AEM4210_PS1_Solutions

# AEM4210_PS1_Solutions - AEM 4210 Derivatives and Risk...

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AEM 4210 Derivatives and Risk Management Spring Semester 2010 Homework Assignment 1 Suggested Solutions Price Distributions Sheet Question 1: Using a single line graph, graph any 5 series (remember to label the axis and provide a title). What do these graphs tell you? (4 points) Figure 1 The price paths of series1-5 are different from each other. For examples, the price path of series2 tends to increase overtime, while the price path of series4 tends to decrease overtime. Market prices follow a random path up and down, without any influence by past price movements, making it impossible to predict with any accuracy which direction the market will move at any point. This is the example of “Random Walk” market price. Price changes are independent of each other, so the past movement or trend of a stock price or market cannot be used to predict its future movement. Thus, it is impossible to outperform the market without taking on additional risk. Question 2: Go to row 260. Graph the values in row 260. Note that all prices start at 100 but end with different values depending on the price path. (2 points) 1

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Figure 2 Question 3: What are the mean, standard deviation, and skewness of the prices in row 260 for drift of 5% (B2) and volatility of 25% (B3)? (3 points) Table 1 Mean of the prices in row 260 105.0522 Standard Deviation of the prices in row 260 27.74962 Skewness of the prices in row 260 0.363061 2
Question 4: Increase volatility to 0.50 while keeping drift at 5% and repeat questions 1) to 3). (9 points) Figure 3 For each series, the trend of the price path in Figure 1 and Figure 3 are similar. However, the range of the prices in Figure 3 is wider because the volatility increases to

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## This note was uploaded on 05/10/2010 for the course AEM 4210 at Cornell University (Engineering School).

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AEM4210_PS1_Solutions - AEM 4210 Derivatives and Risk...

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