A stock price is currently $41. At the end of three months, it will be either $45 or $36. The risk free interest rate is 7% with continuous compounding.

a) Use the no-arbitrage binomial method to calculate the value of a 3-month European call option on the stock with strike price $42. Determine delta to create a risk free portfolio of options and shares; find the value of this portfolio after three months and discount it to determine the option value today.

b) Calculate the same option value using the risk-neutral-method. Calculate the risk neutral probability of the stock price going up; use it to calculate the expected value of the option after three months; discount it to get the option value today.