1. Lecture 17

2.  Calculate the Annualized variance of the daily relative price change  Square root to arrive at standard deviation  Standard deviation is the volatility

3.  Develop Spreadsheet  Download data from internet http://finance.yahoo.com

4.  All variables in the option price can be observed, other than volatility.  Even the price of the option can be observed in the secondary markets.  Volatility cannot be observed, it can only be calculated.  Given the market price of the option, the volatility can be “reverse engineered.”

5. Use Numa to calculate implied volatility. Example (same option) P = 41r = 10%PRICE = 2.67 EX = 40t = 30 days / 365v = ???? Implied volatility = 42.16%

6.  CBOE Example  Use Actual option ◦ Calculate historical volatility ◦ Calculate implied volatility http://www.math.columbia.edu/~smirnov/options13.html http://www.cboe.com http://www.numa.com

7.  Given a normal or lognormal distribution of returns, it is possible to calculate the probability of having an stock price above or below a target price.  Wouldn’t it be nice to know the probability of making a profit or the probability of being “in the money?”

8. Steps for Infinite Distribution of Outcomes

9. Example Example (same option) P = 41r = 10%v =.42 EX = 40t = 30 days / 365

10. Example (same option) P = 41r = 10%v =.42 EX = 40t = 30 days / 365 $2.67 40 42.67 37% 58% 63%

11. Example Price = 36Ex-Div in 60 days @ $0.72 t = 90/365r = 10% P D = 36 -.72 e -.10(.1644) = 35.2917 Put-Call Parity Amer D+ C + S - P s > Put > Se -rt - P s + C + D Euro Put = Se -rt - P s + C + D + CC

12.  Class discussion