have an FX liability, may be able to buy FX at a lower rate than F, I.e., decrease outlays.
• If have an FX receivable, may be able to sell FX at higher rate than F, I.e. increase inflows.
• FX liability: Borrow domestic, buy FX spot, invest foreign synthesizes buy outright forward.
• FX receivable: Borrow foreign, sell FX spot, invest domestic synthesizes sell outright forward.
MMH: 2 complementary interpretations
• Create an offsetting FX cash flow: if FX receivable, create FX outflow; if FX payable, create FX inflow.
• Advance FX transaction date: instead of forward transaction, perform spot transaction now.
Money market hedge: numerical example
• Canadian firm will receive U$1M 6 months from now.
• S bid = C$1.38; F bid (6 months) = C$1.39.
• U$ borrowing rate = 8% APR
• Canadian deposit rate = 10% APR
• If use outright forward will receive C$1.39 6 months hence. Can you enhance this?
Is a money market hedge better?
• Borrow U$1M/1.04 = U$0.9615M• Sell U$’s in spot, receive C$1.3269M• Invest C$’s at C$ deposit rate, receive after
6 months C$1.3269M x 1.05 = C$1.3933M• Payoff U$ loan U$0.9615 x 1.04 = U$1M
with projected receivable. Note: U$ loan principal designed to achieve this.
• Money market hedge superior by C$3,300.
Money market hedge: FX liability
• Canadian firm has a liability of PS(sterling)1M due a year hence.
• F ask (1 year) = C$2.40; S ask = C$2.30.
• Canadian borrowing rate=7% APR or EAR
• UK deposit rate=4% APR or EAR
• Which is better? Buy outright forward or construct a money market hedge?
Buy forward or MMH?
• If buy PS forward (outright), pay C$2.4M a year hence.
• If construct money market hedge, pay synthesized forward rate, FMMH = C$2.37 per PS or C$2.37M a year hence.
• Save C$30,000 by constructing MMH.• MMH steps: borrow C$, buy PS spot, invest
PS.
MMH transactions: FX liability
• Now: Borrow (2.3)PS1M/1.04=C$2.21M• Buy PS spot C$2.21/2.3=PS.96M• Invest PS at 4%• After 1 year: Close out PS deposit, obtain
PS.96(1.04)=PS1M; this is used to meet liability.
• Pay off C$ loan, i.e., C$2.21M(1.07) = C$2.37M = PS1M(FMMH)
Option collar as synthetic forward
• Same exercise price for both put and call.
• Buy put & sell call synthesizes sell forward.
• Sell put & buy call synthesizes buy forward.
• Foc = synthetic forward rate
• Apply buy low & sell high rule.
• Hedge FX receivable: higher is better.
• Hedge FX payable: lower is better.
Forward rate synthesized with option collar
C, P = call, put premiums with common X.
FV = future value using domestic rate borrowing (if initial cash flow negative) or deposit (if initial cash flow positive).
)( PCFVXFoc
FV calculation
• Initial CF < 0, use borrowing rate• Initial CF > 0, use deposit rate• Rationale: Initial cash flow, minus the deposit or
plus the borrowing, must be zero.• Why must the initial cash flow be zero? Because
we want to be noughty!, i.e. To make the option collar a synthesized forward contract.
• Recall that a forward contract, whose contractual rate equals the prevailing forward rate, has a value of nought at inception.
Sell outright forward or option collar?
• Canadian with U$1M receivable due 6 months hence.
• Canadian deposit rate = 7% APR
• 6-month forward rate on U$ = C$1.39
• X=C$1.37: Per U$ P = C$0.09, C = C$0.14
• Foc=C$1.42 ergo rather than sell outright forward, Foc it!
Option collar transactions now
• Buy put, -C$0.09M
• Sell call, C$0.14M
• Invest initial net cash flow of C$0.05M in bank account, -C$0.05M
• Note: If initial net cash flow is < 0, must finance it. Ergo, use borrowing rate.
Option collar cash flows after 6 months
• Receive exercise price, C$1.37M, for sure either exercise put or the call gets exercised against you (Canadian firm).
• Deliver U$1M with projected receipt
• Close out bank account, receive C$0.05Mx(1.035) = C$0.05175M
• Net CF = C$1.42M > Foutright = C$1.39M
Hedging Protocol
• Determine best forward hedge: outright, MMH, or OC.
• Put your best forward forward.
• Compare best forward hedge with option, I.e., calculate B = breakeven rate.
• Example case: ¡Yo quiero Taco Bell!
2nd Generation FX Options
Designed to reduce up-front hedging cost:• 1. Asian- underlying variable is not spot
rate at a point in time in future by average spot rate over an interval of time.
