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2020 CFA LEVEL II > Derivative > Flashcards

Derivative Flashcards

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CFA flashcards
1
Q

FP =

A

S0 × (1 + Rf)^T

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2
Q

V0 of long forward contract

A

0

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3
Q

V (long) during holding

A

St - [FP/(1+RF)^(T-t)]

short position = negative of long position

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4
Q

VT (at maturity)

A

St -FP

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5
Q

FP (on a stock) =

A

(S0 − PVD) × (1 + Rf)T
= [(S0 × (1 + Rf)T] − FVD

days=365

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6
Q

Vt(long position on a stock)

A

(St- PVDt) - [FP / (1+rf)^(T-t)]

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7
Q

FP(on equity index)

A

S0 * e^(Rfc-dvd yld) *T

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8
Q

FP(on fixed income security)

A

(S0 - PVC)*(1+Rf)^T

t=365

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9
Q

Vt(long position on fixed income security)

A

(St-PVCt) - [(FP/(1+rf)^(T-t)]

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10
Q

QFP

A

= FP/CF
=full (1+Rf)^T - AIT-FVC) / CF

AIT =accrued interest at future contract maturity
=(days since last coupon ptm nav / days b/w coupon ptm NTD ) * Counpon ptm —-frequent of coupon payment

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11
Q

FRAs forward rate agreements - long

A

= # of months until the contract expires
- # of month until the underlying loan is settled
= maturity of the loan

rights to borrow money

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12
Q

libor rates used in

A

FRA
swap
caps/ floors
* days/360

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13
Q

Equity, bond, currencies, stock option use 365

A

(1+r)^(days/365) periodic compounding

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14
Q

equity index

A

e^r*days/365 continuous compounding

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15
Q

Synthetic call

A

put + stock - riskless discount bond

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16
Q

synthetic put

A

call - stock + riskless discount bond

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17
Q

SFR= rfixed

A

(1-ZN)
/ (SUM OF Z)

z= 1/ (1+libor *(days/360))

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18
Q

value to payer =

A

Sum (z) * (SFR new - SFP old) * days/360 * notional amount

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19
Q

put-call parity must hold for arbitrage

A

P+S = C+Xe^(-rt)

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20
Q

value of equity swap

A

= (FPt -FP0)NA

/ (1+SFR)(t-t)

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21
Q

Ft = Currency forward price

A

price = so * (1+rpc)^t/365 / (1+rbc)^t/365
Vt = FPt -FP0
/ (1+rpc)^(T-t)

if continously compounded =Ft = S0^(Rprice-Rbase)*T

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22
Q

probability of upward movement

πU

A

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

downward movement = 1- πU

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23
Q

assumptions underlying the Black-Scholes-Merton (BSM) model

A

The return on the underlying asset follows a lognormal distribution and the price change is smooth.

The (continuous) risk-free rate is constant and known.

The volatility and yield of the underlying asset is constant and known.

Markets are frictionless.

The options are European.

no cash flows on the underlying asset

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24
Q

number of call options needed to delta hedge

A

=
number of shares hedged /
delta of call option

25
Q

long fra

A

pay fixed, receive floating

=long call + short put

26
Q

short fra

A

pay float, receive fixed

27
Q

value of fra =

A

(long rate-short rate)*days/360 * notional / [(1+long rate * days/360)]

28
Q

FRA (60)= (new rate)

A

(1+long * days/360)/(1+short * days/360) * days/360 -1

29
Q

SFR(swap fixed rate)

A

(1-last DF)/(SUM OF DF) * settlement periods per year

30
Q

value of payer swap=

A

sum df *(SFR new - SFR old)/(#settlements/year) * Notional

= pv(cash inflow) - pv(cash outflow)

pv(cash flow) = sum DF* cash flow i

31
Q

equity swap pv=

A

(current index value - index level at last settlement)
*notional

value = pv(cash inflow) - pv(cash outflow)

32
Q

Hedge ratio

A

(C+-C-)/ (S+-S-)

# OF LONG POSITION = # OF OPTION * HEDGE RATIO * S+
# OF SHORT option=# OF OPTION * C+ call price 
=#shares hedged / delta
33
Q

fractional units of stock =

A

(C+-C-)/ (S+-S-)

34
Q

Interest rate call

PMT for interest rate calls

A

long receives pmt if reference rate > the strike (fixed)

= max(0,NP*(reference rate - strike) * days/365)

35
Q

interest rate put

PMT for interest rate puts

A

long receives payment if reference rate fall below the strike rate

= max(0,NP*(strike-reference rate) * days/365)

36
Q

cap

A

= series of Interest rate calls

37
Q

floor =

A

series of interest rate puts

38
Q

payer swap =

A

long cap + short floor with same strike

39
Q

payer swaption

A

right to enter swap as fixed-rate payer
iwin if rates increase

payer swap = long payer swaption + short receiver swaption

40
Q

receiver swaption

A

right to enter swap as fixed-rate receiver
win if rates fall

receiver swap = long receiver swaption + short payer swaption

41
Q

BSM European call value C0 =

A 
So*N(d1) -                               xe^-rft * N(d2)
long N(d1) unit of stock         short N(d2) units of zbc
42
Q

BSM currency option C0=

A

S0e^-rbc * N(d1) - Xe^-rpc*T * N(d2)

43
Q

Delta S

most sensitive when option is at the money

A

asset price = (C1-C0) / (S1-S0)
> 0 positive related to call
< 0 negative related to puts

44
Q

Vega Sigma

A

Volatility

> 0 positive related to call/put

45
Q

Rho

A

Rf interest rate
> 0 positive related to call
< 0 negative related to puts

46
Q

Theta T

A

Time to expiration
< 0 value goes to 0
value goes to 0

47
Q

X

A

exercise price

negative related for calls
positive related for puts

48
Q

change in Co=

A

delta call * change in stock price
=e^(-signa*T) *N(d1) * change in stock price

for no dividend paying stock
put delta = call delta-1
change in p = (N(d1)-1) * change in S

49
Q

OF SHORT option

A

=#shares hedged / delta

call delta <1, need more calls than shares

50
Q

Gamma

A

rate of change in delta as stock price changes

change in call = call delta * change in S + 1/2 gamma * (change in S)^2

51
Q

A swap is equivalent to a series of:

A

off-market FRAs.

52
Q

the higher the gamma

the more delta changes as the asset price changes

A

the worse a delta hedge will perform over time

53
Q

A payer swaption gives its holder:

A

the right to enter a swap in the future as the fixed-rate payer.

54
Q

delta hedging

A

a long position in a stock with a short position in call option, so value of the portfolio does not change with the value of the stock

55
Q

of short calls required

A

of shares/call delta

56
Q

Over the life of a swap, the price of the swap:

A

The price of a swap, quoted as the fixed rate in the swap, is determined at contract initiation and remains fixed for the life of the swap.

57
Q

The price of a forward contract is

A

established at the initiation of the contract and is expressed in different terms, depending on the underlying assets. It is the price that makes the contract value zero, and depends on current interest rates through the cost-of-carry calculation.

58
Q

Backwadation

A

Spot > FP

59
Q

The two fundamental rules of the arbitrageur

A

(a) do not use your own money and

(b) do not take any price risk.

2020 CFA LEVEL II (15 decks)

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