Topic 5/6 - Options

Question 1

If
S = 100 , X = 101
and the call premium is
C = 6
what is the time value of the
call option?

Answer 1

C = TV+IV
the call is out the money so IV = 0
C = TV
=6

Question 2

How do you close an open long position in a put option contract before expiry?

Answer 2

Take an opposite position in an identical contract (sell an id

Question 2

If
S = 102, X = 101
and the put premium is
P = 4
, what is the time value of the
put option?

Question 3

If
S = 100 , X = 120
what is the intrinsic value of a call option?

Question 4

Draw, label and explain a diagram showing the pay-off at the expiry of a long call
option.

Answer 4

The limited loss is the premium paid to the short call. After this point the line remains horizontal in the negatives as the share price doesn’t rise to the strike price.
This is out of the money

Losses are incurred until the long call slopes upwards. Price is increasing at this point

Where it crosses the x-axis this is the breakeven point (at the money).

After this point the price increases and the profits for the long is unlimited

Question 5

Draw label and explain a diagram showing the pay-off at expiry for a short put
option.

Question 6

If the price of stock A varies more than the price of stock B, explain whether the call option on stock A has a higher or lower premium than the call option for stock B, other things being equal.

Answer 6

The options are the same except that the price of stock A has greater variability.
Call options on A and B therefore have zero exercise value for any value of the stock price below the exercise price X.

There is a greater probability of having S>X for stock A than for stock B, so there is a greater chance stock A will expire in the money.
The call option on A is therefore more valuable and has the higher premium

Question 7

Explain why a put option would not be exercised at expiry if X < S.

Answer 7

The put option is a contract in which the holder of the long position has the right to sell the asset at the exercise price, X.
The option would not be exercised if the spot price, S, were higher than the exercise price because it would be more profitable to sell the asset on the spot market

Question 8

The time value of a call option

Answer 8

The value of an option before expiry consists of time value (TV) + intrinsic value (IV).
Intrinsic value = difference between the exercise price and the asset price.
Time value = value that accrues to the option as a result other being a possibility of a favourable change in the price of the underlying asset

Time value is the distance between the dashed line and the profit and loss at expiry diagram

Question 9

The intrinsic value of a call option

Answer 9

It reflects the value of the option when exercised.
The holder of the call option will only exercise if the exercise prise is less than the current market price.
The total value of the option is time value +intrinsic value (C=TV+IV), where the intrinsic value is max (0, S-X).

Question 10

The Vega of a call option

Question 11

Show how to create a synthetic stock position, using put and call options

Question 12

Construct a pay-off table for a butterfly spread formed from call options. Assume that
X2 = 0.5(X1 + X3 )
and show that the maximum loss to this portfolio is the
net option premium.

Question 13

What is the buyer of an option?

Answer 13

they hold a long position, have the right to exercise the option. They pay a price called a premium

Question 14

What is the seller of an option

Answer 14

The seller of an option holds the short position.

They have an obligation to trade the underlying asset if the option is excercised.

They are pid the premium

Question 15

Compare options to futures/forwards

Answer 15

In options, only the short has the obligation to trade, the long has the choice. This compares with F/F where both parties have the obligation to trade.

premium vs no premium

Question 16

Hedging and options/ FF contracts

Answer 16

Options provide insurance by allowing investors to both protect themselves against price uncertainty but also gain from advantageous movements in price.

This compares with F/F, where forwards are used to deal with future uncertainty by fixing the price for the underlying asset for the hedger.

Question 17

Speculation and options / FF contracts

Answer 17

With options, the loss is limited to the premium paid for the option.

This compares with forwards where the potential loss and gain can be large.

Question 18

Put options

Answer 18

Give the holder the right to sell the underlying asset at the exercise (strike) price

Question 19

Call option

Answer 19

Give the holder the right to buy the underlying asset as the exercise (strike) price

Question 20

Long call

Answer 20

Bought the option to buy the underlying asset at an agreed price

Question 21

Short call

Answer 21

Sold the right to buy an option at an agreed price

Question 22

Long put

Answer 22

Bought the option to sell the underlying asset at an agreed price

Question 23

Short put

Answer 23

Sold the option to sell the underlying asset at an agreed price

Question 24

What position does the writer of the option have?

Answer 24

Short position.

They have an obligation to buy the asset if a put is exercised.

They have an obligation to sell the asset if a call option is exercised