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Bounds and Option Values

 

Option

Minimum Value

Maximum Value

European call (c)

ct ≥ Max(0,St-(X/(1+RFR)t)

St

American Call (C)

Ct ≥ Max(0, St-(X/(1+RFR)t)

St

European put (p)

pt ≥Max(0,(X/(1+RFR)t)-St)

X/(1+RFR)t

American put (P)

Pt ≥ Max(0, (X-St))

X

Where t is the time to expiration

 

Example

If a European call option is written on a dividend paying stock, an increase in which of the following will not automatically result in an increased option price?

  1. The stock price
  2. The risk-free rate
  3. The time to expiration
  4. The volatility of the stock price
     
Solution

C.
The time to expiration
 

 

 

 





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