Valuation of Contingent Claims

Question 1

What does Δ represent in option

Answer 1

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

Question 2

What is Δ hedging?

Answer 2

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

Question 3

Formula for Δ hedge

Answer 3

Δ Neutral = - Δ portfolio / Δ hedge

Question 4

What is Γ in option

Answer 4

Γ: Gamma
Second derivative of Δ

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

Question 5

What does Γ measure

Answer 5

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

Question 6

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

Answer 6

The underlying securities.

Question 7

What is θ in options

Answer 7

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 8

What will our θ be if we long options

Answer 8

Negative θ

Time is our enemy

Question 9

What will our θ be if we short options

Answer 9

Positive θ

Option decay in value

Question 10

What is ν in options

Answer 10

ν: vega

Change in option for change in volatility

Question 11

How will our vega be if we long options?

Answer 11

Positive vega (Long volatility)

Question 12

How will our vega be if we short options?

Answer 12

Negative Vega (Short volatility)

Question 13

What is ρ in options

Answer 13

ρ: Rho

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

Question 14

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

Answer 14

Non dividend: 0 to1

Dividend: 0 to e^(-δT)

Question 15

What is the implied volatility in options based off of?

Answer 15

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

Question 16

What probability is N(d2) in the BSM?

Answer 16

probability the option expires in-the-money

Question 17

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

Answer 17

The Spot exchange rates as expressed as Sd/f

Question 18

What is the Stock component in the BSM

Answer 18

S x N(d1)

Question 19

What is the Bond component in the BSM

Answer 19

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

Question 20

What is a Collar option strategy?

Answer 20

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 21

What is a straddle option strategy?

Answer 21

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 22

When does gamma at its highest value?

Answer 22

When the option is near, or at the money

Question 23

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

Answer 23

• 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 25

What kind of Greeks does a Long call have?

Answer 25

Long call

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

Question 26

What kind of Greeks does a Long puts have?

Answer 26

Long Puts

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

Question 27

Why is the hedge ratio for put options negative?

Answer 27

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