Please assist me to obtain solutions for the question below

Suppose that at time / a portfolio (o, , w,) is held, where o, represents the number of units of a stock, with price S, , held at time / and y, is the number of units of a cash bond, with price B, , held at time r. The processes + and w are previsible. Let V(() =4, S, + w, B, be the value of the portfolio at time . (i) Explain what it means for this portfolio to be self-financing. [2] Consider a stock paying a continuous dividend at a rate 6 and denote its price at any time / by S, Let C, and , be the price at time ? of a European call option and European put option respectively, written on the stock S, each with strike price X and maturity Ter. The instantaneous risk-free rate is denoted by r. (ii) Prove put-call parity in this context by constructing two self-financing portfolios whose value must be equal by the principle of no arbitrage [6] [Total 8] Consider a non-dividend-paying share with price S, at time r (in years) in a market with continuously compounded risk-free rate of interest r. (i) Show that the fair price at / - 0 of a forward contract on the share maturing at time Tis K = Sperr. [5] A share is currently worth So-(20. The continuously compounded risk-froc rate of interest is 1% per annum. (ii) Calculate the fair price at / = 0 of a forward contract written on the share with delivery at / = 2. (iii) Give an expression for the value to the investor of the forward contract in part (ii) at time / 2, in terms of $, , r and r. [2] An investor enters into the above forward contract at time / = 0. At time / = 1 the risk-free rate of interest has increased to 4% per annum. The share price has not changed. (iv) Calculate the value to the investor of the forward contract at f = 1. [1] (v) Determine each of the following Greeks for the contract value at time = 1: delta theta vega [3] ['Total 12]