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Derivatives Notes

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This is an extract of our Derivatives document, which we sell as part of our Banking Law Notes collection written by the top tier of King's College London students.

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Types of derivative contracts
● Definition of derivatives: A financial asset whose value is driven by the value of some other (financial) asset(s).
● Types of derivatives:
○ Forwards;
○ Futures;
○ Swaps; and
○ Options.
Forwards and Futures:
● Forward contract = Unconditional promise to buy or sell some underlying asset at a specified price (the "forward price") on a specified date (the "settlement" or the
"maturity date").
○ This can cover financial assets and tangible assets.
○ Usually used in foreign exchange markets, where the underlying asset will be in a different currency.
● Futures contract = Similar to a forward, except the underlying asset is not actually transferred but (cash-)settled by offset and parties' positions are marked to market on a daily basis.
○ The result form the offset = Either the buyer or the seller has to pay
(depending on who wins the "bet").
○ Mutual compensation for marginal changes (i.e. margin calls).
○ Exchange-traded.
● A swap is an unconditional promise between two counterparties to exchange cash flows and is calculated on a different basis form the other.
○ Interest rate swap: Based on nominal amount, fixed interest payments are exchanged for floating interest payments.
○ Currency swap: Payments in one currency are exchanged for payments in a different currency.
○ Equity swap (Contract for difference) Cashflows based on share price movements (up or down) are exchanged for a fixed "premium".
○ Credit default swap: In exchange for a fee, one counterparty compensates the other for any losses on credit contracts with a third party.
● A right (but not an obligation) to purchase or sell an underlying financial asset at a specified price, on or by a specified date.
○ Call option = Right to buy.
○ Put option = Right to sell. ○ American Call or Put = May be exercised up to and on the expiration date.
○ European Call or Put = May be exercised only on the expiration date.
○ Warrant = Usually a call sold by the iss50uer itself, and, upon exercising it, the company will issue a new share.
● Most calls and puts are traded amongst parties who do not actually own any of the underlying assets.
● Specifications:
○ Underlying security (price at time t = st)
○ Strike price (K) = The price that must be paid by the option holder for exercising the option
○ Expiration date (T)
○ At the money option, strike price (K) = market price of the security at time t
○ "In the money" call = K < st; "out of the money" call = K > st
○ "In the money" put = K > st; "out of the money" put = K < st
○ Intrinsic value = st - K
○ Value (i.e. price) of the call or put option at time t = ct or pt respectively
■ Note that the value of the option is linked to the value of the underlying security, but they are not the same.
Put-call parity and option pricing
● 1-year European call with K = 50 and c0 = 10
● 1-year European put with K = 50 and c0 = 10
Share price T

Buying a call

Buying a put

0 -10

40 25


15 50



75 15


100 40


125 65


150 90


175 115


● How are these values calculated?
○ Costs incurred in buying and exercising a call option = Value of the call option
+ Strike price; Benefits accrued in exercising a call option = Value of the underlying security; Buying a call therefore = ST - c0 - K.

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