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Derivatives

Derivatives. Lecture 17. Volatility. Calculate the Annualized variance of the daily relative price change Square root to arrive at standard deviation Standard deviation is the volatility. Volatility . Develop Spreadsheet Download data from internet http://finance.yahoo.com.

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Derivatives

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  1. Derivatives Lecture 17

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

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

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

  6. Implied Volatility • 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. Expected Returns • 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. Expected Return Steps for Infinite Distribution of Outcomes

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

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

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

  12. Expensing Stock Options • Class discussion

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