Lower bound of options

FOR OPTIONS IN THE MONEY:
Lower bound options for American calls is the Instrinsic value:
Security Price - Strike Price = lower bound
Lower bound options for American Puts is the opposite
Strike Price - Security Price= lower bound
Lower bound options for European Calls is
Security Price - (strikeprice of call/1 + riskfree rate ^ the time of the option exp 90/360) = lower bound
Lower bound options for European Puts is the opposite
(strikeprice of call/1 + riskfree rate ^ the time of the option exp 90/360) -
Security Price = lower bound
IF THE OPTION IS OUT OF THE MONEY FOR EITHER CALL/PUT EUROPEAN/AMERICAN it’s 0
 
Honestly it’s really not the difficult. I used to struggle with this but then I saw a really good Stalla lecture slide on it and it’s not that bad. Everything is the opposite for calls and puts. Either Security price goes first or Strike price goes first. Also know that a European call/put can never be worth more than an American Call/Put. So if you calc it out at the european is worth more than the American call is worth the higher price.
Example.
European call after calculating lower bound is worth 5
American call is lower bound is worth 4.
Automatically the American call is now worth 5. Does that make sense?
 
Careful, lower bound American call = Lower bound European call
 
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