3. A European call option is on sales in the market in year 0. The underlying asset is now at $10. The strike price of the call is $12 and the maturity period of the call are 2 years. Risk-free rate provided in the market is 6%. The asset is either multiplied by 1.2 or 0.8 in the next year. That is, it is either $14.4, $9.6 or $6.4 in the second year. (a) In this part, we are currently in year 1. i. (3 points) If the asset has risen to the price $12, using replicating portfolio, what would be the fair price of the call option in this year? Explain explicitly how you replicate the portfolio. ii. (2 points) On the contrary, if the asset has dropped to the price $8 instead, what would be the fair price of the call option in this year? Explain this without any formula. (b) In this part, we are currently in year 0. i. (3 points) From what you have done in part (a), given that you know how the price of this underlying asset move, you should be able to realize the price of the call option in each scenario in year 1. Given that the market is efficient, so this call price exactly reveal the risk-neutral payoff of the call option. Replicate the portfolio in Year 0 explicitly and hence find the call price in year 0. 3. A European call option is on sales in the market in year 0. The underlying asset is now at $10. The strike price of the call is $12 and the maturity period of the call are 2 years. Risk-free rate provided in the market is 6%. The asset is either multiplied by 1.2 or 0.8 in the next year. That is, it is either $14.4, $9.6 or $6.4 in the second year. (a) In this part, we are currently in year 1. i. (3 points) If the asset has risen to the price $12, using replicating portfolio, what would be the fair price of the call option in this year? Explain explicitly how you replicate the portfolio. ii. (2 points) On the contrary, if the asset has dropped to the price $8 instead, what would be the fair price of the call option in this year? Explain this without any formula. (b) In this part, we are currently in year 0. i. (3 points) From what you have done in part (a), given that you know how the price of this underlying asset move, you should be able to realize the price of the call option in each scenario in year 1. Given that the market is efficient, so this call price exactly reveal the risk-neutral payoff of the call option. Replicate the portfolio in Year 0 explicitly and hence find the call price in year 0
