kindly answer this question precisely

Consider the following long position in European and American call options written on a stock, with strikes and times to expiry as set out in the table below. Option European/American Strike price Time to expiry American 400 3 years American 400 2 years American 420 3 years European 400 3 years European 400 2 years Rank these options in order of value to the extent that this is possible. [5] Consider the following model for the short-rate r: dr, = ur,di + odz, where u and o are fixed parameters and Z is a standard Brownian motion. Comment on the suitability of this model for the short-rate. [4] An alternative model for the short-rate is the Vasicek model: dr, = o(u - r,)di +odZ,. (ii] Derive an expression for ; rtu)du . [6] (iii) State the distribution of I, ruldu. [1] [Total 11] (i) State the equation for the capital market line in the Capital Asset Pricing Model (CAPM), defining all the terms used. [3] In a market where the CAPM is assumed to hold, the expected annual return on the market portfolio is 12%%, the variance is 4%% and the effective risk-free annual rate is 4%. An Agent wants an expected annual return of 18% on a portfolio worth (1.200,000. (ii) Calculate the standard deviation of the return on the corresponding efficient portfolio. iid Calculate the amount of money invested in each component of the Agent's portfolio. [3] [Total 8]