Derivatives of Foreign Exchange Markets

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Derivatives of Foreign Exchange Markets

• Dr. J. D. Han
• Kings College
• University of Western Ontario

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2. Forward FOREX

• Forward FOREX market
• In the long-run, Forward FOREX is a kind of
  gamble evolving the forward rate and the current
  rate.
• It is a financial speculation by itself.
• However, it could offset FOREX market
  volatility as another business risk.
• In the short-run, Forward FOREX rate may
  deviate from the Covered Interest Parity and
  provide short-term arbitrage opportunities (side
  function).

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1. How does Forward FX Transaction work?

• Organization
• Buy a currency at an agreed rate on the trade
  date which is now , and deliver/pay later at the
  settlement date.
• The intervals or Value dates are 1, 2, 3, 6, or
  12 months
• Mostly, over-the-counter (O. T. C.) transactions

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2) Who wins and loses in Forward FOREX market in
the long-run?

• The Buyer of a Forward currency is in the
  long-position and the seller is in the
  short-position.
• When the actual current rate goes up, the buyer
  on the long-position wins.
• On the settlement date, compare the current
  market rate and the agreed rate. By the excess of
  the former to the latter, payment goes from the
  buyers account to the sellers. vice versa.

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Once again, how does the Forward Market game play?

• A and B sells and buys a currency, agreeing on
  the Forward FOREX rate or F for the settlement
  date.
• When the settlement date comes, compare the
  forward rate F and the current FOREX rate E1 on
  that day.
• If E1 gtF, the buyer (on long position) wins and
  get the difference E1 F from the seller (on
  short position)

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Derivative

• Definition of Derivatives
• whose values depend on underlying financial
  assets
• Principle
• Hedging behaviors beget a series of derivatives
• Different Kinds of Derivatives
• - Short-selling in Stock Market
• Forward-related Derivatives
• Forwards, Futures, Swaps
• - Options-related Derivatives

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3. There will be 3 kinds of people to participate
in the Forward FOREX market

• If you are so sure that the true E1 will be
  higher or lower than F. You like this possible
  change. You have no other risk to cover from. You
  are now assuming new risks through forward
  market. You are a speculator.
• Although you are not so sure about E1, you do not
  like any change in E, and want to cover from its
  risk through forward market. You are a hedger.
• You are not taking up any risk and are simply
  cherry-picking. You may be an arbitrager.

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4. Forward Market for Hedging
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1) How does it work?

• A Canadian exporter to U.S. to receive US 1
  million in 12 months.
• The current FOREX rate is E0.
• What he really needs is Canadian
• There is no guarantee that he will get Canadian
  1/E million.
• He will suffer loss if E goes up or the U.S.
  depreciates in a year This is his original risk
  from FOREX volatility.
• He can cover from the FOREX risk by going into a
  forward FOREX contract.
• He should sell U.S. forward or be short on U.S.
  forward to Royal Bank at the agreed rate F. The
  possible changes from this financial transaction
  offsets the above original risk. Hedging Risk
  with Risk

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2) Numerical Example

• John has a receivable of U.S. 1 million from the
  U.S. in a year. He will have to pay his Canadian
  suppliers in Canadian dollars. The current
  exchange rate is 1.2.
• He should hedge from the FOREX market risk by
  (buying/selling choose one) the U.S in the
  forward market with his bank.
• Suppose that he manages to get the one year
  forward rate F of 1.2.
• 1) Suppose that in a year the current FOREX rate
  turns out to be 1.3 Canadian dollars to 1 U.S.
  dollars. What will happen to the cash flows of
  Johns accounts, business and financial?
• 2) Suppose that in a year the current FOREX rate
  turns out to be 1.1. What will happen to the
  cash flows of Johns business and financial
  accounts?

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3) Forward Market for Hedging Illustrated
Suppose that you are an Canadian exporter, and
you have a receivable of US 1 million coming in
1 year.
i
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(1) FX Risk of Original Business Think about
Unexpected Gains or Loss OF your
ASSET(RECEIVALBE IN THIS CASE) you might have
due to fluctuations of spot FOREX rates (only
Spot FOREX is used)
Suppose So1.20 Now
Possiblity 2 S1 1.10 Unexpected Loss from
FOREX - C 0.10 m
i
Zero profit line
S1
Possibility 1 S1 1.30 Windfall Gains from
FOREX C 0.10 m
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In General, the previous graph shows
in the T accounts

• There will be gains in net worth if S1 goes up
  and thus the Assets increases in C .
• There will be loss in net worth if S1 falls and
  thus Assets decreases in C.

