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
ECF(C$)
US$1million
S(C$/US)
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
Contract
Cash Flow
F(C$/U$)
S(C$/U$)
Hedge with Forward Contract
Hedged Cash Flow
F x U$1million
S(C$/U$)
Hedge with Put Option
• Put option is the right, not obligation like
forward contract, to sell U$ 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
X
S
Hedge with Put Option
Hedged Cash Flow
X
S
Which is better? Sell forward or
Buy put?
B = breakeven point
S<B, sell forward better
S>B, buy put better
B
S
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
Exposed Cash
Flow
S
-U$ 5 M
Buy U$ Forward: Contract Cash
Flow
U$5M
F
S
Buy Call on U$: Contract Cash
Flow
U$5M
X
S
Hedged Cash Flows
B
X
S
Call Hedge
-F x U$5M
Forward Hedge
Buy forward versus buy call
Contract
Cash
Flows
B
S
B, breakeven FX rate between
call and buy forward hedges
• B = forward rate - FV of call option
premium
• FV (future value) uses the hedger’s
borrowing rate.
• S<B call option better ex-post.
• S>B buy forward better ex-post.
Calculation of B
• Canadian firm with U$ 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
Contract
Cash Flow
L=$0.3774
U=$0.4
S
Salomon’s Range Forward
FX Liability
Hedged Cash
Flow
L
U
S
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$1,682
C$0.051
S(C$/Bh)
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$1,682
Telus faces unlimited losses
C$0.051
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
(C  P)  e
 RT
(F  X )
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 calculations
R
EAR
1
1  R T
APR
CC
1
1  TR 
e
 RT
Value of buy forward contract
post inception
e
 RT
( FN  FO )
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
e
 RT
( Fo  FN )
FN , FO
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
S
FN
FO
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 5month 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$1,000C$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).
Bid Ask Spread: Conversion to Direct Quotation
• US firm’s perspective: Y is FX, $ is reference
Bid
Ask
Y/$
6.1
6.2
$/Y
(1/6.2) = .16
(1/6.1) =.164
• 2 Steps: Calculate reciprocals; Apply crisscross rule
• Bank buys $ at Y6.1 identical to Bank sells Y at $0.164
• Bank sells $ at Y6.2 identical to Bank buys Y at $0.16
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
Buy put on U$10M
JY125
Sell call on
U$30M
S(JY/U$)
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-theroad 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
FN (d1 )  XN (d 2 )
P  e  R T  FN (d1 )  XN (d 2 )
C e
 RDT
D
N(d2) – probability call exercised
N(-d2) – probability put exercised
Use 1.10 BS option valuation spreadsheet to
implement Forward Rate Model
• Current stock price = Forward rate
• Risk-free interest rate and Dividend yield
both = Domestic risk-free rate.
• Exercise price, Life of option, 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%.
• Spreadsheet value: 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

P   e
C e
 RF T
SN (d1 )  e
 RF T
 RDT
XN (d 2 )

SN (d1 )  e  RDT XN (d 2 )

RF – foreign risk-free rate, plays role of
dividend-yield of stock on which stock
option is written.
Use 1.10 BS option valuation spreadsheet to
implement Spot Rate Model
• Current stock price = Spot rate
• Risk-free interest rate = Domestic risk-free
rate
• Dividend yield = Foreign risk-free rate.
• Exercise price, Life of option, 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 riskfree rate = 10% CC, SFR risk-free rate = 7% CC
and volatility (standard deviation) = 24.8%.
• Spreadsheet value: 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 bidask 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
FT 1  RD 
RsEAR :


S 0  1  RF 
FT
 RD  RF T
RsCC :
e
S0
T
FT 1  TRD 
RsAPR :


S 0 1  TRF 
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
Foc  X  FV (C  P)
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).
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!
nd
2
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
(compound)call on trad.call vs.
trad.call
• 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