Foreign Exchange Exposure

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					   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          • Indirect Quotation
• Number of home            • Number of FX units
  (domestic, reference)       per unit of home
  currency units per unit     (domestic, reference)
  of FX.                      currency.
• Direct quote is inverse   • Indirect quote is
  of indirect quote.          inverse of direct quote.
• Assumed in this           • Not employed in this
  course (intuitive).         course (less intuitive).
    Examples of Two Quotation
• For Canadian firm.
• Direct quote on greenback, US$: C$1.35
• Indirect quote on greenback US$: US$0.74
• 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
• 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

     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
• 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

Cash Flow

      Hedge with Forward Contract
        Hedged Cash Flow

F x U$1million

       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$/US).
• P, put premium, price paid now for option.
• Put contract cash flow = X – S if S<X; 0
Put Contract Cash Flow

   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


  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

      -U$ 5 M
Buy U$ Forward: Contract Cash


          F             S
Buy Call on U$: Contract Cash


             X        S
        Hedged Cash Flows


                   Call Hedge

-F x U$5M            Forward Hedge
  B, breakeven FX rate between
   call and buy forward hedges
• B = forward rate - FV of call option
• FV (future value) uses the hedger’s
  borrowing rate.
• S<B call option better ex-post.
• S>B buy forward better ex-post.
   Buy forward versus buy call

           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
    Forward vs. Option Hedges:
      Fundamental Trade-off
• Forward – no up-front     • Option – up-front
  outlay (at inception        outlay (option
  value of forward = 0)       premium) but no
  but potential               opportunity cost later,
  opportunity cost later.     ignoring option
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


                   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
• FX payable: viable is FX rate does not rise
• 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
• 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
• 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
• 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

Cash Flow


                        U=$0.4   S
    Salomon’s Range Forward

FX Liability    L   U         S
Hedged Cash
     To alternative ways of
  committing to buy (sell) FX in
                 • Forward Contract
• Futures Contract
• Traded anonymously       • Deal directly with
  on an exchange.            bank.
• “Marking to market” –    • No cash flows until
  there are daily cash
  flow experienced.        • Empirical result: For
                             FX, futures rate =
• Assume: futures rate =     forward rate on
  forward rate.              average.
      Conditional (contingent)
• 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=
    Telus’ Risk Exposure


             C$0.051   S(C$/Bh)
   Effect of dual currency prices
• Client chooses to pay currency adjusted
• 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

    Linkage between forward and
•   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

                       RT
(C  P)  e                     (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.
Value of buy forward contract
       post inception

      RT
 e          ( 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

       FO       FN
    Post inception buy forward
• Bought 13-month sterling forward a month
  ago at then prevailing forward rate, F13 =
• 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
           Value of sell forward post
     RT
e          ( 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

           FN      FO
    Post inception sell forward
• 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
        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 de Cobertura (example)
•   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 de Cobertura (example)
• 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
   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$2,098.
         FX Bid-Ask Spread
• Bank is willing to buy FX at Bid.
• Bank is willing to sell at (is asking) Ask.
• Terms adopt bank’s perspective.
• Hedging firm must buy FX at higher Ask
  and sell FX at low Bid.
• Buying one currency means selling the
  other currency. Implies: Bid in one currency
  is the Ask of the other currency.
FX Bid-Ask Spread (transactions
• % round trip cost = (1-(bid/ask)).
• Bid on U$ = C$1.48; Ask = C$1.51.
• Implies Bid on C$ = 1/C$1.51; Ask =
• (1 – (1.48/1.51) ) = 2% = (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
Hiro’s Hedge: Options Collar

               Buy put on U$10M

       JY125                      S(JY/U$)
                 Sell call on
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
 C e    RDT
             FN (d1 )  XN (d 2 )
 P  e  R T  FN (d1 )  XN (d 2 )

 N(d2) – probability call exercised
 N(-d2) – probability put exercised
   Use calculator to
 implement Forward Rate Model
• Under calculators click options
• Stock price = Forward rate
• Interest rate and Dividend yield both =
  Domestic risk-free rate.
• Exercise 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%.
• value, C = C$84,000.
• 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
C e   RF T
                SN (d1 )  e    RDT
                                       XN (d 2 )   
P   e    RF T
                    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 calculator to
   implement Spot Rate Model
• Under calculators click options
• Stock price = Spot rate
• Interest rate = Domestic risk-free rate;
  Dividend yield = Foreign risk-free rate.
• Exercise 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%.
• value, C = C$84,000.
• 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
                FT 1  RD 
        RsEAR:                    
                S 0 1  RF 
        RsCC :      e  RD  RF 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
• 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
•   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
• 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
• 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
• 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
    MMH transactions: FX liability
• Now: Borrow (2.3)PS1M/1.04=C$2.21M
• Buy PS spot C$2.21/2.3=PS.96M
• Invest PS at 4%
• After 1 year: Close out PS deposit, obtain
  PS.96(1.04)=PS1M; this is used to meet
• Pay off C$ loan, i.e., C$2.21M(1.07) =
  C$2.37M = PS1M(FMMH)
       Option collar as synthetic
•   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: Same logic that applies to the use of
  WACC in investment appraisal (vide: course
• Notwithstanding that, in a specific year, may have
  abundant unused bank-borrowing capacity to
  finance project, must use WACC
• Calculation procedures applied as long-term
  Sell outright forward or option
• 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
• 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!
    2 nd   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 expiration
• Asian options are not American
             Barrier Options
• New parameter B, the barrier, is defined.
• If B is crossed (spot rate = B), the option is
  either created or cancelled automatically.
  Creation/Cancellation occurs only once
  during life of option.
• Premium is lower than traditional option.
• Why? Option may not exist initially or
  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 & out puts, up & out calls do not make
  sense. Why? Option is cancelled precisely when
  you need it!
                Barrier Puts
• 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
  from a hedging perspective. Outs are out!
  Hedging FX receivable with a
          barrier put
• Down & in puts are viable.
• Lower premium compared to standard 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!
             Barrier Calls
• 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
  from a hedging perspective. Outs are out!
  Why are out barrier options not
suitable for hedging an FX liability?
• Up & out call: hedge is cancelled precisely
  when needed.
• Down & out call: exposure to zig-zag
  behaviour in the spot rate remains, i.e., rate
  drops, call is cancelled, then rate rises.
    Hedging FX payable with a
           barrier call
• Up & in calls are viable.
• Lower premium compared to standard call.
• Beware Down & out calls! Why? Exposure
  to zig-zag behavior in FX rate.
• If FX rate drops below the barrier, the call
  is cancelled. If FX rate then rises, you are
          Compound Options
• Option on an option: call on call (for FX
  liability) or call on 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 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 put.
• Premium on bid-contingent put is
  approximated by the following product:
  (premium on traditional put) X (probability
  of winning the bid).

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