introduction to financial derivatives
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Introduction to Financial Derivatives. Lecture #4 on option Jinho Bae May 8, 2008. Ch 8. Option pricing models. I. Value of an option Intrinsic value Time value II. Factors that affect the price of an option. I. Value of an option. Value of an option =Option premium=Option price - PowerPoint PPT PresentationTRANSCRIPT
Introduction to Financial Derivatives
Lecture #4 on option
Jinho Bae
May 8, 2008
Ch 8. Option pricing models
I. Value of an option– Intrinsic value – Time value
II. Factors that affect the price of an option
I. Value of an option
• Value of an option =Option premium=Option price
• The price that an option holder pays to an option writer for the right to sell or buy an asset
• Value of an option= Intrinsic value + Time value
• When the spot price (S) exceeds the strike price (X)
Intrinsic value=S-X>0
e.g) Google call option with X=$460
Google share price S=$465
Intrinsic value=S-X=$5
I-1-1. Intrinsic value of a call option
Intrinsic value of a call option
• When the spot price (S) does not exceed the strike price (X)
Intrinsic value=0
e.g) Google call option with X=$460
Google share price S=$450
Intrinsic value=0
• Mathematical expression of intrinsic value of a call option
max(S-X, 0)• When S>X, S-X>0 take S-X • When S<X, S-X<0 take 0
Intrinsic value of a call option
valueIntrinsic value
X S
Intrinsic value of a call option
I-1-2. Intrinsic value of a put option
• When the strike price (X) exceeds the spot price (S)
Intrinsic value=X-S>0
e.g) Google put option with X=$460
Google share price S=$450
Intrinsic value=X-S=$10
Intrinsic value of a put option
• When the strike price (X) does not exceed the spot price (S)
Intrinsic value=0
e.g) Google call option with X=$460
Google share price S=$465
Intrinsic value=0
Intrinsic value of a put option
• Mathematical expression of intrinsic value of a put option
max(X-S, 0)• When X>S, X-S>0 take X-S• When X<S, X-S<0 take 0
Intrinsic value of a put option
value
Intrinsic value
X S
Relationship between intrinsic value and ITM, OTM, ATM
S>X
Call ITM
Intrinsic value >0
Put OTM
Intrinsic value=0
S=X
ATM
Intrinsic value=0
ATM
Intrinsic value=0
S<X
OTM
Intrinsic value=0
ITM
Intrinsic value >0
I-2. Time value of an option
• The value of an option arising from the time left to maturity
• Time value = Option premium - Intrinsic value
e.g) IBM call option with X=$100 trades at $10 IBM share price S=$106 Intrinsic value=S-X=$6 Time value= $10-$6=$4
Two elements of time value of an option
1) Time value 1: Expected payoff when holding the option until maturity
2) Time value 2: Time value associated with cash flow from selling or buying underlying asset of the option
1) Time value 1
Two scenarios of asset price movement until maturity
• Asset price moves in a favorable direction unlimited positive payoff
• Asset price moves in an unfavorable direction no or bounded loss
Expected payoff is positive.
E.g) IBM call option, X= $100, maturity=1 month
① current S=$100 (ATM)
If ST (at maturity) > $100 Payoff: ST - $100
If ST (at maturity) < $100 No loss
Expected payoff from changes in the asset price until maturity > 0
Possibilities of changes in the asset price until maturity
Price change Probability
20 increase 1/8
10 increase 2/8
0 2/8
10 decrease 2/8
20 decrease 1/8
S STProbabil
ityPayoff Expected payoff
100
1/8
2/8
2/8
2/8
1/8
② current S=$90 (OTM)
Intrinsic value=$0
If ST (at maturity) > $100 Payoff: ST - $100
If ST (at maturity) < $100 No loss
S STProbabi
lityPayoff Expected
payoff
90
1/8
2/8
2/8
2/8
1/8
Expected payoff Greater than 0. However, smaller than that for ATM. Why?
③ current S=$110 (ITM)
Intrinsic value =$10
If asset price increases above 110 Payoff increases proportionally
If asset price increases below 110, intrinsic value decreases but bounded from 10.
S STProbabil
ityPayoff Expected
payoff
110
1/8
2/8
2/8
2/8
1/8
Expected payoff Greater than 0. However, smaller than that for ATM.
Time value 1 of a call option
X SCurrent spot price
value
Time value 1
OTM ATM
Time value 1 of a put option
X SCurrent spot price
value
Time value 1
ATM OTM