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Silver Mine
Current price of silver is 900 €/kg. Suppose that one year from now it can be 1200, 1000 or 800€ /kg, with equal probabilities. We are considering an investment in a silver mine. Our best assessment regarding possible payoffs from this investment one year from now are 200, 140 and 100 million euros, depending on the price of silver. At the same time, a one-year risk-free discount bond with a face value of 1000€ currently trades at 960€, and a one-year European call option with a strike price of 1000 e/kg currently trades at 36 €/kg.
What should be the fair value of the mine? (Hint: Consider what are the possible payoffs for all the assets at t = 1.)
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