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(2) HedgingThe Canadian exporter is
risk-averse, and willing to pay for the
elimination of the risk of having the loss
through Forward FX transactions.What
position(buy- Long or sell-Short) should he take
with respect which currency(U.S. or Canadian
dollars)?
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Forward Hedging Gains and Loss of Forward
Contract Short Position of US
ForwardSuppse now he can sell one-year Forward
U.S. dollars at F 1.20What will be his pay-off
one year later?
F0
Possibility1 E1gt F For instance,S1
1.30 Possible Loss - C 0.10 m
S1
Possibility 2 E1lt F For instance, E1 1.10 If
you have not done the Forward contact, you will
get only C 1.10 million. However, the forward
contact will bring you C 1.20 million. Gain from
Hedging itself C 0.10 m
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Note that Hedging creates an offsetting position
to the initial risk
Hedging itself creates the following in the T
accounts

• There will be loss in net worth if E1 goes up and
  thus the Liabilities increase in C .
• There will be gains in net worth if E1 falls and
  thus Liabilities decreases in C.

Net 1.2 m 1x E1 million
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The General principle of hedging is, In
insurance, you bet on the worst possibility.

• He hates the depreciation of the U.S. dollar
  against the Canadian dollar in business.
• Thus in insurance, he should bet on the
  depreciation of the U.S. dollar or the
  appreciation of the Canadian dollar.
• In Forward Market, he should buy(be short on)
  ____ and sell(be long on) ____.

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General Principle of Risk-Hedging Illustrated

• First, Assess your original FOREX market risk

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As E goes up, you get profits, or loss


E
-
-
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Second, offset the possible FOREX market risk
with Hedging
Long position (with FOREX receivable) You
gain when its future spot FX rate or E1rises
above your contracted Forward rate F.
E
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Note that Selling FX Forward, or the short
position has the down-ward sloping Pay-off line
Short position (with FOREX payable) You win
when E1 falls below your contracted Forward rate
F.
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Then, combining the above two graphs, we get
Whether the future spot FOREX rate or E1falls or
rises, the net profits will be constant all the
time, being equal to the implicit insurance
premium he has paid (C 0.01 million).
1.Initial FOREX Risk before Hedging


Zero profit line
-
-
2. Forward Hedging Short Position (with FOREX)
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4) Limitation of Forward Hedging-This is not
the best ideal Hedging The hedging has
eliminated the upside potential along with the
downside risk.-Would there be any other Hedging
that preserve the upside potential?
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• 5. Forward Market for Arbitrage
• Covered Interest Parity Theorem revisited
• Arbitrage takes place only in the short-run at
  disequilibrium
• Brisk Arbitrages will ensure wipe out profit
  margin in the Long-run equilibrium given by the
  Covered Interest Parity Theorem equation as we
  recall. The resultant Forward rate is the fair
  rate

• Recall Covered Interest Parity Theorem
• 1 i 1/S(1 if ) F

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Sample Question

• You are a Canadian
• Spot exchange rate 1.20 Cd / 1 U.S.
• Canadian Domestic Interest rate 5
• U.S. Interest rate 6
• What should be the fair Forward Rate which
  comes with no unilateral capital flows from one
  country to the other?

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• Rate of return on Investment in Canada
• 1 (10.05) - 1 0.05
• Rate of return on Investment in U.S.
• Converting C1 into U.S. 1/E
• Depositing at the U.S. bank, and in a year, you
  will surely get
• U.S. 1/E x (10.06)
• Converting it back to Canadian dollars for sure
  by using the Forward Market today
• 1/ E x (1 0.06) x F
• The rate of return is
• 1/ E x (1 0.06) x F -1.
• This will be in approximation
• 0.06 (F- E)/ E
• At Equilibrium,
• 0.05 0.06 (F- 1.2) /1.2

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Fair Forward Exchange Rate in the Long Run?

• F 1.2 x 0.99
• This is the equilibrium forward rate in the
  long-run after free flows of capital or brisk
  arbitrages are all done in the competitive
  financial market.

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• In reality, in the short-run, the Actual Forward
  FX rate could deviate from the Fair Long-run
  equilibrium Forward FX rate related to the
  Covered Interest Rate Parity Theorem.
• Then, there is a chance for profitable Arbitrage.
• Eventually, brisk Arbitrage will result into the
  equality between the actual Forward Rate and the
  fair Forward Rate.