Derivatives

Question 0

Forward price of an equity

Answer 0

= (S0 - PVD) x (1 + Rf)^T

= [S0 x (1 + Rf)^T] - FVD

Question 1

Value of long forward contract

Answer 1

= Spot price - PV(forward price)

= St - FP/(1+Rf)^(T-t)

Question 2

Value of forward on coupon-paying bonds

Answer 2

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

Question 3

Put-call parity

Answer 3

call + PV(ZCB) = put + stock

Question 4

Risk-neutral probability of an up move

Answer 4

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

Question 5

Size of a down-move

Answer 5

1/(size of up move)

Question 6

Option’s delta

Answer 6

(Up-value of call - Down-value of call)/(Up-value of stock - Down-value of stock)

units in shares/option

Question 7

Assumptions of Black-Scholes

Answer 7

• Price of underlying asset follows a lognormal distribution
• Risk-free rate and volatility are constant and known
• Markets are frictionless
• Underlying asset has no cash flow
• Options are European style

Question 8

Delta-neutral hedge

Answer 8

Combination of long stock and short calls to hedge value of portfolio

of options needed = # of shares hedged/delta

Question 9

What is delta and how are call and put options affected?

Answer 9

Change in option price as asset price changes

• positive for calls: option value increases as underlying increases
• negative for puts: option value decreases as underlying increases

Question 10

What is vega and how does call and put options affected?

Answer 10

Change in option price as volatility changes

• positive for calls and puts

Question 11

What is rho and how does call and put options affected?

Answer 11

Change in option price as risk free rate changes

• positive for calls
• negative for puts

Question 12

What is theta and how are call and put options affected?

Answer 12

Change in option price with the passage of time

• as calls and puts approach maturity (passage of time increases), option value decreases, except for deep in-the-money put options

Question 13

What is gamma and how does it affect dynamic hedging?

Answer 13

Change in delta as the price of the underlying changes

Hedges that use high gamma options (ATM options) will require frequent rebalancing

Question 14

Value of plain vanilla swap

Answer 14

(1 - Zn)/(Z1 + Z2 +…+ Zn)

Question 15

Use calls and puts to describe the position of a cap buyer

Answer 15

• long call on LIBOR

- long put on bond prices

Question 16

Use calls and puts to describe the position of a floor buyer

Answer 16

• long put on LIBOR

- long call on bond prices

Question 17

Value of currency forward

Answer 17

St/(1+Rfc)^(T-t) - FT/(1+Rdc)^(T-t)

Question 18

What are Eurodollar futures?

Answer 18

• Similar to forward rate agreements
• Based on 90-day LIBOR
• Calculated as 100 minus annualized LIBOR

Question 19

Normal backwardation

Answer 19

Futures prices are expected to be less than expected future spot prices (hedging activity by sellers)

Question 20

Normal contango

Answer 20

Futures prices are expected to be greater than expected future spot prices (hedging activity by buyers)

Question 21

Delta for call option

Answer 21

= 1 - delta of put option

= Δoption price/Δstock price

Question 22

Backwardation

Answer 22

Futures price < spot price

Question 23

Contango

Answer 23

Futures price > spot price

Question 24

Forward rate of a 2x5 contract

Answer 24

[(1+r150)/(1+r60)-1]*(360/90)

Question 25

Put-call parity for futures and forwards

Answer 25

C + (X-F)/(1+Rf)^T = P

Question 26

Who is short the credit risk for CDS?

Answer 26

The protection buyer because he benefits when spreads widen

Question 27

What are credit events to trigger payment for a CDS?

Answer 27

• bankruptcy
• failure to pay scheduled principal or interest
• restructuring

Must be determined by supermajority vote of 12 members of the ISDA committee

Question 28

Upfront premium for CDS (%)

Answer 28

(credit spread - fixed coupon) x duration of CDS

Question 29

Value of protection leg of a CDS

Answer 29

= value of risk-free bond - expected payoff on risky bond

= credit risk

Question 30

Upfront payment for a CDS

Answer 30

PV(protection leg) - PV(premium leg)

if positive, protection buyer is making an upfront payment

Question 31

Price of CDS

Answer 31

100 - upfront premium %

per 100 par

Question 32

What is a payer swaption equivalent to?

Answer 32

Put option on a bond

Question 33

What is a receiver swaption equivalent to?

Answer 33

Call option on a bond

Question 34

Use options to describe a payer swap

Answer 34

Long call and short put on interest rate options

Question 35

Use options to describe a receiver swap

Answer 35

Long put and short call on interest rate options

Question 36

How do storage costs affect the forward price?

Answer 36

Increases forward prices

Question 37

When would futures prices be higher than forward prices?

Answer 37

Asset is positively correlated to interest rates