A stock price is currently $20 and in each of two time steps the stock price may go up by 10% or down by 10%. Each time step is 3 months long. The risk-free rate is 12% per annum with continuous compounding. (required degrees of decimal accuracy: 4 decimal places)
1.1 Plot the two-step binomial tree and describe the evolution of the stock price.

1.2 Explain briefly the idea of the no-arbitrage arguments for valuing a European option using binomial tree; and use the no-arbitrage arguments approach to determine the current price of the corresponding European call option with a strike price of $21 and time to maturity of 6 months. 

1.3 Explain briefly the three steps of the risk-neutral valuation approach for valuing a European option using binomial tree; and use the risk-neutral valuation approach to determine the current price of the corresponding European call option with a strike price of $21 and time to maturity of 6 months.
 

1.4 The binomial model is a discrete-time version of the geometric Brownian motion model, which is the basis for the Black-Scholes-Merton Model. Discuss and critically review the assumption about volatility underlying the Black-Scholes-Merton Model.