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Forward price with a cash dividend

MediumFinance & Derivatives~4m

A stock trades at $100 and will pay a $2 cash dividend in 6 months. The risk-free rate is 5% per year, continuously compounded. What is the no-arbitrage price of a 1-year forward on the stock? (in dollars, to 2 decimals)

Show hints (2)+
  1. The forward holder doesn't get the dividend: use S0−PV(div)S_0 - PV(\text{div}) as the effective spot.
  2. F=(100−2e−0.025) e0.05F = (100 - 2e^{-0.025})\,e^{0.05}.

Answer

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103.08 (± 0.02)

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