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BLB 300 > Ch 10 - Properties of Stock Options > Flashcards

Ch 10 - Properties of Stock Options Flashcards

The factors affecting stock option prices

1
Q

Name the FIRST 3 of the total 6 factors affecting stock option prices.

A
  1. S0 - the current stock price
  2. K - the strike price
  3. T - the time to expiration
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2
Q

Name the LAST 3 of the total 6 factors affecting stock option prices.

A
  1. Theta - the volatility of the stock price
  2. r - the risk-free interest rate
  3. The dividends expected to be paid
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3
Q

What is the difference between Futures and Options contracts with regards to price?

A

Forwards/Futures contract parties agree to a fixed price to be paid at some point in the future = FUTURES PRICE

The fixed price of a call or option holder for the underlying is the EXERCISE PRICE / STRIKE PRICE

Futures price obligated to be paid. Strike price is at the discretion of the option holder.

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4
Q

What is the difference between Futures and Options contracts with regards to value of the contract at inception?

A

Future/Forward contract has zero value at inception
Value changes positively/negatively over the life of the contract - depends on changes in rates and prices

Option has positive value at inception.
Buyer must pay for the option which the seller receives i.e. the OPTION PREMIUM

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5
Q

What is the payoff of an exercised call option?

A

Payoff = stock price - strike price = amount stock price greater than strike

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6
Q

How does the value of a call increase/decrease?

A

Call options become:

  • more valuable as stock price increases
  • less valuable as stock price decreases
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7
Q

What is the payoff of an exercised put option?

A

Payoff = Strike price - stock price = amount strike greater than stock

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8
Q

How does the value of a put increase/decrease?

A

Put options become:

  • less valuable as stock price increases
  • more valuable as stock price decreases
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9
Q

How does the length of the time to expiration change the price of an American Option?

A

The longer the time to expiration the more expensive the option

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10
Q

How does the length of the time to expiration change the price of an European Option?

A

Can only be exercised at maturity,
GENERALLY become more expensive as time to expiration increases
EXCEPTIONS:
- expiration date ex dividend payout date

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11
Q

How does volatility affect call options?

A

Since volatility increases the chances of doing very well or very poorly, a call option holder will benefit from the price increases and has a limited downside from price decreases. Hence the price increases.

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12
Q

How does volatility affect put options?

A

Since volatility increases the chances of doing very well or very poorly, a put option holder will benefit from the price decreases and has a limited downside from price increases. Hence the price increases.

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13
Q

How does the RFR affect option pricing?

A
  • Investors req. return increases as RFR increases
  • PV of future cash flow rec. by holder decreases
    Result: Increases the value of call options and decrease the value of put options
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14
Q

Why does a higher RFR affect puts negatively?

A

Holder has share but misses out on higher RFR investment until exercise

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15
Q

Why does a higher RFR affect calls positively?

A

Holder has the cash not the share so can invest cash at higher rate

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16
Q

What variables does the RFR affect and how?

A

It affects the stock price inversely; RFR increase –> S decrease and vice versa
Also affects option price directly

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17
Q

What is the net effect of an RFR increase/decrease on option prices?

A

RFR increase –> S decrease –> decrease Call & increase Put

RFR decrease –> S increase –> increase Call & decrease Put

18
Q

How do dividends affect option prices?

A

Div payout –> decrease S
Hence:
Call decrease
Put increase

19
Q

Why does early exercise of an American put become more attractive as the RFR increases and volatility decreases?

A

The early exercise of an American put is attractive when the interest eearned on the strike price is greater than the insurance element lost.
Interest rates increase –> interest earned on strike price increases —> more attractive
Volatility decreases –> insurance element is less valuable —> more attractive

20
Q

Why is early exercise of an American call option never optimal?

A

Delaying exercise means holder able to earn interest (on strike price) for longer (TVM)
Delay provides insurance against stock price falling lower than strike price by expiration date.

Assume holder has K cash and that interest rates are zero.
Early exercise means holder’s position worth St at expiration.
Delaying means position is max(K, St) at expiration.

21
Q

Why is it important that options are not priced above their upper bound or below their lower bounds?

A

Above upper bound or below lower bound means arbitration possible

22
Q

What can a call option never be worth more than?

A

The stock i.e. the underlying

23
Q

What is the upper bound for call options and why?

A

The stock price, S0.

You will not pay more for the right to buy than what the stock price is worth at that point in time?

24
Q

What is the upper bound for an American put option and why?

A

K, the strike/exercise price

You will not pay more for the right to sell than the amount that you call sell the share for.

25
Q

What is the upper bound for an European put option and why?

A

Ke^(-rT), the present value of the strike/exercise price

You will not pay more for the right to sell than the amount that you call sell the share for at maturity.

26
Q

What is the formula for the lower bound for the price of a European call option on a non-dividend-paying stock?

A

S0 - Ke^(-rT)

27
Q

What is the formula for the lower bound for put option on a non-dividend-paying stock?

A

Ke^(-rT) - S0

28
Q

What is the value of a European call at maturity?

A

c >= max[ S0 - Ke^(-rT), 0 ]

29
Q

What is the value of a European put at maturity?

A

p >= max[ Ke^(-rT) - S0, 0 ]

30
Q

Should American puts be exercised early? Why?

A

If it is sufficiently deep in the money, always.

It becomes more attractive as S0 decreases, as r increases, and as the volatility decreases.

31
Q

Portfolio A:
- call option and zero coupon bond
Portfolio B:
- put option and share

What are they worth at maturity?

A

They are both worth max (St, K) at maturity, since:

Portfolio A :
Call option max (St - K, 0)
Zero-coupon bond max (K, K)
TOTAL max (St, K)

Portfolio C :
Put option max (K - St, 0)
Share max (St, St)
TOTAL max (St, K)

32
Q

Give the put-call parity relationship (no divs).

A

c + Ke^(-rT) = p + S0

where:
c = S - K
p = K - S

33
Q

Give the put-call parity relationship of American option prices (assuming no dividends).

A

S0 - K <= C - P <= S0 - Ke^(-rT)

34
Q

What are the reasons for not exercising an American call early (no divs)?

A
  • No income is sacrificed (divs)
  • You delay paying the strike price
  • Holding the call provides insurance against the stock falling below strike price
35
Q

Would you exercise an American call early if the stock is overpriced and you could exercise the option to sell the stock?

A

No, since;

  • Better to sell the option than to exercise early
  • Price obtained for the option will be greater than its intrinsic value (overpriced)
36
Q

Give the general formula for an European call on dividend paying stock.

A

c >= S0 - D - Ke^(-rT)

37
Q

Give the general formula for an European put on a dividend paying stock.

A

p >= D + Ke^(-rt) - S0

38
Q

What is the effect of dividends on European call option prices?

A

Divs decrease the call option price

39
Q

What is the effect of dividends on European put option prices?

A

Divs increase the put option price

40
Q

Is it optimal to exercise an American call option early on a dividend paying stock?

Is it optimal to exercise early at any other time?

A

It is if it is exercised immediately prior to its ex-dividend date
(since dividend will decrease the stock price —> decrease call value)

It is not optimal to exercise early at any other time

41
Q

Give the put-call parity relationship (with divs).

A

c + D + Ke^(-rT) = p + S0

where:
c = S - K
p = K - S

42
Q

Give the put-call parity relationship of American option prices (with dividends).

A

S0 - D - K <= C - P <= S0 - Ke^(-rT)

BLB 300 (16 decks)

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