5.

**Theorem 8.4: If the market has no arbitrage opportunities, then the price of any derivative that can be replicated with traded assets such as stock and cash, is the discounted expected payoff of the derivative in the risk-neutral world.

A stock is currently priced at $25. In 6 months it will be either $26 or $30. The risk-free rate is 12% per annum with continuous compound- ing. (a) Verify the assumption on u and d given following Theorem 8.4. (b) What is the price of a European put option expiring in 6 months with strike price $28 (c) If your portfolio is long this European put, how many stocks should your portfolio have to be risk-free? A stock is currently priced at $25. In 6 months it will be either $26 or $30. The risk-free rate is 12% per annum with continuous compound- ing. (a) Verify the assumption on u and d given following Theorem 8.4. (b) What is the price of a European put option expiring in 6 months with strike price $28 (c) If your portfolio is long this European put, how many stocks should your portfolio have to be risk-free