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CFA Level 2 > Derivatives > Flashcards

Derivatives Flashcards

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1
Q

Carry arbitrage model

A

a no-arbitrage approach in which the underlying instrument is either bought or sold along with an opposite position in a forward contract

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2
Q

Market Value of the forwards contract on initiation date

A

0

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3
Q

Value at expiration of a long position in a forward contract

A

S(T) - F(T)

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4
Q

value at expiration of a short position in a forward contract

A

F(T) - S(T)

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5
Q

Calculate value of forward contract based off given forward price and interest rate

A

Forward price given - initial price / (1+interest rate)^(T-t)

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6
Q

After marking to market, the futures value of an existing contract

A

0

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6
Q

Equities Futures Contract Price with Continuously Compounding Rate

A

Spot rate * e ^ (interest rate + carry costs - dividend yield)(T-t)

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6
Q

Equities Futures Contract Price with Discrete Dividend Paid

A

(Spot Rate * (1+interest rate)^(T-t)) + carry costs - dividend

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6
Q

Who is long in an FRA agreement

A

The fixed rate payer and floating rate receiver

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7
Q

Forward Rate Agreement

A

An OTC forward contract in which the underlying is an interest rate

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7
Q

When does fixed payer in FRA agreement profit

A

When the MRR rises

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8
Q

Advanced Set

A

An arrangement when the interest rate is set at the time the agreement is made

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9
Q

Settled in arrears

A

An arrangement when the interest payments are made at maturity

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10
Q

Advanced Settle

A

An arrangement in which the FRA expires and settles at the same time

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11
Q

Calculate FRA Fixed Rate

A

[(1 + LTT/360)/(1 + STT/360)-1] / (LT-ST/360)

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12
Q

Forward pricing of contract under carry arbitrage model

A

F0 = FV ( S0 + CC0- CB0)

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13
Q

Forward valuation of contract under carry arbitrage model

A

Vt = PV (Ft-F0)

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14
Q

Fixed rate of interest rate swap

A

1 - present value of final year swap / sum of present values of all swaps

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15
Q

Optimal hedge ratio

A

h = C+ - c- / s+ - s-

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16
Q

Risk neutral probability of an up move

A

(1+ Rf - d) / (u-d)

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17
Q

Put call parity

A

c = S - PV(X) + p

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18
Q

Value of fixed rate interest swap at time T after initiation

A

NA * (current fixed swap - starting fixed swap rate) * (sum of present value factors for all time periods)

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19
Q

Value of receiver rate interest swap at time T after initiation

A

NA * (starting fixed swap rate - current fixed swap rate) * (sum of present value factors for all time periods)

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20
Q

2 Key Characteristics of Payments on Currency Swaps

A

1) Payment on each leg is in different currency
2) Payments are not netted

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21
Q

Notional amount on a currency swap

A

Initial amount * exchange rate

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22
Q

Is continuous trading available in BSM model

A

Yes

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23
Q

Is Short selling allowed in BSM model

A

yes

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24
Q

Are there brokerage costs in BSM model

A

no

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25
Q

Are there arbitrage opportunities in BSM model

A

No

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26
Q

Is the volatility of the underlying known in BSM model

A

Yes

27
Q

Is the volatility constant in BSM model

A

yes

28
Q

Are returns normally distributed in BSM model

A

Yes

29
Q

Can prices randomly jump from one to another in BSM model

A

No

29
Q

If puts are sold on stock, what is the appropriate delta hedge

A

Short sell shares of that stock

30
Q

optimal number of hedging units

A
  • (portfolio delta / delta of hedging instrument)
31
Q

Delta

A

change in a given instrument fora given small change in the value of the stock, holding everything else constant

32
Q

Gamma

A

change in delta for a given small change in the stock’s value

33
Q

Effect of buying options on gamma

A

always increases gamma when options are purchased

34
Q

Theta

A

change in a portfolio for a given small change in calendar time, holding all else constant

typically always negative

35
Q

Vega

A

change in a given portfolio for a given small change in volatility, holding all else constant

very high when options are near the money

36
Q

Rho

A

change in given portfolio for a given small change in the risk-free rate, holding all else constant

