Question

Consider an American call on a non-dividend-paying stock. Which of the following is NOT true?

The value of the American call is greater than that of a comparable European call.

The holder of the American call should never exercise it early.

The value of the American call is the same as that of a comparable European call.

The holder would generate a greater payoff by selling the American call than by exercising it early.

Answer 1

When considering an American call on a non- dividend - paying stock the following quote is NOT TRUE:

The value of the American call is greater than that of a comparable European call.

In USA's derivative market the holder of the a call should ALWAYS be exercise at maturity only.

The European call CAN be excercised only on due date and American call WILL be excercised only on due date. Thus, the European call value will be Same as American call value.

The above fact will be explained through the following example:

The following facts for American call option non-dividend paying share

Facts:

Spot price = $50

Strike price =$40

Maturity period = 1 month

Interest rate = 10% p.a.

The investor has two alternatives

1. Excercise the call option spot and sell the shares at spot

2. Short sell the share at spot market and excercise the call option after one month at maturity.

Cash flow for option 1: Excercise the call option spot and sell the shares at spot:

Spot sell the share = $50

Less: Purchase by excercising call at strike price at spot = $40

Profit    = $10

Cash flow for option 2: Excercise the call option at maturity/due date and short sell the shares at spot:

Short sell the share =  $50

Less: Present value of purchase price by excercising

call at strike price at maturity    = $39.67

Profit = $10.33

Note: As per Cordinal rule in finance is to receive money as early as possible whereas payment should be made later. Thus, excercise call option at maturity/due date is making more profit than early excercise. Hence, all other given statements are true,except the value of the American call is greater than that of a comparable European call.