Question

Explain why the arguments leading to put−call parity for European options cannot be used to give a similar result for American options.

Answer 1

Arguments leading to put call parity of European options cannot be used to give a similar result for American options because American options are known for early exercise so they will cause departure in the present value of two portfolios and hence the put call parity would not hold.

American options need to have expiry on maturity in order to sustain with the theory of put call parity.

European option only allow exercise at the time of maturity so they will truly reflect the put call parity.