125.350 principles of option pricing

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125.350 principles of option pricing
2013-06-19 06:38:22
principles option pricing

week 3
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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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