Derivatives

Weight on the exam = 5%

Number of formulas = 11

Value of a long FRA at settlement
FRA (Forward Rate Agreement) is an over-the-counter contract between parties that determines the rate of interest, or the currency exchange rate, to be paid or received on an obligation beginning at a future start date.

FRA_{long} - value of a long FRA at settlement

NP - notional principal

float - floating rate

forw - forward rate

days - number of days in the loan term

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Intrinsic value of a call
Intrinsic value of a call is the amount by which a call option is in the money, calculated by taking the difference between the strike price and the market price of the underlier.

C_{int} - intrinsic value of a call

S - the price of the underlying stock

X - the exercise price of the option

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Intrinsic value of a put
Intrinsic value of a put is the amount by which a put option is in the money, calculated by taking the difference between the strike price and the market price of the underlier.

P_{int} - intrinsic value of a put

S - the price of the underlying stock

X - the exercise price of the option

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Option value
Option value is the right, but not the obligation, to buy (for a call option) or sell (for a put option) a specific amount of a given stock, commodity, currency, index, or debt, at a specified price (the strike price) during a specified period of time.

V_{opt} - option value

V_{int} - intrinsic value

V_{time} - time value

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European call option
This is how minimum and maximum value of European call option is determined.

Minimum value

Maximum value

c_{t} - the price of a European call option at time t at any time prior to expiration at time t=T

T - the time to expiration

S_{t} - the price of the underlying stock at time t

X - the exercise price of the option

r_{f} - risk free rate

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American call option
This is how minimum and maximum value of American call option is determined.

Minimum value

Maximum value

C_{T} - the price of a Americal call option at time t at any time prior to expiration at time t=T

T - the time to expiration

S_{t} - the price of the underlying stock at time t

X - the exercise price of the option

r_{f} - risk free rate

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European put option
This is how minimum and maximum value of European put option is determined.

Minimum value

Maximum value

p_{t} - the price of a European put option at time t at any time prior to expiration at time t=T

T - the time to expiration

S_{t} - the price of the underlying stock at time t

X - the exercise price of the option

r_{f} - risk free rate

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American put option
This is how minimum and maximum value of American put option is determined.

Minimum value

Maximum value

P_{t} - the price of a American put option at time t at any time prior to expiration at time t=T

T - the time to expiration

S_{t} - the price of the underlying stock at time t

X - the exercise price of the option

r_{f} - risk free rate

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Put-call parity
Put-call parity defines a relationship between the price of a European call option and European put option —both with the identical strike price and expiry, and the underlying being a liquid asset.

c - call option

p - put option

T - the time to expiration

S - the price of the underlying stock

X - the exercise price of the option

r_{f} - risk free rate

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Put-call parity with asset cash flows
The equation describes the effect of cash flows on put-call parity

C - call option

P - put option

T - the time to expiration

PV_{CF} - present value of the cash flows

S_{0} - the price of the underlying stock

X - the exercise price of the option

r_{f} - risk free rate

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Plain-vanilla interest rate swap
In plain-vanilla interest rate swap Party A agrees to pay Party B a predetermined, fixed rate of interest on a notional principal on specific dates for a specified period of time. Concurrently, Party B agrees to make payments based on a floating interest rate to Party A on that same notional principal on the same specified dates for the same specified time period. In a plain vanilla swap, the two cash flows are paid in the same currency.

nFRP_{t} - net fixed-rate payment

FR_{swap} - swap fixed rate

LIBOR_{t-1} - London Interbank Offer Rate (LIBOR) at time t-1

days - number of days

NP - notional principal

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