Derivatives Flashcards
contingent claim
is a derivative in which with a right, but not an obligation, to make a final payment contingent on the performance of the underlying.
option
is a derivative contract in which one party, the buyer, pays a
sum of money to the other party, the seller or writer, and receives the right
to either buy or sell an underlying asset at a fixed price either on a specific
expiration date or at any time prior to the expiration date.
Call Option with physical delivery
a call option with physical delivery,
upon exercise the underlying asset is delivered to the call buyer, who pays the call
seller the exercise price.
put option with physical delivery
put buyer delivers the underlying asset to the put seller and receives the strike price.
Exercise Price
The fixed price at which the underlying asset can be purchased is called the exercise price (also called the “strike price,” the “strike,” or the “striking price”). This price
is somewhat analogous to the forward price because it represents the price at which
the underlying will be purchased or sold if the option is exercised.
Option Premium
it is the present value of the cash flows that are expected to be received by the
holder of the option during the life of the option.
In the money
if the underlying value exceeds the exercise price (ST > X), then the option
value is positive and equal to ST – X
Out of the money
When the
underlying value is less than the exercise price,
At the money
When ST = X,
Equity Swaps
permit investors to pay the return on one stock index and receive the return on
another index or a fixed rate
Notional Principal
The notional principal of a swap is not exchanged in the case of an interest rate swap
Price Limits
Price limits are important in helping the clearinghouse manage its
credit exposure. Sharply moving prices make it more difficult for the clearinghouse to collect from parties losing money
Forward Contract
In a forward contract, either party could default, whereas in a contingent claim, default is possible only from the short to the long.
Value of a forward contract
the spot price of the underlying asset
minus the present value of the forward price.
The forward price of an asset with benefits and/or costs
the spot price
compounded at the risk- free rate over the life of the contract minus the
future value of those benefits and costs.
The forward price
the spot price compounded at the risk- free rate over
the life of the contract.
Value of Forward at t=0
Because neither the long nor the short pays anything to the other at the
initiation date of a forward contract, the value of a forward contract when
initiated is zero.
The value of a forward contract at expiration
the spot price of the underlying minus the forward price agreed to in the contract.
value of a futures contract
accumulated gain since the previous settlement, which resets to zero
upon settlement.
off- market forward
A forward transaction that starts with a nonzero value
Lower Exercise price of call option benefits
One is that there are more
values of the underlying at expiration that are above the exercise price, meaning that
there are more outcomes in which the call expires in- the- money. The other benefit
is that assuming the call expires in- the- money, for any value of the underlying, the
option value is greater the lower the exercise price
When to exploit arbitrage oportunities
only worth exploiting if the transaction costs are low
Derivative Pricing Models
all derivative pricing models discount the expected payoff of the derivative at the risk- free rate.
Assets Forward Price
An asset’s forward price is increased by the future value of any
costs and decreased by the future value of any benefits: F0(T) = S0(1 + r)
T – (γ
– θ)(1 + r)
T. If the net cost of carry (benefits less costs) is positive, the forward
price is lower than if the net cost of carry was zero.
Commodity Convenience Yield
When a commodity’s storage costs exceed its convenience yield
benefits, the net cost of carry (benefits less costs) is negative.
Forward and Futures Prices
When interest rates are constant, forwards and futures will likely
have the same prices. The price differential will vary with the volatility of interest rates.
Negative Correlation Futures and Forward
If futures prices and interest rates are negatively correlated, forwards are more desirable to holders of long positions than are futures.
Valuation of the swap
appeals to replication and
the principle of arbitrage. Valuation consists of reproducing the remaining
payments on the swap with other transactions.
The value of a European call option at expiration
the greater of
zero or the value of the underlying minus the exercise price.
The value of a European call option
is inversely related to the exercise price. A lower exercise price means there are more potential outcomes at
which the call expires in- the- money.
the lowest value of a European put
is the
greater of zero or the present value of the exercise price minus the value of the underlying.
Payments, such as dividends,
reduce the value of the underlying
which increases the value of a European put option
A long bond can be synthetically
created by combining a long
asset, a long put, and a short call.
A fiduciary call
a long call with a risk free bond.
A protective put
is created by combining a long asset with a long put
the volatility of the underlying decreases
the value of the
option also decreases, meaning that the upper payoff value of the hedge portfolio combining them declines. However, the lower payoff value remains at zero
If an option is trading above the value predicted by the binomial model
investors can engage in arbitrage by selling a call, buying shares of the
underlying, and funding the transaction by borrowing at the risk- free rate. This
will earn a return in excess of the risk- free rate
At expiration, the values of American and European call options
are effectively the same; both are worth the greater of zero and the exercise value.
When a dividend is declared
an American call option will have
a higher value than a European call option because an American call option
holder can exercise early to capture the value of the dividend.
Put−call forward parity
demonstrates that the outcome of a protective put with a forward contract (long put, long risk- free bond, long forward
contract) equals the outcome of a fiduciary call
synthetically create a long asset position
by buying a call, shorting a put, and buying a bond.
Put–call–forward parity
is based on the assumption that no arbitrage is possible within the spot, forward, and option markets.
a long forward contract and a risk- free bond
creates a synthetic asset
