1. Financial derivatives Introduction
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2. Financial derivatives
A derivative (afleiða) is an instrument whose value depends on the values of other more basic underlying variables.
More specifically, a derivative is a contract about buying or selling a specific asset or portfolio (eignasafn) for a specific price (K) at a time tT, where T is the duration of the contract.
The asset can contain
stock,
currency,
products, etc.
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3. Ways derivatives are used
To insure against changes or risk (hedgers).
To get a high profit from a certain market behavior (speculators).
To get a quick low-risk profit (arbitrageurs).
To change the nature of an investment without the costs of selling one portfolio and buying another.
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4. Examples of derivatives (1)
Forward contract (framvirkur samningur)
A forward contract is an agreement between two individuals/companies to buy or sell an asset at a certain time T in the future for a certain price K (the delivery price (handsalsverð)).
Futures contract (framtíðarsamningur)
Similar to a forward contract, exept that it is only traded on an exchange (kauphöll) and can be bought and sold by third parties before the end of the contract.
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5. Examples of derivatives (2)
Swaps (skiptasamningur)
A swap is an agreement to exchange cash flows at specified future times according to certain specified rules.
Options (valsamningar)
Call option (kaupvalsamningur)
The contract holder chooses whether he buys the asset (excercises the contract) for a price K at time T or not.
Put option (söluvalsamningur)
The contract holder chooses whether he sells the asset for a pric K at time T or not.
A European option can be excercised only on the expiration date (t=T).
An American option can be excercised at any time up to the expiration date (tT).
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6. Example of a forward contract
On January 20, 1998 a trader (long position) enters into an agreement to buy £1 million in three months at an exchange rate of
This obligates the trader to pay $1,619,600 (=K) for £1 million on April 20, 1998
If the exchange rate rose to 1.65, the spot price ST is $1,650,000 and the payoff is
ST – K = $1,650,000 - $1,619,600 = $30,400
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7. Long and short forward position profits
Long position (buyer)
Short position (seller)
Profit ST
Profit ST K K
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8. Example of a call option
A trader (option holder) buys a European call option with 1,000 shares in deCode with a strike price of $14 and an expiration date of one year. The option price is $0.5, so the holder pays $500 (V) for the contract.
If the deCode share rises to $17, the option holder has a margin of $2.5 per share and makes a profit of
P = ST – K - V = ($17 - $14)*1,000 - $500 = $2,500.
If the share rises to only $14.2, the option holder still exercises the contract, since instead of losing the $500, he only loses
$500 - ($14.2 – $14.0)*1,000 = $300
In general, a call option is exercised if
-V < ST – K
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9. Long call option profit
Profit from buying a deCode European call option:
option price = $0.5, strike price = $14, option life = 12 months 3 2 1 11 12 13 14 15 16 17
Profit ($)
Terminal
stock price ($)
-0.5
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10. Recent examples of derivatives
Futures fund
Framval 1 (Mbl, 15/2/2001, pg. C 7)
Built from seven types of futures contracts: currency, stock, etc.
Decode options (Mbl. 6/2/2001)
Call/Put options at $5, $7.5 or $10
Expiration date: March, April, July, October
Option price depends on price/share and duration
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Return on investment
Market interests
Let r be the market interest rate for one year (return without risk).
If the return from stock is lower than r, then we choose of course to put our money in risk-free return.
If interest rates are calculated continuously, and T is the time to maturity, then the risk free return is:
F0 = S(t0)erT
Considering basic return as r (no gain over risk-free market), then, if we do not place the money, its value decreases to:
F0 = S(t0)e-rT
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12. Value of forward contracts
Let r be the risk-free interest rate, F0 the forward price for a contract and K the delivery price.
The value f of the contract with time to maturity T is:
f = (F0 - K)e-rT
At a general time t, 0 <= t <= T:
f = (F0 - K)e-r(T-t)
Example – six month long forward contract on stock
Risk-free interest rate is 10%
The forward price is $25, the delivery price is $24
f = (S(t0)erT - K)e-rT = S(t0) - Ke-rT = $25 - $24 e-0.1*0.5 = $2.17
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