# EX 11 - STAT 400 1 Spring 2011 Examples for(2 Models of the...

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Examples for 03/11/2011 (2) Spring 2011 1. Models of the pricing of stock options often make the assumption of a normal distribution. An investor believes that the price of an Burger Queen stock option is a normally distributed random variable with mean \$18 and standard deviation \$3. He also believes that the price of an Dairy King stock option is a normally distributed random variable with mean \$14 and standard deviation \$2. Assume the stock options of these two companies are independent. The investor buys 8shares of Burger Queen stock option and 9 shares of Dairy King stock option. What is the probability that the value of this portfolio will exceed \$300? BQ has Normal distribution, μ BQ = \$18, σ BQ = \$3. DK has Normal distribution, μ DK = \$14, σ DK = \$2. Value of the portfolio VP = 8 × BQ + 9 × DK. Then VP has Normal distribution. μ VP = 8 × μ BQ + 9 × μ DK = 8 × 18 + 9 × 14 = \$270. 2 VP σ = 8 2 × 2 BQ σ + 9 2 × 2 DK σ = 64 × 9 + 81 × 4 = 900. σ VP = \$30. P( VP > 300 ) =

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## This note was uploaded on 11/28/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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EX 11 - STAT 400 1 Spring 2011 Examples for(2 Models of the...

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