Session 17 - Option Markets and Contracts

Question 1

Put-call Parity

Answer 1

Put = Call - Spot + [strike/(1+risk free)^time]

Question 2

Risk neutral probability of an up-move

Answer 2

= (1 + Rf - size of down move) / (size of an up-move - size of a down-move)

Question 3

1-Period Option Delta

Answer 3

= (up move call value - down move call value) / (up move stock value - down move stock value)

Question 4

Delta

Answer 4

Describes the relationship between asset price and option price. Call option deltas are positive because as the underlying asset price increases, call option value also increases. In contrast, the delta of a put option is negative because the put value falls as the asset price increases.

Question 5

Vega

Answer 5

Measures the sensitivity of the option price to changes in the volatility of returns on the underlying asset. Both call and put options are more valuable, all else equal, the higher the volatility, so Vega is positive for calls and puts.

Question 6

Rho

Answer 6

Measures the sensitivity of the option price to changes in the risk-free rate. The price of a European call or put option does not change much if we use different inputs for the risk-free rate, so rho is not a very important sensitivity measure.

Question 7

Theta

Answer 7

Measures sensitivity of the option price to the passage of time. As time passes and a call option approaches maturity, its value declines, all else equal. This is called “time decay”. This is also true for most put options (deep in-the-money put options close to maturity may actually increase in value as time passes).

Question 8

Delta-neutral portfolio (or delta-neutral hedge)

Answer 8

The goal is to combine a long position in a stock with a short position in a call option so that the value of the portfolio does not change when the value of the stock changes. It is a risk-free combination of a long stock position and short calls where the number of calls to sell is equal to:

of options needed to hedge delta = # of shares hedged / delta of call option

Question 9

Gamma

Answer 9

Measures the rate of change in delta as the underlying stock price changes. It can be viewed as a measure of how poorly a dynamic hedge will perform when it is not rebalanced in response to a change in the asset price.

Question 10

Impact of cash flows in the underlying asset on options

Answer 10

• Decrease the value of a call option

- increase the value of a put option

Question 11

Payer Swaption

Answer 11

The right to enter into a specific swap at some date in the future as the fixed-rate payer at a rate specified in the swaption. If swap fixed rates increase (as interest rates increase), the right to enter the pay side becomes more valuable.

Question 12

Receiver Swaption

Answer 12

The right to enter into a specific swap at some date in the future as the fixed-rate received. This becomes more valuable as swap fixed rates decrease.