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# I need help with question 1 and 2 of this problem. Not sure how to use algebra to find Ft equation src="/qa/attachment/10756990/" alt="Picture 1.png" /> ATTACHMENT PREVIEW Download attachment Picture 1.png Question 1 (3 marks) An asset follows the following Geometric Brownian Motion: d5 = ySdt + oSdz Consider a derivative on the asset that pays off 5% at maturity. This derivative works like a power option with a very low exercise price, and is suitable for speculators who want to place a highly leveraged bet on the price of the underlying. (a) Derive the formula to price this derivative using the risk-neutral valuation method. (b) Show that your formula in (a) satisfies the Black-Scholes-Merton Partial Differential Equation: (if (if 1 62 f _ _ __ 22= at+65rs+265205 rf Hint: - Express the risk neutral valuation formula as ft = e ”(T—3E0 (5%), where tis the current time. - The formula for the expectation of 3% where 51 follows a lognormai distribution is shown in Lecture 4 slides.

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