Suppose that the annual volatility () of spot silver is 20% and that we are trying to

Suppose that the annual volatility (σ) of spot silver is 20% and that we are trying to price a European call option written on silver. The spot price is $17 per ounce, the exercise price of the option is $18, and it has exactly 12 months till expiration. Silver pays no dividend and the continuously compounded risk-free rate of interest is 2% per year
a) Using time intervals of six months ( ?t = 1/2 years), construct the binomial price tree for silver for twelve months. Also calculate the risk-neutral probabilities.

b) Determine the call price today using binomial pricing. Make sure that you construct the call price tree fully. What is the risk-neutral probability, calculated at t=0, that this call option will be in the money at expiration?