Question

The 2 questions I struggle with are the following:

True or false? Please justify and explain your answer.

1. Since the theta of a European call option on a non-dividend paying underlying stock is negative, the value of such an option is expected to decrease, on average, over time.

2. We cannot use a European option pricing formulas to price an American put option on a non-dividend-paying stock.

Thanks a lot in advance.

Answer 1

1. True. Theta is a measure of sensitivity of option price with respect to time. Theta of call option is alsways negative as the option loses value with time and time only flows in one direction. Thus, with time the value of an option is expected to decrease.

2. True. An American option is like a European option, with the only difference being that it can be exercised early too. This right is not present in European options which can only be exercised at maturity. Early exercise of a call option in case of non dividend paying stock would have no extra value. Thus, for call options, American and European options price would be same. But for put options, early exercise will give immediate cash inflow to the holder and these proceeds can then be invested. For deep in the money put options this can be extremely beneficial. Black scholes can be applied to non dividend paying stock for call options but not put options.

Comment in case of any query.