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Derivatives, Am I right?

Is it correct?

Call 

  • no cash flows: Pa=Pe
  • cash flows: Pa>Pe

Put

  • no cash flows:Pa>Pe
  • cash flows:Pa>Pe

Pa-price of american option Pe- price of european o

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Are you asking about lower bounds? Just remember that European option can not be exercised early whilst American can

for Calls Amercian and European C = max(0; S-X/(1+Rf)n) A>=E American is worth al leat as European calls

 for Puts European can not be excercise early P= (max0.X/(1+Rf)n)

american P=max(0. X-S) A>E  due to immediate execution  value is a bit different