Intrinsic and time value of an ITM call

Question

A stock trades at $5$ . A European call on it with strike $2$ is priced at $4.7$ . Writing $I$ for intrinsic value and $E$ for extrinsic value, compute $I^2+E^2$ .

Short answer

$11.89$ . Immediate exercise would pay $5-2=3$ , so $I=3$ and the remaining $E=4.7-3=1.7$ is time value; $9+2.89=11.89$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Market Model and Risk-Neutral Valuation
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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