2.6 Derivatives and Risk-Neutral Valuation

Question 1

Slope of the term structure of forward prices is governed by the underlying security’s financing cost (r) and dividend yield (y)

Describe the slope:
1. r=q:
2. r>q:
3. r<q:

Answer 1

1. r=q: flat
2. r>q: upward
3. r<q: downward

Question 2

Define cost of carry

Answer 2

Direct financial difference between holding a position in the cash market and holding a position in the forward market, .e.g physical wheat’s storage cost

Question 3

What are the four factors that differentiate forward pricing on financial assets vs physical assets?

Answer 3

1. Forecast of supply and demand changes
2. Storage cost differentials
3. Convenience yield differentials
4. Difficulties with short-selling

Question 4

What’s the difference between Bull and Bear Spread?

Answer 4

Bull = short call + long call with lower strike price

Bear = short put + long put with higher strike

Question 5

What’s the difference between Straddle and Strangle?

Answer 5

Straddle: call and put with same sign

Strangle: call and put with the same sign, but different strike price

Question 6

What is Put Call parity?

Answer 6

Call + Bond - Put = Asset
OR
Stock + Put = Bond + Call

Question 7

What does option price depend on? Five variables

Answer 7

1) the underlying asset price
2) the strike price
3) the underlying asset’s return volatility
4) the option’s time to expiration
5) the risk-free rate.

Question 8

What are the five popular Greeks that demonstrate option sensitivities?

Answer 8

1. Delta: asset value
2. Vega: asset vols
3. Theta: time to maturity
4. Rho: risk free rate
5. Gamma

Question 9

Uses of option sensitivities in Risk Management

Answer 9

1. Hedging
2. Manage risk to each derivative
3. Identify effect of finite changes on value of position, e.g. convexity of bond

Question 10

Define the following Greeks:
1. Omnicron
2. Gamma
3. Elasticity
4. Lambda

Answer 10

1. Omicron presents an option’s sensitivity to changes in credit risk/spread.
2. Gamma is an option value’s second partial derivative with respect to the option’s underlying asset.
3. Elasticity represents the percentage change in an asset’s value with respect to a percentage change in another value.
4. Lambda represents an option’s price elasticity with respect to its underlying asset price

Question 11

According to put-call parity, which of the following is equivalent to a risk-free, zero-coupon bond?
1. Risk reversal
2. Long collar
3. Covered call
4. Protective put

Answer 11

Bond = Stock + Put - Call

Long collar = + Put - Call

3. Covered call = Long asset + Short call (= Asset – Call)
4. Risk reversal = Long call + Short put (= Call – Put)
5. Protective put = Long asset + Long put (= Asset + Put)

Note: A collar position is equivalent to a protective put and a covered call.