1

If an American call option and an American put option both have the same strike price K and expire at time T, with no dividends, how can we find a relationship between their prices? I get that if they are both held till expiry, we can use the put-call parity for European options, but if they aren't, how can we use the arbitrage argument to find the relationship between their prices? I am not sure why they will not have the same price

amalia peters
  • 21
  • 1
    Hint: write European put-call parity as $c_t - p_t= S_t - KB(t,T)$. Now use the fact that American call options that don't pay dividends are not exercised early (so $C_t =c_t$) and that American put options have extra optionality (i.e. $P_t \geq p_t$). – Jose Avilez May 14 '21 at 00:18
  • "I am not sure why they will not have the same price". Intuitively, for the options to have the same price, the professional analysts who are pricing the options would have to conclude that the potential profit from the stock price rising equals the potential profit from the stock price falling. In (for examples) either a bull market or a bear market, such a conclusion is probably wrong. – user2661923 May 14 '21 at 02:21

0 Answers0