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Derivatives

 

Weight on the exam = 5%

Number of formulas = 11

CFA formulas

quantitative economics financials

corpfin portfolio equity

fixedincome derivatives alternative

 

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

FRAlong - 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.

ivc

Cint - 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.

ivp

Pint - 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.

opv

Vopt - option value

Vint - intrinsic value

Vtime - time value

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European call option

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

Minimum value

ecmin

Maximum value

ecmax

ct - 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

St - the price of the underlying stock at time t

X - the exercise price of the option

rf - 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

acmin

Maximum value

acmax

CT - 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

St - the price of the underlying stock at time t

X - the exercise price of the option

rf - 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

epmin

Maximum value

epmax

pt - 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

St - the price of the underlying stock at time t

X - the exercise price of the option

rf - 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

apmin

Maximum value

apmax

Pt - 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

St - the price of the underlying stock at time t

X - the exercise price of the option

rf - 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.

pcp

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

rf - 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

pcpacf

C - call option

P - put option

T - the time to expiration

PVCF - present value of the cash flows

S0 - the price of the underlying stock

X - the exercise price of the option

rf - 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.

pvirs

nFRPt - net fixed-rate payment

FRswap - swap fixed rate

LIBORt-1 - London Interbank Offer Rate (LIBOR) at time t-1

days - number of days

NP - notional principal

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