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Introduction to Options: Types, Pricing, and Key Concepts in Financial Engineering

This lecture provides an overview of options in financial engineering, discussing their characteristics, types, and pricing methods. It covers essential concepts such as call and put options, option premiums, intrinsic and time value, and the key components influencing option prices. The lecture also introduces the Black-Scholes pricing model and explores various options, including American and European types. Participants will learn about moneyness, market makers, and current events impacting options, providing a comprehensive foundation for understanding options in financial markets.

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Introduction to Options: Types, Pricing, and Key Concepts in Financial Engineering

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  1. Financial Engineering Lecture 2

  2. Option Review

  3. Options Review • Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time. • Call Option - The right to buy a security at a specified price within a specified time. • Put Option - The right to sell a security at a specified price within a specified time. • Option Premium - The price paid for the option, above the price of the underlying security. • Intrinsic Value - Diff between the strike price and the stock price • Time Premium - Value of option above the intrinsic value • Exercise Price - (Striking Price) The price at which you buy or sell the security. • Expiration Date - The last date on which the option can be exercised.

  4. Option Review Option ends by… • Expiration • Exercise • Sales • American option • European option • Intrinsic Value = P – E • Time Premium = O + E – P • Moneyness • In the money • Out of the money • At the money

  5. Option Review Profit Loss Asset Price

  6. Option Concepts • Market Makers • Round Trip • Lot size is 100 shares • Naked positions • Covered positions CBOE Quotes (web) • Open interest • Volume • Bid-ask • Prices

  7. Option Value Price 0 30 60 90 (expiration) Time (days)

  8. Time Decay Example – Given an exercise price of $55, what are the likely call option premiums, given stock prices of 50, 56, and 60 dollars?

  9. Time Decay • Intrinsic Value & Time Premium graphed Days to Expiration 90 60 30 Option Price Stock Price

  10. Exotic Options • Swaptions • Index options • Futures options • Currency options • Convertible bond • Warrant

  11. Barrier Options • Knock out options • Down and out • Up and out • Knock in options • Down and in • Up and in

  12. Current Events • Executive Stock Options • “To Expense or Not to Expense”

  13. Option Value Components of the Option Price 1 - Underlying stock price 2 - Striking or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate) 6 - PV of Dividends = D = (div)e-rt

  14. Option Value Black-Scholes Option Pricing Model

  15. Black-Scholes Option Pricing Model OC- Call Option Price P - Stock Price N(d1) - Cumulative normal density function of (d1) PV(EX) - Present Value of Strike or Exercise price N(d2) - Cumulative normal density function of (d2) r - discount rate (90 day comm paper rate or risk free rate) t - time to maturity of option (as % of year) v - volatility - annualized standard deviation of daily returns

  16. Black-Scholes Option Pricing Model

  17. Black-Scholes Option Pricing Model N(d1)=

  18. Cumulative Normal Density Function

  19. Cumulative Normal Density Function

  20. Call Option Example - Genentech What is the price of a call option given the following? P = 80 r = 5% v = .4068 EX = 80 t = 180 days / 365

  21. Call Option Example - Genentech What is the price of a call option given the following? P = 80 r = 5% v = .4068 EX = 80 t = 180 days / 365

  22. Call Option Example - Genentech What is the price of a call option given the following? P = 80 r = 5% v = .4068 EX = 80 t = 180 days / 365

  23. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  24. .3070 = .3 = .00 = .007

  25. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  26. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  27. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  28. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 41 40 .422 2 ln + ( .1 + ) 30/365 (d1) = .42 30/365 (d1) = .3335 N(d1) =.6306

  29. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 41 40 .422 2 ln + ( .1 + ) 30/365 (d1) = .42 30/365 (d1) = .3335 N(d1) =.6306

  30. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 (d2) = d1 - v t = .3335 - .42 (.0907) (d2) = .2131 N(d2) = .5844

  31. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 OC = Ps[N(d1)] - S[N(d2)]e-rt OC = 41[.6306] - 40[.5844]e - (.10)(.0822) OC = $ 2.67

  32. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365

  33. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 • Intrinsic Value = 41-40 = 1 • Time Premium = 2.67 + 40 - 41 = 1.67 • Profit to Date = 2.67 - 1.70 = .97 • Due to price shifting faster than decay in time premium

  34. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  35. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  36. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  37. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  38. Put Option Black-Scholes Op = EX[N(-d2)]e-rt - Ps[N(-d1)] Put-Call Parity (general concept) Put Price = Oc + EX - P - Carrying Cost + D Carrying cost = r x EX x t Call + EXe-rt = Put + Ps Put = Call + EXe-rt - Ps

  39. Put Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 N(-d1) = .3694 N(-d2)= .4156 Black-Scholes Op = EX[N(-d2)]e-rt - Ps[N(-d1)] Op = 40[.4156]e-.10(.0822) - 41[.3694] Op = 1.34

  40. Put Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 Put-Call Parity Put = Call + EXe-rt - Ps Put = 2.67 + 40e-.10(.0822) - 41 Put = 42.34 - 41 = 1.34

  41. Put Option Put-Call Parity & American Puts Ps - EX < Call - Put < Ps - EXe-rt Call + EX - Ps > Put > EXe-rt - Ps + call Example - American Call 2.67 + 40 - 41 > Put > 2.67 + 40e-.10(.0822) - 41 1.67 > Put > 1.34 With Dividends, simply add the PV of dividends

  42. 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

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