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CFA 2 > Derivatives > Flashcards

Derivatives Flashcards

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CFA flashcards
1
Q

Pricing

vs

Valuation

A

Pricing generally takes place at initiation

Valuation value is determined at any given time following initiation

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2
Q

Fair value of a future =

A

Cash price + cost of carry

Ie cost of buying and holding until delivery at a future date.

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3
Q

Forward PRICE =
given spot and rf

Forward price given dividend =

PV dividend =

Forward VALUE =

A

Forward = Spot x (1+r)^T

Forward = Spot - PV dividend x (1+r) ^t

PV Dividend = Dividend / (1 + rf)^n/365

ie if prepricing the forward at day 100 and there is a dividend day 110 you discount 1+rf ^10/365 and subtract this from Spot from ON DAY 100!

Forward VALUE = (Forward PRICE on day 100 - Forward PRICE on day 0) / (1+rf)^remaining t

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4
Q

How often are gold futures marked to market?

Forward value =

A

Gold futures are marked to market daily

Forward value = Current stock price day 100 - PV of cash flows remaining - PV of original forward

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5
Q

3% Effective Annual Rate into continuous compound =

A

1.03 LN = 2.9559%

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6
Q

2 x 3 FRA means what?

A

FRA 2 x 3

Contract expires in two months.
Loan is settled in 3 months

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7
Q

FRA given

90 day LIBOR = 3.5%
180 day LIBOR = 3.9%

A

1 + (Rlong x n/360) / 1+(Rshort x n/360) - 1 = 1.065%

Reannualise = 0.01056 x (360/difference) = 4.26%

Difference = 180 - 90 = 90

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8
Q

Future price =

CTD Future =
cheapest to deliver future

A

Future price = CTD Future / Conversion factor

CTD Future = (Future price - PV of CF Until expiry) x 1 + rf^T

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9
Q

Forward currency =

A

Forward currency = Spot x (1+Rprice)^t / (1+Rbase)^t

e.g. t = 180/365

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10
Q

Interest rate swap =

Value at initiation

A

Value at initiation of a swap is always zero.

It is a series of call and put options equal to the swap rate.

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11
Q

Swap Fixed Rate SFR =

Discount factor =
LIBOR 90 days 4%

A

SFR = [(1- final discount factor) / sum of discount factors] x no settlement periods PER YEAR

Discount factor = 1 / 1 + (LIBOR x n/360)

1 / 1 + (0.04 x 90/360) = 0.9901
LIBOR 90 days 4%

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12
Q

Pay fixed receive floating is the same as =

A

Pay fixed = issuing a fixed coupon bond

Receive floating = Long FRN

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13
Q

Currency swaps are fixed or floating or a combination of both?

A

Currency swaps can be a combination of fixed and fixed, fixed and floating or floating and floating.

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14
Q

FRA payments are made on ‘notional principal amount’ when is this exchanged?

A

Almost always at the start of a contract but occasionally at the end.

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15
Q

Value of equity swap =

A

Step 1:
equity value = End value / start value x notional value = Ansa

Step 2:
Bond = (swap payment x sum of discount factors) + (1 x final discount factor) x notional value = Ansb

Step 3
Swap value today = Equity Ansa - Bond Ansb

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16
Q

Indices swap

FTSE d0 = 4000, FTSE d90 = 4200
S&P d0 = 12600, S&P d90 = 12900

Notional = £50m

Market value of swap =

A

Market value of swap = (Return from receiver leg - return on payer leg) x notional value

(12,900/12,600) - (4,200/4,000) x £50m = £1.309m

17
Q

Binomial tree - Probability of an up/down move.

Probability of an UP move =

A

UP = (1 + Rf - D) / U - D

Down = 1 - Up

18
Q

Black-Scholes-Merton option model =

A

Underlying assets follow a brownian motion process which change smoothly.
Interest rate is annualised continuously compounded.
Normally distributed Rf rate is KNOWN and CONSTANT
Options are European
Volatility is KNOWN and CONSTANT

19
Q

BSM Long call C0 =

A

C0 = (S x N(d1)) - (e^-rfT x X x N(d2))

Nd1 = Buy stock
Nd2 = Subtract = sell zero coupon bond
Spot = 20
rf = 4%
Exercise price = 17
Nd1 = 0.64
Nd2 = 0.522

call = [20 x 0.64] - [(-0.04 x 1) 2nd LN x 17 x 0.522]

Note MINUS rf x T

20
Q

BSM Long Put =

A

P0 = (e^rfT x X x N(-d2)) - (S0 x N(-d1))

N(-d2) = Buy zero coupon bond
N(-d1) = Sell stock
21
Q

What is the black model?

A

The model value European forwards and futures.

Call = e^-rfT x [Ft x Nd1 - X x Nd2]
Put = e^-rfT x [X x 1 - Nd2] - f x T x [1-Nd1]
22
Q

Individual interest rate call options =

Long cap plus short floor with same interest rate =

Portfolio of long interest rate put options =

A

Individual interest rate call options = cap

Long cap plus short floor with same interest rate = pay fixed, receive floating interest rate swap

Portfolio of long interest rate put options = long floor

23
Q

What is a swaption?

A

Swaptions gives the holder the right to enter into an interest rate swap fixed and floating. A series of annuity cash flows.

24
Q

Payer swaption

Receiver swaption

A

Payer swaption = fixed rate payer, equivalent to a long put on a bond. More valuable as rates rise.

Receiver swaption = fixed rate receiver

25
Q

Delta =

No of calls to sell =

A

Delta = Change in option price / Change in share price

Delta = (no shares x 1) + (No call options x delta of call options)

No of calls to sell = Portfolio delta aka no shares / Delta of call option

26
Q

Increase in interest rates
Call options
Put options

Increase in interest rates
Call options
Put options

A

Increase in interest rates
Call options = increase
Put options = decrease

Increase in interest rates
Call options = increase
Put options = increase

27
Q

What is Gamma

Long options
Short options

Positive or negative and how to correct them

highest when

A

Gamma is rate of change of delta

Long options = Positive Gamma correct with a short call
Short options = Negative Gamma correct with a long call

Highest when at-the-money.

28
Q

Vega =

Theta =

A

Vega is a volatility measure. Always positive value and exactly the same for puts and calls

Theta is a measure of time decay. Both puts and calls have NEGATIVE Theta which increases as expiry approaches.

29
Q

Rho =

Positive Rho =

Positive Gamma =

A

Rho shows options prices changes to a change in the Risk Free rate. Positively related to calls and negatively to puts.

Positive Rho = long call and short put

Positive Gamma = long call and long put

30
Q

If you think implied vol is greater than the market =

If you think implied vol is less than the market =

A

If you think implied vol is greater than the market Buy the put option

If you think implied vol is less than the market sell the call option.

CFA 2 (10 decks)

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