The stock trades at $S_0 = 7$. A zero-coupon bond paying $1$ at time $T$ costs $0.9$. European calls expiring at $T$ are available: | Strike | 20 | 15 | 10 | 5 | |---|---|---|---|---| | Call price | 0.1 | 0.7 | 1.4 | 4.2 | What is the fair time-$0$ value of a claim paying $\max(3S_T, 15)$ at $T$?

Replicating a floored multiple of the stock

Question

The stock trades at $S_0 = 7$ . A zero-coupon bond paying $1$ at time $T$ costs $0.9$ . European calls expiring at $T$ are available:

Strike	20	15	10	5
Call price	0.1	0.7	1.4	4.2

What is the fair time- $0$ value of a claim paying $\max(3S_T, 15)$ at $T$ ?

Short answer

$26.1$ . Write the payoff as $15 + 3\max(S_T - 5, 0)$ : it is $15$ bonds plus three $5$ -strike calls. Its value is $15(0.9) + 3(4.2) = 13.5 + 12.6 = 26.1$ .

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

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Lessons behind this question

Duration and Convexity: Measuring and Managing Interest Rate Sensitivity
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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