Consider the following binomial option pricing problem involving European options. Price a call option that has six months to go before expiring. The underlying has a price is 50 and the call option strike price is 60. The annualized risk-free rate is 5%. Every three months, the value of the stock can either increase by 20% or decrease by 20%. Use a two-step binomial tree (each step is six months)

Now price the same Call option of part 1 using the Black-Scholes model. The annualized volatility of the underling is 38%.

Now say that you have a put option with a strike of 70 on a stock whose price today is 65. The option has maturity of 9 months and it is worth 10.8 dollars. Compute the implied volatility.