Hello guys. Help me solve these out.

Question 1 The market price of a security can be modelled by assuming that it will either increase by 12% or decrease by 15% each month, independently of the price movement in other months. No dividends are payable during the next two months. The continuously-compounded monthly risk-free rate of interest is 1%. The current market price of the security is 127 . (i) Use the binomial model to calculate the value of a two-month European put option on the security with a strike price of 125. [3] (ii) Calculate the value of a two-month American put option on the same security with the same strike price. [3] (iii) Calculate the value of a two-month American call option on the same security with the same strike price. [2] [Total 8]Question 2 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 by 2%, or decreases by 1% You may assume that the force of interest is o = 5.5% pa and that there are 365 days in a year. No dividends are to be paid over the next five days. (i) Calculate the risk-neutral probability of an up-step on any given day. [2] (ii) 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: max . $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 5-day special option (strike price K = 1.065, ) on f10,000 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. [3] [Total 14]