Call price from a put via put-call parity

Question

A stock trades at $8$ . Interest is $2\%$ per year, continuously compounded, and a bond pays $1$ at $T=1$ . European puts expiring at $T$ are quoted at these prices: strike $5$ at $0.4$ , strike $10$ at $3.2$ and strike $15$ at $5.6$ . What is the time- $0$ value of a European call struck at $10$ ? Round to two decimals.

Short answer

$1.40$ . A call's payoff equals one share plus the put's payoff minus a fixed $K$ , i.e. $(S_T-K)^+=S_T+(K-S_T)^+-K$ . So the call is worth $8+3.2-10e^{-0.02}\approx1.40$ ; only the strike- $10$ put is needed.

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

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