Chapter 10 - Characteristics of derivative securities Flashcards
Derivative
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.
Option
def: gives the investor the right, but not the obligation, to buy or sell a specified asset on a specified future date.
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holder is not obliged to pay
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the writer is obliged to trade if the holder of the option wants to
Call vs Put option
CALL: gives the right, but not the obligation, to BUY a specified asset on a set date in the future for a specified price
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PUT: gives the right, but not the obligation, to SELL a specified asset on a set date in the future for a specified price
European vs American option
EURO: option that can only be exercised AT EXPIRY
AMERICAN: option that can be exercised ON ANY DATE BEFORE ITS EXPIRY
Long vs Short position
LONG: contract has been PURCHASED
SHORT: contract has been SOLD
Arbitrage opportunity
def: situation where we can make a certain profit with no risk
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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
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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
Principle of no arbitrage & law of one price
PONA: arbitrage opportunities do not exist
LOP: 2 securities or combo of securities that give exactly the same payments must have the same price
Notation (preliminary concepts)
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
Give the -the-money characteristics of a CALL option
- in-the-money: St>K
- out-of-the-money: St<K
- at-the-money: St=K
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payoff: f(ST)=max{ST-K,0} at time T
Give the -the-money characteristics of a PUT option
- in-the-money: St<K
- out-of-the-money: St>K
- at-the-money: St=K
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payoff: f(ST)=max{K-ST,0} at time T
Intrinsic value
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}
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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
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time value or option value = Current price of option - instrinsic value
6 Factors affecting option prices
- underlying share price (St)
- strike price (K)
*time to expiry (t-T) - volatility of the underlying share(σ)
- rf interest rate (r)
- dividend (d)
What impact does the underlying share price have on a call & put option?
CALL: higher share price means higher intrinsic value = higher premium
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PUT: higher share price means lower intrinsic value = lower premium
What impact does the strike price have on a call & put option?
CALL: higher strike price means lower intrinsic value = lower premium
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PUT: higher strike price means higher intrinsic value = higher premium
What impact does the time-to-expiry have on a call & put option?
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.
What impact does the volatility of the underlying share have on a call & put option?
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.
What impact does the rf interest rate have on a call & put option?
CALL: increase in rf rate means higher value
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PUT: higher interest = lower value
What impact does the income received on the underlying security have on a call & put option?
CALL: higher income = lower value of option
PUT: higher income = higher value of option
pg 15- 22*****
Bounds for option prices
St >= ct >= max {St-Ke^-r(T-t), 0)
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St>= Ct >= max {St-Ke^-r(T-t), 0)
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Ke^-r(T-t) >= pt >= max {Ke^-r(T-t) -St, 0}
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K >= Pt >= max {K - St, 0}
Put-call parity
ct + Ke^-r(T-t) = pt + St*e^-q(T-t)
where q is the dividend rate
portfolios for put-call on pg 30**
