Forward commitment replication was shown in earlier lessons to involve borrowing at the risk-free rate to purchase the underlying in the case of a long position or selling the underlying short and lending the proceeds at the risk-free rate for a short position. We also showed that a long underlying position combined with a short…
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The time value of an option is equal to the difference between the current option price and the option’s current payoff (or exercise value): Call Option Time Value:
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An option’s exercise value at any time t was shown to be its current payoff. The relationship between the option’s total value and its exercise price expresses the option’s moneyness. Also, the degree to which an option is in or out of the money affects the sensitivity of an option’s price to underlying price changes. For example, a so-called deep-in-the-money option,…
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An option buyer will exercise a call or put option at maturity only if it returns a positive payoff—that is: If not exercised, the option expires worthless and the option buyer’s loss equals the premium paid. At any time before maturity (t < T), buyers and sellers often gauge an option’s value by comparing the underlying spot price (St )…
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The non-linear or asymmetric payoff profile of an option causes us to approach these derivative instruments differently than for a forward commitment. When evaluating these derivatives, whose value depends critically on whether the spot price crosses an exercise threshold at maturity, buyers and sellers frequently rely on three measures—exercise value, moneyness, and time value—to gauge…
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