1- Consider a European call option on a non-dividend-paying stock where the stock price is $50, the strike price is $50, the risk-free rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Calculate u, d, a and p for a two-step tree. [Use 4 decimal places in your calculations.] Value the option using a two-step tree. [Give your final answer to 2 decimal places.] Make sure that you show or explain all calculations. Make sure you answer both parts a and b above. Make sure you complete the tree below.

Suppose that the premium on a European put option, p = $3. The time to maturity, T = 1 year. The strike price is $20. The stock price of the underlying common stock is $12 today. The risk-free interest rate is 8% per annum. The stock does not pay dividends.Observe that there is an arbitrage opportunity.Clearly state what the trader would do to make a profit. Make sure that you demonstrate the relation that must be satisfied to eliminate the arbitrage opportunity.