# Derivatives

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```					         DERIVATIVE MARKETS
2.1. Forward Markets
2.2. Futures Markets
2.3. Options

FORWARD MARKETS:
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
relationship.
(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
accordingly.
*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 )
(1  rlen *)                    (1  rbor*)
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 MARKETS
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)
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.
SOME FUTURES MARKET CONCEPTS:

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.
OPTIONS
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
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.
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
a put at lower X
a call at higher 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

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