A common source of confusion in option pricing is the following result:

An American call option on a non dividend paying stock should not be exercised before maturity when interest rates are positive.

At first glance, this feels counterintuitive. The American feature allows early exercise, so it is natural to ask why a rational investor would never use this flexibility.

To understand the answer properly, we must examine early exercise from multiple complementary angles: intuition, financing logic, payoff dominance, time value, and trading alternatives.

Throughout this discussion, we assume:

• The option is an American call
• The underlying stock pays no dividends
• The risk free interest rate is positive
• The option is in the money

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What early exercise actually does

When you exercise a call option early:

• You pay the strike price X immediately
• You receive the stock immediately
• The option ceases to exist

This last point is critical. Once exercised, you lose all remaining flexibility. The option no longer protects you against downside risk, and it no longer benefits from uncertainty or volatility.

So early exercise is not simply about locking in a positive payoff. It is about giving up optionality in exchange for ownership of the stock.

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Scenario based intuition

Let us now examine the main price scenarios students typically think about.

Scenario 1: You believe the stock price has peaked and will remain constant

Suppose the current stock price is S, and you believe it will remain at S until maturity.

If you exercise today, you pay X today and receive a stock worth S.
If you wait until maturity, you pay the same X and receive the same stock worth S.

The payoff is identical.

However, interest rates are positive. Paying X today means you forgo the interest you could have earned on X until maturity. Since the payoff is the same but the cost is higher, early exercise is strictly worse.

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Scenario 2: You believe the stock price will increase further

If you expect the stock price to rise, waiting becomes even more attractive.

By not exercising:

• You benefit fully from the upside
• You do not commit X early
• You retain protection in case the stock unexpectedly falls

One might argue that exercising early and holding the stock would also allow you to benefit from the increase. That is true. But you still paid X earlier than necessary.

The logic from the first scenario still applies. Why pay X today if you can pay the same X later and obtain the same asset? Early exercise again destroys value.

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Scenario 3: You believe the stock price will fall

This is the scenario that causes the most discomfort.

If you believe the stock has peaked and will now decline, exercising early means buying a stock you expect to lose value. That is clearly not optimal.

Instead, you can:

• Keep the call option unexercised
• Short the stock if you want to express a bearish view

If the stock falls below X, you allow the option to expire worthless and profit from the short position.
If the stock rises instead, the call option limits your loss.

Crucially, this strategy can be implemented with a European call as well. The American feature provides no additional benefit here. Early exercise is unnecessary.

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A dominance argument using portfolios

Now consider the problem more formally.

Compare two positions before maturity:

Position A

• Hold the American call option

Position B

• Exercise the call immediately
• Hold the stock
• Finance the purchase by paying X today

Position A dominates Position B:

• Both have upside exposure
• Only Position A has downside protection
• Position A does not require early payment of X
• Position A retains flexibility

Since the exercised position is dominated in all states of the world, exercising early cannot be optimal.

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Time value is the central argument

Before maturity, an option consists of:

• Intrinsic value
• Time value

The time value reflects uncertainty, volatility, and flexibility. For a non dividend paying stock, this time value is strictly positive prior to maturity.

When you exercise early:

• You receive only intrinsic value
• You permanently destroy the time value

Instead of exercising, you can always sell the option in the market for more than its intrinsic value. From an economic standpoint, exercising early is inferior to selling the option.

This point alone is sufficient to rule out early exercise.

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The role of positive interest rates

Positive interest rates strengthen all the arguments above.

Holding the option allows you to delay the payment of X until maturity. Delaying a payment has real economic value when interest rates are positive.

Early exercise forces you to give up this benefit without receiving any compensation.

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Implication for American versus European calls

Since early exercise is never optimal under these assumptions:

• The early exercise feature has zero value
• The American call and European call have the same price
• The optimal exercise policy is to wait until maturity

This equivalence breaks down only when dividends are introduced, because dividends reward stock ownership rather than option holding.

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Final takeaway

Early exercise of an American call option on a non dividend paying stock is never optimal when interest rates are positive.

This is not because of a specific belief about future prices, but because early exercise:

• Forces premature payment of the strike
• Destroys time value
• Produces a dominated payoff relative to holding the option
• Can always be improved upon by selling the option instead

Understanding this result is essential for mastering option pricing and for appreciating the economic role of optionality itself.