Part 1:
1. The Citco's current stock price is $35 at t=0. At the end of the year (t=1), the stock price is expected to either increase to $40 or decrease to $30. The risk-free rate is 6% per annum with continuous compounding. What is the value of an one-year European put option with a strike price of $33? Use the one-step binomial tree.
2. A stock price is $100 now and will be either $108 or $93 in a year. The risk-free rate is 8% per annum with continuous compounding. Using the risk-neutral valuation, find the price of its one-year European call option with a strike price of $102.
3. A stock price is currently $55. The stock price is expected to increase by 20% or decrease by 15% every year. The risk-free rate is 7% per annum with continuous compounding. Using the two-step binomial tree, find the price of its two-year European call option with a strike price of $59.
4. A stock price is currently $80. The stock price is expected to increase by 20% or decrease by 30% every year. The risk-free rate is 9% per annum with continuous compounding. Using the two-step binomial tree, find the price of its two-year American put option with a strike price of $75.
Part 2:
1. If the volatility per annum is 35%, what is the volatility per trading day based on the 252-trading day formula?
2. Find the price of a six month European call option on a non-dividend-paying stock with a strike price of $20 when the current stock price is $18, the risk-free rate is 6% per annum, and the volatility (sigma) is 30% per annum. Use the Black-Scholes-Merton model and the standard normal distribution table on page 590 and 591.
3. Explain the implied volatility.