Forward price with one cash dividend mid-year

Question

A stock trades at $1$ . The continuously compounded interest rate is $5\%$ , and a dividend of $0.10$ will be paid in six months. What is the fair price for one-year forward delivery?

Short answer

About $0.949$ . Subtract the present value of the dividend and grow the rest at the risk-free rate: $F=(1-0.1e^{-0.025})e^{0.05}=e^{0.05}-0.1e^{0.025}\approx0.9487$ .

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.24, p.18; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Forward and Futures Prices: Cost-of-Carry, Known Income, and Continuous Yields

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