• 2. Barrier- barrier must be crossed for the option to be created or cancelled.
• 3. Compound- option on an option or option conditional on some event.
Asian Options
• Appropriate for a firm that receives or pays a continuous stream of FX cash flows.
• E.g., firm receives EUR1M monthly. How to hedge for one year?
• 1. Twelve put options, each on EUR1M or• 2. One Asian put on EUR12M for the entire year.• Note: lower volatility ergo lower premium, i.e.,
hedge 2 is cheaper.
Pros & Cons of Asian put hedge
• Pro: cheaper due to lower volatility of underlying asset. Reason: law of large numbers.
• Con: the risk you are hedging against is not quite the same as the risk to which you are exposed.
• Example: At end of Jan, you are exposed to SJan, but you hedge against risk of SAverage and hedge payoff occurs at year-end not end of January.
Why are Asian options European?
• Asian option’s payoff depends on average spot rate during option’s life
• Must arrive at expiration date of option to determine average spot rate
• Cannot determine payoff until expiry
• Asian options are not American
• Asian options are European
Barrier Options
• New parameter B, the barrier, is defined.• If B is crossed (spot rate = B), the
trad.option is either created or cancelled automatically. Creation/Cancellation occurs only once during life of option.
• Premium is lower than traditional option.• Why? Trad.option may not exist initially or
trad.option may be prematurely cancelled.
Barrier Options
• Up vs. down: Will FX rate, S, rise or fall to barrier? Up: So < B; Down: So > B.
• In vs. out: Will the FX option be automatically created or cancelled?
• Put vs. call?• Total of 8 types but only 2 are viable hedges.• Down & in puts, up & in calls make sense. Why?
Option hedges are created only when needed!
Barrier Puts
• Hedge FX receivable; adverse event: S drops• B < So: Down & in – created when needed; Down
& out – cancelled when needed.• So < B: – Up & in – created when not needed; Up
& Out – cancelled when not needed but exposure to zig-zag behavior remains.
• Conclusion: only Down & In Puts make sense as hedges. Outs are out! Some Ins are in!
Hedging FX receivable with a barrier put
• Down & in put is the only one viable hedge.
• Lower premium compared to traditional put.
• Beware Up & out puts! Why? Exposure to zig-zag behavior in FX rate.
• If FX rate rises past barrier, the Up & out put is canceled. If FX rate then drops, you’re exposed!
Down&In versus trad. Put payoff
B
Barrier Calls
• Hedge FX payable; adverse event: S rises• B < So: Down & in – created when not
needed; Down & out – cancelled when not needed but exposure to zig-zag behavior.
• So < B: Up & in – created when needed; Up & out – cancelled when needed.
• Conclusion: only Up & in Calls may sense as hedges. Outs are out! Some Ins are in!
Why are out barrier options not suitable for hedging an FX liability?
• Outs are out for 2 distinct reasons.
• Up & out call: hedge is cancelled precisely when needed.
• Down & out call: exposure to zig-zag behaviour in the spot rate remains, i.e., S drops, call is cancelled, then S rises. Now you are exposed!
Hedging FX payable with a barrier call
• Up & in call is the only one viable hedge.
• Lower premium compared to trad.call.
• Beware Down & out calls! Exposure to FX zig-zag behavior.
• If FX rate drops below the barrier, the down & out is cancelled. If S then rises, you are now exposed!
Up&In versus trad. Call payoff
B
Compound Options
• Option on an option: call on trad.call (for FX liability) or call on trad.put (for FX receivable).
• Event-contingent options: option is created only if event occurs. Cross-border tender offer: use takeover contingent FX call. Bid on foreign project: use FX put contingent on bid winning.
• Lower up front premium.
What compound options are appropriate hedges?
• Situation: submit a bid to construct expressway in Djakarta (Indonesia).
• Buy call on a trad.put on the Rupiah
• Buy event-contingent put on the Rupiah where “event” is defined as your winning the contract.
Why are premiums lower for the two compound options?
• Call on a put has lower value than the underlying traditional put.
• Premium on bid-contingent put is approximated by the following product: (premium on traditional put) X (probability of winning the bid).
(compound)call on trad.put vs. trad.put
• Hedge FX receivable• Call on trad. put has lower up-front cost• Analogy to stock purchase: buy stock vs. buy call
then possibly exercise the call (latter: purchase in 2 installments)
• Protection required only if S drops • Greater flexibility with compound call: exercise
the call only if S drops
• Hedge FX payable• Call on trad.call has lower up-front cost• Analogy to stock purchase: buy stock vs. buy call
then possibly exercise the call (latter: purchase in 2 installments)
• Protection required only if S rises• Greater flexibility with compound call: exercise
that call only if S rises
(compound)call on trad.call vs. trad.call
