An American-style call option with six months to maturity has a strike price of $41. The underlying stock now sells for $50. The call premium is $14 and the interest rate is 10%. What is the time value of the call?

Question

BlackTom AI · Accepted Answer

First, let's restate the problem: an American-style call with six months to maturity has strike K = 41, underlying price S = 50, premium (price) = 14, and the interest rate is 10%. We are asked for the time value.

Time value of a call option is defined as the option premium minus its intrinsic value: Time value = Premium - Intrinsic value.

Compute the intrinsic value: for a call, Intrinsic value = max(S - K, 0) = max(50 - 41, 0) = 9.

Now subtract to find the time value: Time value = Premium - Intrinsic value = 14 - 9 = 5.

Another way to think about it is that the premium consists of intrinsic value (the immediate exercise value if you exercise now) plus time value (the value of potential upside and volatility over the remaining time to maturity). Here, the intrinsic value is 9, so the remaining 5 is the time value.

Note on whether the option is American or European: for an in-the-money call on a non-dividend-paying stock, early exercise is typically not optimal, so the premium largely reflects time value in addition to intrinsic value; this aligns with the calculation above.

Since the provided options list only a single choice and it states the time value as $5, this matches the computed time value. The essential check is ensuring we correctly separate premium into intrinsic value and time value, which we did.

An American-style call option with six months to maturity has a strike price of $41. The underlying stock now sells for $50. The call premium is $14 and the interest rate is 10%. What is the time value of the call?单项选择题

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