Your Name RN Question 2 (20 points): Mary defines a price jump for a stock when

Question

Your Name RN Question 2 (20 points): Mary defines a price jump for a stock when its monthly price change is at least 10%. Such price jumps makes her nervous as a risk-averse investor. From past data, Mary estimates that there is a 30% chance that stock ABC experiences a monthly price jump. Furthermore, Mary estimates that ABC's price jumps are independent from month-to-month. Suppose Mary includes ABC in her investments. 1. What is the probability that a complete year will pass without Mary experiencing a singe price jump in ABC? 2. In a given year, what is the probability that Mary will see at least two price jumps in ABC? (State any assumptions you make clearly.)

Explanation / Answer

a) Assuming that each jump is independent and each period is independent, the probability that there is no jump in the whole year that is in 12 months is computed as:

= ( 1 - 0.3)*(1 - 0.3)*...... 12 times

= ( 1- 0.3)12

= 0.712

= 0.0138

Therefore 0.0138 is the required probability here.

b) Probability that in a year, Mary will see at least two price jumps could be computed as:

= 1 - Probability of no jump - Probability of having one jump over the year

= 1 - 0.0138 - 12*0.3*(1-0.3)11

= 0.9150

Therefore 0.9150 is the required probability here.

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