37
Q

Implied volatility

A

Standard deviation that causes an option pricing model to give the current option price

38
Q

Basis

A

the difference between the spot price and the futures price, as the maturity date of the futures contract nears, the basis converges towards 0

39
Q

Expectations approach to value options

A

Discount at the risk-free rate the expected future payoff based on risk neutral probabilities

40
Q

Settlement amount as pay-fixed party

A

NA * (MRR rate - FRA rate) * time /360 / (1+ discount rate) * time/360

41
Q

Value of Swap contract time into the contract

A

1) Calculate the fixed swap rate (1-last pv) / sum pv
2) (og rate - rate from step 1) * sum pv * NA

42
Q

Position to take when call option is overpriced

A

Sell the call, buy the shares, and borrow

43
Q

value on a forward contract on index or stock

A

Present value of (price of forward contract when it was entered - price of forward contract today)

exp(-risk free rate * time)*(difference between price of forward contract when it was entered and price of forward contract today)

44
Q

Equilibrium Futures Contract price based on the carry arb model

A

Q = (1/CF) * FV(B0+AI)-AT - FVCI

CF = conversion factor
B0 = clean price
AI = accrued interest
AT = would be accrued interest

45
Q

Two rules of arbitrage

A

1) Do not use your own money
2) Do not take any price risk

46
Q

Value additivity principal

A

The value of the portfolio is the sum of the values of the assets that make up the portfolio

47
Q

Market value of a futures contract, prior to marking to market

A

(current price - previous close price) * multiplier

multiplier - set contract size

48
Q

Reverse Carry Arbitrage

A

Short sale of the underlying and an offsetting opposite position in the derivative

49
Q

Future value of asset adjusted for carry cash flows

A

FV (Spot + Carry costs - carry benefits)

50
Q

Dividend index point

A

measure of the quantity of dividends attributable to a particular index

51
Q

Carry arbitrage model for continuous compounding

A

F0 = S0 * e ^ [ (r+CC-CB)*T ]

52
Q

Typical way that FRAs are settled at expiration

A

Advanced set, advanced settle

53
Q

Conversion factor for a futures contract

A

Approximate decimal price at which a $1par of security would trade at if it had a 6% YTM

54
Q

Two Generic Expressions in Carry Models

A

1) Forward Pricing - FV(B0 + CC - CB)
2) Forward Valuation - PV(Ft-F0)

55
Q

Difference between a swap and a FRA

A

a swap hedges multiple periods, whereas FRA hedges one period

56
Q

Typically the way that swaps are settled at expiration

A

Advanced set, settled in arrears

57
Q

Value of a interest rate swap for fixed receiver

A

NA * (FSt - FS0) * PV (value of pay fixed swap)

58
Q

Value of Currency Swap at Time t

A

[NA(a) * (payment rate of a * sum of PV(a) + PV of relevant spot rate(a))] - [exchange rate * NA(b) * (payment rate of b * sum of PV(b) + PV of relevant spot rate(b))]

59
Q

Futures vs forwards

A

Futures are marked to market every day

60
Q

Impact of dividends on call and put option, under black scholes model

A

dividends lower the value of the call option only

61
Q

Impact of increased interest rates on call and put options

A

move the values further apart, calls increase, puts decrease

62
Q

when is option gamma the highest

A

when the option is near or at the money

63
Q

when can you not use the bsm model, using black model instead

A

when the underlying is costless to carry

64
Q

Rho on call options vs Rho on put options

A

Rho on call options is positive

65
Q

gamma on a long put

A

0

66
Q

gamma on a long call

A

1

67
Q

impact on d1 and d2 under black scholes model when dividends are introduced

A

both d1 and d2 are lowered because d2 has d1 in its formula

68
Q

when is vega high

A

when an option trades near or at the money

69
Q
A

CFA Level 2 (11 decks)

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