Pricing an absolute-distance payoff around 15

Question

A stock trades at $7$ , a bond paying $1$ at $T$ costs $0.9$ , and European calls expiring at $T$ are quoted at strikes $5,10,15,20$ for $4.2,1.4,0.7,0.1$ respectively. What is the time- $0$ value of a claim paying $|S_T-15|$ at $T$ ?

Short answer

$7.9$ . The payoff is a straddle at $15$ and can be built as $15-S_T+2(S_T-15)^+$ : fifteen bonds, short one share, two $15$ -strike calls. That costs $13.5-7+1.4=7.9$ .

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

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

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

Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free