Derivatives

Question 1

How to value a swap rate at Y days?

Answer 1

1) Fixed rate * (Y/360)
2) Calculate new fixed rate ( (1-z) / (x + y + z) )
3) NA * (# in 1 - # in 2) * (x + y + z)

Question 2

How to value currency swap after Y days?

Answer 2

Amount in USD * (Fixed rate * (x + y + z) + z) - (Amount in CAD/new FX) * (CAD fixed rate * (x + y + z) + z)

Question 3

How to value an equity swap?

Answer 3

NA * (Equity return - Floating rate)

Question 4

What does 3 X 9 FRA mean?

Answer 4

To be received in 3 months based on 6 month rate

Question 5

What is the hedge ratio formula?

Answer 5

h = (c+ - c-)/(s+ - s-)

Question 6

What is delta?

Answer 6

Change in price of option given change in price of underlying
Delta for call is always positive
Delta for put is always negative

Question 7

What is gamma?

Answer 7

Change in delta given small change in price of underlying

Question 8

What is theta?

Answer 8

Change in value of option given small change in calendar time
Typically negative

Question 9

What is vega?

Answer 9

Change in value of option given small change in volatility

Always positive

Question 10

What is rho?

Answer 10

Change in value of option given small change in risk-free rate
Call: positive
Put: negative

Question 11

What is a covered call?

Answer 11

Own asset
Sell call (obligation to sell)

Question 12

What is a protective put?

Answer 12

Own asset
Long put (right to sell)

Question 13

What is an option spread?

Answer 13

Investor buys one option and writes another of the same type

Question 14

What is a bull spread?

Answer 14

Buy a call

Write a call with higher exercise price

Question 15

What is a bear spread?

Answer 15

Buy a put

Write a put with lower exercise price

Question 16

What is the max profit for a bear spread?

Answer 16

Strike of long put - strike of short put - net premium paid

Question 17

What is a collar?

Answer 17

Own asset
Sell call
Buy put

Question 18

What is a calendar spread?

Answer 18

Buy long-dated option
Write shorter-dated option

Objective: take advantage of faster time decay with shorter-term option

Question 19

What is a straddle?

Answer 19

Investor buys put and call with the same exercise price

Hope for high volatility

Question 20

What is a synthetic long?

Answer 20

Buy call + Sell put

Question 21

What is a synthetic short?

Answer 21

Sell call + Buy put

Question 22

What is a synthetic put?

Answer 22

Buy call + Short stock

Question 23

What is a synthetic call?

Answer 23

Buy stock + Buy put

Question 24

What are the motivations for entering into a covered call?

Answer 24

1) Income generation
2) Improving on the market
3) Target price realisation

Question 25

What are the insurance policy comparison with put option?

Answer 25

Premium: Time value
Value of asset: Price of stock
Face value: Exercise price
Term of policy: Time until expiration
Likelihood of loss: Volatility of stock

Question 26

What is the formula for π in binomial option?

Answer 26

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

Question 27

What is the formula for call in binomial model?

Answer 27

c= PV(πc+ + (1-π)c-)

Question 28

What is the formula for put in binomial model?

Answer 28

p = PV[πp+ + (1 – π)p–]

Question 29

What are the assumptions of the BSM model?

Answer 29

Lognormal distribution of the return

Continuous prices

The underlying instrument is liquid, meaning that it can be easily bought and sold.

Continuous trading is available, meaning that in the strictest sense one must be able to trade at every instant.

Short selling of the underlying instrument with full use of the proceeds is permitted.

There are no market frictions, such as transaction costs, regulatory constraints, or taxes.

No-arbitrage opportunities are available in the marketplace.

The options are European-style, meaning that early exercise is not allowed.

The continuously compounded risk-free interest rate is known and constant; borrowing and lending is allowed at the risk-free rate.

The volatility of the return on the underlying is known and constant.

If the underlying instrument pays a yield, it is expressed as a continuous known and constant yield at an annualized rate.

Question 30

What does being long in a FRA mean?

Answer 30

Long is floating receiver: gains when Libor rises

Short is fixed receiver: looses when Libor rises

Question 31

A bond futures contract is most likely accompanied by:

Answer 31

Conversion factor; supposed to make all eligible bonds equal the same amount
Cheapest-to-deliver bond emerges after adjusting for the conversion factor.

Question 32

What is the formula to calculate the futures value of a bond?

Answer 32

= ( (Value of bond)(1+i)^t - (Coupon)(1+i)^t) / Conversion factor

Question 33

What is a cash and carry strategy?`

Answer 33

Buying the stock and selling the forward

Question 34

What is a curve trade?

Answer 34

Trade designed to profit from changing expectations about a company’s credit quality.

Question 35

What is a payer swaption?

Answer 35

Gives the owner an option to enter a swap as the fixed rate payer/floating rate receiver.

Question 36

What is a receiver swaption?

Answer 36

Allows the holder to enter a pay floating swap (pay floating/receive fixed)