Chapter 10 - Characteristics of derivative securities

Question 1

Derivative

Answer 1

def: security or contract which promises to make a payment at a specified time in the future, the amount of which depends upon the behaviour of some underlying (an asset) security up to & including the time of payment.

Question 2

Option

Answer 2

def: gives the investor the right, but not the obligation, to buy or sell a specified asset on a specified future date.
__
holder is not obliged to pay
__
the writer is obliged to trade if the holder of the option wants to

Question 3

Call vs Put option

Answer 3

CALL: gives the right, but not the obligation, to BUY a specified asset on a set date in the future for a specified price
_
PUT: gives the right, but not the obligation, to SELL a specified asset on a set date in the future for a specified price

Question 4

European vs American option

Answer 4

EURO: option that can only be exercised AT EXPIRY
AMERICAN: option that can be exercised ON ANY DATE BEFORE ITS EXPIRY

Question 5

Long vs Short position

Answer 5

LONG: contract has been PURCHASED
SHORT: contract has been SOLD

Question 6

Arbitrage opportunity

Answer 6

def: situation where we can make a certain profit with no risk
_
2 conditions:
i) start at 0 with a portfolio that has a net value of 0 (ZERO-COST PORTFOLIO)
ii) at some future time T:
-P(loss) = 0
-P(profit) > 0
__
the problem if an opportunity like this existed then all active market participants would do the same & market prices would quickly change to remove the arbitrage opportunity

Question 7

Principle of no arbitrage & law of one price

Answer 7

PONA: arbitrage opportunities do not exist
LOP: 2 securities or combo of securities that give exactly the same payments must have the same price

Question 8

Notation (preliminary concepts)

Answer 8

t - current time
St - underlying share price at time t
K - strike or exercise price
T - option expiry date
ct - price of Euro call option
pt - price of Euro put option
Ct - price of American call option
Pt - price of American put option
r - rf continuously compounding rate of interest

Question 9

Give the -the-money characteristics of a CALL option

Answer 9

• in-the-money: St>K
• out-of-the-money: St<K
• at-the-money: St=K
  _
  payoff: f(ST)=max{ST-K,0} at time T

Question 10

Give the -the-money characteristics of a PUT option

Answer 10

• in-the-money: St<K
• out-of-the-money: St>K
• at-the-money: St=K
  _
  payoff: f(ST)=max{K-ST,0} at time T

Question 11

Intrinsic value

Answer 11

def: value assuming expiry of the contract immediately rather than at some time in the future.
-> call option: max{St-K,0}
-> put option: max{K-St,0}
__
intrinsic value of an option is:
- positive if it’s in-the-money
- zero if it’s at-the-money
-zero if it’s out-of-the-money
__
time value or option value = Current price of option - instrinsic value

Question 12

6 Factors affecting option prices

Answer 12

• underlying share price (St)
• strike price (K)
  *time to expiry (t-T)
• volatility of the underlying share(σ)
• rf interest rate (r)
• dividend (d)

Question 13

What impact does the underlying share price have on a call & put option?

Answer 13

CALL: higher share price means higher intrinsic value = higher premium
_
PUT: higher share price means lower intrinsic value = lower premium

Question 14

What impact does the strike price have on a call & put option?

Answer 14

CALL: higher strike price means lower intrinsic value = lower premium
_
PUT: higher strike price means higher intrinsic value = higher premium

Question 15

What impact does the time-to-expiry have on a call & put option?

Answer 15

The longer the time-to-expiry, the greater the chance that the underlying share price can move significantly in favour of the holder of the option before expiry.

Question 16

What impact does the volatility of the underlying share have on a call & put option?

Answer 16

The higher the volatility of the underlying share, the greater the chance that the underlying share price can move significantly in favour of the holder of the option before expiry. So the value of an option will increase with the volatility of the underlying share.

Question 17

What impact does the rf interest rate have on a call & put option?

Answer 17

CALL: increase in rf rate means higher value
_
PUT: higher interest = lower value

Question 18

What impact does the income received on the underlying security have on a call & put option?

Answer 18

CALL: higher income = lower value of option
PUT: higher income = higher value of option

Question 19

pg 15- 22*****

Question 20

Bounds for option prices

Answer 20

St >= ct >= max {St-Ke^-r(T-t), 0)
_
St>= Ct >= max {St-Ke^-r(T-t), 0)
_
Ke^-r(T-t) >= pt >= max {Ke^-r(T-t) -St, 0}
_
K >= Pt >= max {K - St, 0}

Question 21

Put-call parity

Answer 21

ct + Ke^-r(T-t) = pt + St*e^-q(T-t)
where q is the dividend rate

Question 22

portfolios for put-call on pg 30**