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2.1. Forward Markets
2.2. Futures Markets
2.3. Options

A forward contract is an agreement between a
 bank and its client to buy or sell a financial
 asset for a delivery on a future date at a
 predetermined price.
            (1  rt ,T )
Ft ,T  S
            (1  rt ,T *)
                            Pricing Forwards
 Forward price (F) is linked to the spot price (S) by an arbitrage
                                                 (1  rt ,T )
 For FX forwards:               Ft ,T  St
                                                (1  rt ,T *)

 Synthetic Forward (long FC): Borrow the domestic currency at r →
   convert it into FX at St → lend the proceeds at r* .
 Arbitrage between synthetic and actual forward will ensure that the
   above equation always holds.

 Case 1: A Magyar Exporter sold cars to Austria and will receive the proceeds 86 days
   later. S=268.20, rHUF=8.5% rEUR= 1%.
              a) What should the Fin.Mngr. of the Magyar exporter do?
              b) What would be the appropriate forward rate?
The general rule: Benefits and costs of holding the asset
    should accrue to the buyer; and that of receiving the
    money to the seller. Forward price should be set
*Clue: Buyer at denominator; seller at numerator.

                         1 r
For Gold:         F S                        c = cost of depositing
                         1 c
T-Bond futures:                1 r           ytm = yield to maturity
                      F S
                             1  ytm

Case 2: CNY/USD = 0.1460/67         F200 = 0.1360/95
CNY: r(bor)=4% r(len)=6%            USD: r(bor)=0.5%   r(len)=1%
Is there any arbitrage opportunity?
         Bank’s Forward Quotations
                (1  rbor )                      (1  rlen )
  Fbid    Sbid                   Fask    Sask
                (1  rlen *)                    (1  rbor*)
Forward bid-ask spread is larger than the spot, and gets
  larger the further the maturity (for 2 reasons: more default
  risk, less liquidity).

Characteristics of Forward Contracts and Markets:
OTC market, tailor-made, typically a credit instrument (but
  sometimes a collateral may be asked)
Futures are standardized forward contracts, traded
  in organized exchanges and ensured by a central
  clearing house.
A margin is always required, deposited at the
  Clearing House. (Initial Margin vs. Maintenance margin)
Standardized contracts permit centralized trading
  without market makers.
In a futures market, the size, the maturity (delivery)
  date, and the specifications of the traded asset (for
  commodities and agriculturals) are standardized.
The differences between forwards and futures
  Forward contact is typically a credit instrument between
  a bank and its client; in futures delivery is reinforced only
  by depositing a margin.
  Forwards are tailor-made (the bank sets the maturity
  date and the amount by responding to its client’s needs),
  futures contracts are standardized.
  Forwards are an OTC instrument, futures trade in
  organized centralized exchanges supported by
  centralized clearing houses.
  Thus, settlement and margins are strictly regulated in
  futures; subject to ‘relations’ in forwards
  In futures, there is daily mark-to-market, in forwards not
  (therefore, the payoff structure with futures is slightly
  different from forwards; you may gain or lose slightly
  more with futures)
  In futures, the clearing house is the counterparty to
  alloutstanding contracts.

Mark-to-market: daily updating of margin.
Basis: F − S
Open Interest: The number of outstanding contracts (bets)
Cash Settlement vs. Physical Delivery

  Eurodollar futures:
F = 100 – r
(a bet on the interest rate that will prevail on T)
Used to hedge interest rate risk.
    An option is the right but not the obligation to buy or
    sell a financial asset at a predetermined price.
It is an agreement whereby the option seller (writer)
    gives the option buyer this right, in exchange for a
    premium (called option price)
    Two types of options: Call Options: The right to buy
    Put options: The right to sell
    Two styles of options:
American options: Can be exercised at any time till expiration,
  European options can only be exercised on the maturity date.
 Options can trade both OTC and in
 organized exchanges.
 Strike (Exercise) Price: X
Every option with a different strike price and
 maturity date is a different instrument.
Option Price (Premium): C, P
  An option is called:
In the money if S > X (call) S < X (put)
At the money if S = X
Out-of-money if S < X (call) S > X (put)
      (deep-in-the money, deep out-of-money)
Option prices (CME)   (S = 1.4260)
Intrinsic Value (option value on expiration):
CT = max (0, ST−X)         PT = max (X−ST, 0)

These exercise values Ct and Pt are lower bounds on option
    prices before T.

Factors affecting option prices:
1) St−X
2)   T – t : time to maturity
3)   (expected) volatility
4)   interest rates

Delta:      ΔCt / ΔSt           or   ΔPt / ΔSt
                   Exercise Questions

Do you think an American or European option identical in
other respects (type, maturity date, strike price, etc.) should
have a higher price ?

How and when would you use options to hedge against
exchange rate risk? Give examples.

S=2.29/31. A Bulgarian exporter expects a profit of BGN
50,000 from an export transaction of GBP 500,000. The
finance manager of Bulgarian exporter expects GBP to rise,
however he would get fired if the export transaction ends up
with a loss. What can he do?
              Option Strategies
Combining two or more options or instruments
Simply: vertically add payoff structures of each
  of the instruments.

Covered Call Writing: sell a call + hold S
Vertical Bull Spread: buy a call at high X + write
 a put at lower X
Vertical Bear Spread: buy a put at lower X + sell
 a call at higher X
Straddle: buy a put and a call at the same X
Strangle: buy an out-of-money call and
out-of-money put

OTC options on interest rates:
Cap: is a call option on borrowing rate
Collar: is a put option on lending rate
CDS = Credit Default Swap