1. (a) i. ii. Explain why the following equation is an appropriate model of stock price behaviour ds µSdt + Sdz where u is the expected return for the stock and is the stock's volatility. = Demonstrate why this equation is not appropriate as a model of short-term interest rate behaviour.

The accompanying data represent the annual rates of return of two companies' stock for the past 12 years. Complete parts (a) through (k). O A. OB. 0.50- 0.50- 0.00- 0.00- -0.50- -0.50- -0.3 RR of Company 2 0.0 0.3 -0.3 0.0 0.3 RR of Company 1 OC. 0.30- 0.50- 0.00- 0.00- -0.30- -0.50- o.0 0'5 0.0 0.3 -0.5 RR of Company 2 0.5 -0.3 RR of Company 1 (b) Determine the correlation coefficient between rate of return of Company 1 and Company 2. The correlation coefficient is 0.966. (Round to three decimal places as needed.) (c) Based on the scatter diagram and correlation coefficient, is there a linear relation between rate of return of Company 1 and Company 2? Yes No (d) Find the least-squares regression line treating the rate of return of Company 1 as the explanatory variable. y=x+O (Round to four decimal places as needed.) RR of Company 1 RR of Company 1 RR of Company 2 RR of Company 2

What is interest?

In the world of mathematical finance, an important skill for any quantitative analyst is to price derivatives. These usually come in the form of options as well as other more exotic financial instruments. For this project we will focus on something called European Call options. We will see how you can estimate the price of an underlying asset (usually a stock) at some time in future T and use this to find how much an option should cost today. First, lets take a look at what a European call option actually is. The idea behind the European call option is that you will enter into a contract with someone that grants you the right, but not the obligation, to purchase some number of shares of a stock at a pre-determined price, called the strike price. In this paper we will say that the payoff for a European call option can be given by: max {S(t) – K, 0}. The reason we do this is because, it would not make sense to exercise the option if the price of the underlying asset is below the strike…