Derivatives

Question 1

What does gamma (γ) represent in forward contract

Answer 1

Benefits

Question 2

What does theta (θ) represent in forward contract

Answer 2

Costs

Question 3

Formula for Forward contract

Answer 3

F0 = [S0 + Pv θ - Pv γ ] * (1+r)^t

Costs and benefits are discounted back to the present value

Question 4

Forward Rate Agreement
Long

Answer 4

Floating Rate Receiver - Pays Fixed Rate

Question 5

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

Answer 5

Forward Rate (3,6)

3 - Months from now
6 - Months duration

Question 5

Forward Rate Agreement

Short

Answer 5

Fixed Rate Receiver - Pays Floating Rate

Question 6

FRA Long Position Formula

Answer 6

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

Question 7

FRA short Position Formula

Answer 7

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

Question 8

Formula for “Cost to purchase deliverable bond”

Answer 8

ST + AI

Bond present price + Accured Interest Interest

Question 9

Formula for “Cost To Deliver”

Answer 9

CTD = ST - (Ft x CF)

Bond Present Value - (Forward Price x Conversion Factor)

Question 10

Fixed Income Forward Price Formula

Answer 10

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

Question 11

Qouted Fixed Income Forward Fomula

Answer 11

QF0 = F0 /Conversion Factor

Question 12

Formula For Currency Forward price
f/d

Answer 12

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

Question 13

Formula For Currency Forward price
d/f

Answer 13

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

Question 14

What will the Forward price be if

Rf = Rd

Answer 14

F0 = S0

Question 15

What will the Forward price be if

Rf > Rd

Answer 15

Ff/d > Sf/d

Fd/f < Sd/F

Question 16

What will the Forward price be if

Rf < Rd

Answer 16

Ff/d < Sf/d

Fd/f > Sd/f

Question 17

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

Answer 17

Zero
No value

Question 18

Receives fixed Rate, and pays floating is the same as

Answer 18

Long fixed bond and short floating bond

Question 19

How to calculate PMT in Swap rate?

Answer 19

1 - Dfn / Sum of DF

Question 20

Formula for Value of Interest Rate Swap

Answer 20

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

Question 21

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

Answer 21

The seller after adjusting for conversion factor

Question 22

Formula for Swap Value

Answer 22

(R0 - Rt+1) x Notional Amount x ∑DF

∑DF is based on the years remaning

Question 23

What is the underlying in a interest rate swap

Answer 23

An interest rate

Question 24

Formula for "Receive Equity" in equity swaps

Answer 24

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

Question 25

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

Answer 25

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.

Question 26

The value of a futuers contract is the difference between...

Answer 26

Future price at experation - Futurers price of the previous day

Question 27

What does Δ represent in option

Answer 27

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

Question 28

What is Δ hedging?

Answer 28

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

Question 29

Formula for Δ hedge

Answer 29

Δ Neutral = - Δ portfolio / Δ hedge

Question 30

What is Γ in options

Answer 30

Γ: Gamma Second derivative of Δ **The change in option Δ for a change in the underlying assets price**

Question 31

What does Γ measure

Answer 31

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

Question 32

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

Answer 32

The underlying securities.

Question 33

What is θ in options

Answer 33

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

Question 34

What will our θ be if we **long** options

Answer 34

Negative θ Time is our enemy

Question 35

What will our θ be if we **short** options

Answer 35

Positive θ Option decay in value

Question 36

What is **ν** in options

Answer 36

**ν**: vega Change in option for change in volatility

Question 37

How will our vega be if we long options?

Answer 37

Positive vega (Long volatility)

Question 38

How will our vega be if we short options?

Answer 38

Negative Vega (Short volatility)

Question 39

What is ρ in options

Answer 39

ρ: Rho Change in option value for a change in the Risk Free Rate

Question 40

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

Answer 40

Non dividend: 0 to1 Dividend: 0 to e^(-δT)

Question 41

What is the implied volatility in options based off of?

Answer 41

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

Question 42

What probability is N(d2) in the BSM?

Answer 42

probability the option expires **in-the-money**

Question 43

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

Answer 43

The Spot exchange rates as expressed as Sd/f

Question 44

What is the Stock component in the BSM

Answer 44

S x N(d1)

Question 45

What is the Bond component in the BSM

Answer 45

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

Question 46

What is the underlying asset in a interest rate option?

Answer 46

Underlying = FRA = LIBOR

Question 47

What position does a Long FRA have?

Answer 47

Borrower

Question 48

What position does a Short FRA have?

Answer 48

Lender

Question 49

Position of Long call in interest rate option

Answer 49

Call: Receive floating

Question 50

Position of long put in interest rate option

Answer 50

Receive fixed rate

Question 51

Position of Short put in interest rate option

Answer 51

Pay Fixed

Question 52

Position of Short call in interest rate option

Answer 52

Pay floating

Question 53

Payer Swaption

Answer 53

Pay fixed, Received floating

Question 54

Receiver Swaption

Answer 54

Receiver Fixed Pay floating

Question 55

What is a **Collar** option strategy?

Answer 55

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.**

Question 56

What is a **straddle** option strategy?

Answer 56

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**

Question 57

When does gamma at its highest value?

Answer 57

When the option is near, or at the money

Question 58

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

Answer 58

* 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.

Question 59

What kind of Greeks does a Long call have?

Answer 59

**Long call** **Delta**: Positive **Gamma**: Positive **Theta**: Negative **Vega**: Positive

Question 60

What kind of Greeks does a Long puts have?

Answer 60

**Long Puts** **Delta**: Negative **Gamma**: Positive **Theta**: Negative **Vega**: Positive

Question 61

Why is the hedge ratio for put options negative?

Answer 61

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