Lecture 1: Options

Question 1

Definition of an Option

Answer 1

The right (not an obligation), to force a transaction to occur at some future time on terms & conditions decided now.

Question 2

Define: Call Option

Answer 2

Buyer obtains right to buy an asset from a seller in the future at a price determined now

Question 3

Define: Put Option

Answer 3

Buyer obtains right to sell an asset to the seller in the future at a price determined now

Question 4

Is a long call the opposite to a long put?

Answer 4

NO. The payoff from a long call is not the opposite of the payoff from a long put.

The opposite of a long call is a short call.

Question 5

What is the value of an option

Answer 5

Intrinsic Value (IV) + Time Value (TV)

Question 6

Define: IV

Answer 6

Payoff (Not profit) from an option if it were exercised immediately

Question 7

Define: TV

Answer 7

Total value of an option minus the intrinsic value of an option.

For a call, intrinsic value is the difference between asset price and exercise price (if the difference is positive), or zero (if the difference is negative).

Question 8

What is the IV from a call option

Answer 8

Max [Snow - X, 0]

Question 9

What is the IV from a put option

Answer 9

Max [X - Snow, 0]

Question 10

What is the moneyness of an option. Do we refer to the IV or the total option value?

Answer 10

Value of underlying asset relative to the exercise price (See IV not total option value)

Question 11

What are the factors affecting IV?

Answer 11

1. ) Current value of underlying asset
2. ) Exercise Price
   3) Expected Dividends

Question 12

What are the factors affecting TV?

Answer 12

1. ) Volatility
2. ) Term to expiry.
3. ) Risk-free interest rate

Question 13

Current Value of Underlying Asset (Relationship / Explanation)

Answer 13

Call: +ve, Put: -ve

Asset more valuable > Increased payoff / increased probability of call option being exercised

Question 14

Exercise Price (Relationship / Explanation)

Answer 14

Call: -ve, Put: +ve

Right to buy asset > Pay more > Less probability of call to be exercised / More payoff for put

Question 15

Expected Dividends (Relationship / Explanation)

Answer 15

Call: -ve; Put: +ve

Dividends > Stock prices decreases > Lower underlying value of asset > decreases payoff/probability of call option being exercised

Question 16

Volatility (Relationship / Explanation)

Answer 16

Call: +ve; Put: +ve

Increased probability of option value higher/;lower than exercise price

Question 17

Term to Expiry (Relationship / Explanation)

Answer 17

Call: +ve; Put: +ve

Increased probability of option value higher/;lower than exercise price

Question 18

Risk-free interest rate (Relationship / Explanation)

Answer 18

Call: +ve; Put: -ve

Call option expects a future cash outflow (X). As r increases, the PV of exercise price decreases, leading to higher payoff.
Put option expects a future cash inflow (X). As r increases, the PV of exercise price decreases, leading to lower payoff.

Question 19

What happens to the buyer of a call option if he exercised his right on the day before the ex-dividend date

Answer 19

The buyer of the option will receive the dividend

Question 20

What happens to the seller of a call option if the buyer exercises his rights after the ex-dividend date

Answer 20

The seller of the option receives the dividend despite not owning the stocks anymore

Question 21

European option v. American option

Answer 21

Value (American) > Value (European)

American Option: Can be exercised at any time (including) expiry date
European Option: Can be exercise only on the expiry date

Question 22

What is the minimum value of a call option

Answer 22

Min C = Max [S - (X/(1+r)), 0] because S - (X/(1+r)) is what will be received today.
However, a call does not require such an irrevocable declaration, and it is therefore worth more than the minimum value shown here.

Question 23

What is the value of a call option on the expiry date.

Answer 23

Call value = Max [S * – X, 0]

Any other value would create an arbitrage opportunity

For example, if the 0 < call value at expiry < S*-X . Buy call >Exercise Option (buy asset) > Sell asset and it will be greater than the price of the call that you purchased!

Question 24

What is the value of a put option on the expiry date. (CHECK)

Answer 24

Put value = Max [X - S*, 0]

Any other value would create an arbitrage opportunity

For example, if the 0 < put value at expiry < X - S*. Buy put > Buy Asset > Exercise option (sell asset) and it will be greater than the price of the put and asset that you purchased!

Question 25

Should an American call option be exercised early?

Answer 25

No. Lose the Time Value of the option.

S - (X/1+r) > S - X

Question 26

When should an American call option be exercised early?

Answer 26

It should be exercised before the ex-dividend date if the benefits of receiving the dividend outweighs the cost of losing the time value of option.

Question 27

Should an American put option be exercised early?

Answer 27

May be optimal for deep-in-the-money put options.

Exercise price received early. By not exercising early, the option holder is incurring the opportunity cost associated with not being able to generate a return from the proceeds received.