Recovering a 10-strike call from three puts

Question

Given a stock at $8$ , a continuously compounded rate of $2\%$ , a bond paying $1$ at $T=1$ , and European puts maturing at $T$ priced as follows: $0.4$ (strike $5$ ), $3.2$ (strike $10$ ), $5.6$ (strike $15$ ). Find, to two decimals, today's price of a European call on the stock with strike $10$ and maturity $T$ .

Short answer

$1.40$ . Put–call parity reads $C=P+S_0-Ke^{-rT}$ . Using the strike- $10$ put, $C=3.2+8-10e^{-0.02}\approx1.40$ ; the other two puts are distractors.

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
No-Arbitrage Bounds and Put-Call Parity
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets

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