# 125.350 principles of option pricing

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 Author: jordan_hs ID: 224308 Filename: 125.350 principles of option pricing Updated: 2013-06-19 10:38:22 Tags: principles option pricing Folders: Description: week 3 Show Answers:

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1. Minimum value of a CALL
• For ANY call:
• C(S0,T,X) ≥ 0

• For AMERICAN calls:
• C(S0,T,X) ≥ Max(0, S0 - X)
2. Time value of an American call
Difference between the call price and the intrinsic value

Reflects what traders are willing to pay for the uncertainty of the underlying stock
3. Maximum Value of a Call
C(S0,T,X) ≤ S0

Maximum value of a call is the price of the stock
4. Value of a Call at Expiration
C(S0,T,X) = Max(0,ST-X)

At expiration, call option is worth the intrinsic value (Rule holds for both types of options)
5. Effect of Time to Expiration
Ca(S0,T2,X) ≥ Ca(S0,T1,X)

A longer-lived American call must always be worth at least as much as a short-lived American call with the same terms
6. Deep-in-the-money and deep-out-of-the-money for a CALL
Deep-in-the-money is when the stock price is very high (time-value likely low)

Deep-out-of-the-money is when the stock price is very low (time value likely high)
7. Effect of Exercise Price
Effect on Option Value
Ce(S0,T,X1) ≥ Ce(S0,T,X2)

-The price of European (and American) call must be at least as high as price of an otherwise identical European (or American) call with a higher exercise price
8. American Call versus European Call
Ca(S0,T,X) ≥ Ce(S0,T,X)

-An american call will be at least as valuable as a European call with the same value
9. Minimum Value of a Put
• FOR ANY PUT:
• P(S0,T,X) ≥ 0

• For American Put:
• Pa(S0,T,X) ≥ Max(0,X - S0)

Because a put option need not be exercised, it's minimum value is zero

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