Refer to the attachment.

A company share price is to be modelled using a 5-step recombining binomial tree. with each step in the tree representing one day. Each day, it is assumed that the share price: increases hy 2%, or decreases by 1% You may assume that the force of interest is 8 =5.5% pa and that there are 365 days in a year. No dividends me to be paid over the next five days, Calculate the risk-neutral probability of an up-step on any given day (#i) Calculate the fair price of a 5-day at-the-money call option on $10,000 worth of shares in this company. [5] A special option is available where the payoff after 5 days is: ITHAN $5 - K.0 where S, is the arithmetic average share price recorded at the end of each of the 5 days and K is the strike price. (iii) Calculate the fair price of a 3-day special option (strike price A = 1.005, ) on [10,000 worth of shares in this company. (4] (iv) Explain whether an at-the-money special option is likely to have a higher value of vega than a standard "vanilla" call option [Toll 14]