A non-dividend stock trades at $S_0 = 8$, the continuously compounded risk-free rate is $2\%$, and bonds paying $1$ at $T = 1$ are available. European puts expiring at $T$ trade as follows: | Strike | 15 | 10 | 5 | |---|---|---|---| | Put price | 5.6 | 3.2 | 0.4 | Find the fair value today of a European call with strike $10$ and the same expiry, to two decimals.

Call value recovered from a put via parity

Question

A non-dividend stock trades at $S_0 = 8$ , the continuously compounded risk-free rate is $2\%$ , and bonds paying $1$ at $T = 1$ are available. European puts expiring at $T$ trade as follows:

Strike	15	10	5
Put price	5.6	3.2	0.4

Find the fair value today of a European call with strike $10$ and the same expiry, to two decimals.

Short answer

$1.40$ . Put-call parity: a call is a long put plus a long share minus $K$ zero-coupon bonds, since both sides pay $\max(S_T,K) - K$ at expiry. So $C = 3.2 + 8 - 10e^{-0.02} \approx 11.2 - 9.802 = 1.40$ .

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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