Derivatives Flashcards

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1
Q

What does gamma (γ) represent in forward contract

A

Benefits

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2
Q

What does theta (θ) represent in forward contract

A

Costs

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3
Q

Formula for Forward contract

A

F0 = [S0 + Pv θ - Pv γ ] * (1+r)^t

Costs and benefits are discounted back to the present value

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4
Q

Forward Rate Agreement
Long

A

Floating Rate Receiver - Pays Fixed Rate

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5
Q

How does a forward contract look for a FRA 3 x 9 Contract

A

Forward Rate (3,6)

3 - Months from now
6 - Months duration

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5
Q

Forward Rate Agreement

Short

A

Fixed Rate Receiver - Pays Floating Rate

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6
Q

FRA Long Position Formula

A

Receives floating, pays fixed
NA( Floating - Fixed x (Days / 360) ) / (1+ Floating Rate x Days/360))

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7
Q

FRA short Position Formula

A

Short - Receive Fixed, Pay floating rate
[ Na x ( Fixed - Floating * Days /360] / (1+fixed * Days /360)

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8
Q

Formula for “Cost to purchase deliverable bond

A

ST + AI

Bond present price + Accured Interest Interest

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9
Q

Formula for “Cost To Deliver

A

CTD = ST - (Ft x CF)

Bond Present Value - (Forward Price x Conversion Factor)

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10
Q

Fixed Income Forward Price Formula

A

F0 = [(S0+AI)-I/(1+r)^t] x (1+r)^t - Accured Interest

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11
Q

Qouted Fixed Income Forward Fomula

A

QF0 = F0 /Conversion Factor

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12
Q

Formula For Currency Forward price
f/d

A

Ff/d = Sf/d x [(1+rf) ^t / (1+rd)^t]

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13
Q

Formula For Currency Forward price
d/f

A

Fd/f = Sd/f x [(1+rd) ^t / (1+rf)^t]

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14
Q

What will the Forward price be if

Rf = Rd

A

F0 = S0

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15
Q

What will the Forward price be if

Rf > Rd

A

Ff/d > Sf/d

Fd/f < Sd/F

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16
Q

What will the Forward price be if

Rf < Rd

A

Ff/d < Sf/d

Fd/f > Sd/f

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17
Q

What is the value of a forward and swap contract at time 0

A

Zero
No value

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18
Q

Receives fixed Rate, and pays floating is the same as

A

Long fixed bond and short floating bond

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19
Q

How to calculate PMT in Swap rate?

A

1 - Dfn / Sum of DF

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20
Q

Formula for Value of Interest Rate Swap

A

( R fixed 0 - R fixed 1) x Notional Amount x sum of DF

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21
Q

Who decideds which bond to deliver in a fixed income future contract

A

The seller after adjusting for conversion factor

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22
Q

Formula for Swap Value

A

(R0 - Rt+1) x Notional Amount x ∑DF

∑DF is based on the years remaning

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23
Q

What is the underlying in a interest rate swap

A

An interest rate

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24
Q

Formula for “Receive Equity” in equity swaps

A

(NA x P0 / Pt+1) - NA x (Rfix x ∑DF + DFn)

25
Q

Company X is in the UK.
Company Y is in Japan.

They enter into a Fixed-for-Fixed currency Swap.

What kind of bond position is this similar to for both parties

A

Company X: Short a JPY bond and long GBP bond.

Company Y: Short GBP bond and Long JPY bond

Reason: They both have to make interest payment (short) in the counterparties currency, and receive (Long) interest payment of their domestic currency.

26
Q

The value of a futuers contract is the difference between…

A

Future price at experation - Futurers price of the previous day

27
Q

What does Δ represent in option

A

Delta: Change in the value of the option, for a change in underlying price

28
Q

What is Δ hedging?

A

Taking an offsetting Δ postion so to be delta neutral
Δ = 0

29
Q

Formula for Δ hedge

A

Δ Neutral = - Δ portfolio / Δ hedge

30
Q

What is Γ in options

A

Γ: Gamma
Second derivative of Δ

The change in option Δ for a change in the underlying assets price

31
Q

What does Γ measure

A

Measures the risk that remains once a portfolio is delta neutral
It can be managed to a specific level, but never eliminated

32
Q

A portfolio that must be gamma neutral can become delta neutral by trading

A

The underlying securities.

33
Q

What is θ in options

A

θ Theta

change in option value for the passage of time

estimates how much value slips away from an option with each passing day

Theta is the rate in which the time value decreases as time goes on

34
Q

What will our θ be if we long options

A

Negative θ

Time is our enemy

35
Q

What will our θ be if we short options

A

Positive θ

Option decay in value

36
Q

What is ν in options

A

ν: vega

Change in option for change in volatility

37
Q

How will our vega be if we long options?

A

Positive vega (Long volatility)

38
Q

How will our vega be if we short options?

A

Negative Vega (Short volatility)

39
Q

What is ρ in options

A

ρ: Rho

Change in option value for a change in the Risk Free Rate

40
Q

What is Delta range for a call option at any moment in time

A

Non dividend: 0 to1

Dividend: 0 to e^(-δT)

41
Q

What is the implied volatility in options based off of?

A

It is the volatility implied by the option prices observed in the market

42
Q

What probability is N(d2) in the BSM?

A

probability the option expires in-the-money

43
Q

With currency options, the volatility in the BSM model is the volatility of the log returns of…

A

The Spot exchange rates as expressed as Sd/f

44
Q

What is the Stock component in the BSM

A

S x N(d1)

45
Q

What is the Bond component in the BSM

A

e^(-r x T) X N(d2)

46
Q

What is the underlying asset in a interest rate option?

A

Underlying = FRA = LIBOR

47
Q

What position does a Long FRA have?

A

Borrower

48
Q

What position does a Short FRA have?

A

Lender

49
Q

Position of Long call in interest rate option

A

Call: Receive floating

50
Q

Position of long put in interest rate option

A

Receive fixed rate

51
Q

Position of Short put in interest rate option

A

Pay Fixed

52
Q

Position of Short call in interest rate option

A

Pay floating

53
Q

Payer Swaption

A

Pay fixed, Received floating

54
Q

Receiver Swaption

A

Receiver Fixed
Pay floating

55
Q

What is a Collar option strategy?

A

buying a downside put and selling an upside call to protect against large losses, but that also limits large upside gains.

Buy put, Sell call.

56
Q

What is a straddle option strategy?

A

buying (or selling) both a call and a put with the same strike price and expiration on the same underlying asset.

Buy or sell put and call option witht he same stike and expiration

57
Q

When does gamma at its highest value?

A

When the option is near, or at the money

58
Q

What is the PV of expected option payoff at expiration in the BSM model?

A
  • The PV is based on the Risk-free interest rate and not the investors required rate of return.
  • The expected option payoff is based on the risk-neutral probabilities.
59
Q

What kind of Greeks does a Long call have?

A

Long call

Delta: Positive
Gamma: Positive
Theta: Negative
Vega: Positive

60
Q

What kind of Greeks does a Long puts have?

A

Long Puts

Delta: Negative
Gamma: Positive
Theta: Negative
Vega: Positive

61
Q

Why is the hedge ratio for put options negative?

A

Option value is inversely proportional to the price of the underlying.