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Payoff and Replications Chapters 8, 10
Review of Option Types <ul><li>A call is an option to buy </li></ul><ul><li>A put is an option to sell </li></ul><ul><li>A...
Option Positions <ul><li>Long (buy) call </li></ul><ul><li>Long (buy) put </li></ul><ul><li>Short (write) call </li></ul><...
Long Call on eBay (Figure 8.1, Page 18 2 )—Limited liability <ul><li>Profit from buying one eBay European call option: opt...
Short Call on eBay  (Figure 8.3, page 18 4 ) —Unlimited liability <ul><li>Profit from writing one eBay European call optio...
Long Put on IBM  (Figure 8.2, page 18 3 ) –Limited profit & liability <ul><li>Profit from buying an IBM European put optio...
Short Put on IBM  (Figure 8.4, page 18 4 ) –Limited liability <ul><li>Profit from writing an IBM European put option: opti...
Payoffs from Options What is the Option Position in Each Case?   <ul><li>K  = Strike price,  S T   = Price of asset at mat...
Which of the position has limited liability? Plot the payoff <ul><li>Long stock </li></ul><ul><li>Short stock </li></ul><u...
Types of  Derivative Strategies Chapter 11 <ul><li>Take a position in the option and the underlying </li></ul><ul><li>Take...
Positions in an Option & the Underlying  (Figure 10.1, page 22 4 ) Profit S T K Profit S T K Profit S T K Profit S T K (a)...
Bull Spread Using Calls (Figure 10.2, page 22 5 ) K 1 <ul><ul><li>K 2 </li></ul></ul>Profit S T
Bull Spread Using Puts Figure 10.3, page 22 6 K 1 K 2 Profit S T
Bear Spread Using Puts Figure 10.4, page 22 7 K 1 K 2 Profit S T
Bear Spread Using Calls Figure 10.5, page 2 29 K 1 K 2 Profit S T
Box Spread <ul><li>A combination of a bull call spread and a bear put spread </li></ul><ul><li>If all options are European...
Butterfly Spread Using Calls Figure 10.6, page 23 1 K 1 K 3 Profit S T K 2
Butterfly Spread Using Puts Figure 10.7, page 23 2 K 1 K 3 Profit S T K 2
Calendar Spread Using Calls Figure 10.8, page 23 2 Profit S T K
Calendar Spread Using Puts Figure 10.9, page 23 3 Profit S T K
A Straddle Combination Figure 10.10, page 23 4 Profit S T K
Strip & Strap Figure  10.11, page 23 5 Profit K S T Profit K S T Strip Strap
A Strangle Combination Figure 10.12, page 23 6 K 1 K 2 Profit S T
Standard contracts <ul><li>Straddles </li></ul><ul><li>Strangles </li></ul><ul><li>Risk reversals </li></ul><ul><li>Binary...
A general replication formula <ul><li>Prove this formula: </li></ul><ul><li>Try to replicate the terminal payoff that pays...
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Replications and Payoffs

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Transcript of "Replications and Payoffs"

  1. 1. Payoff and Replications Chapters 8, 10
  2. 2. Review of Option Types <ul><li>A call is an option to buy </li></ul><ul><li>A put is an option to sell </li></ul><ul><li>A European option can be exercised only at the end of its life </li></ul><ul><li>An American option can be exercised at any time </li></ul>
  3. 3. Option Positions <ul><li>Long (buy) call </li></ul><ul><li>Long (buy) put </li></ul><ul><li>Short (write) call </li></ul><ul><li>Short (write) put </li></ul>
  4. 4. Long Call on eBay (Figure 8.1, Page 18 2 )—Limited liability <ul><li>Profit from buying one eBay European call option: option price = $5, strike price = $100, option life = 2 months </li></ul><ul><li>Correction: Focus on payoff, not “profit” </li></ul>30 20 10 0 -5 70 80 90 100 110 120 130 Profit ($) Terminal stock price ($)
  5. 5. Short Call on eBay (Figure 8.3, page 18 4 ) —Unlimited liability <ul><li>Profit from writing one eBay European call option: option price = $5, strike price = $100 </li></ul>-30 -20 -10 0 5 70 80 90 100 110 120 130 Profit ($): Change to payoff Terminal stock price ($)
  6. 6. Long Put on IBM (Figure 8.2, page 18 3 ) –Limited profit & liability <ul><li>Profit from buying an IBM European put option: option price = $7, strike price = $70 </li></ul>30 20 10 0 -7 70 60 50 40 80 90 100 Profit ($) : Change to payoff Terminal stock price ($)
  7. 7. Short Put on IBM (Figure 8.4, page 18 4 ) –Limited liability <ul><li>Profit from writing an IBM European put option: option price = $7, strike price = $70 </li></ul>-30 -20 -10 7 0 70 60 50 40 80 90 100 Profit ($) Terminal stock price ($)
  8. 8. Payoffs from Options What is the Option Position in Each Case? <ul><li>K = Strike price, S T = Price of asset at maturity </li></ul>Payoff Payoff S T S T K K Payoff Payoff S T S T K K
  9. 9. Which of the position has limited liability? Plot the payoff <ul><li>Long stock </li></ul><ul><li>Short stock </li></ul><ul><li>Long call, put </li></ul><ul><li>Short put </li></ul><ul><li>Short call </li></ul><ul><li>Short 1 call, long 1 put at the same strike </li></ul><ul><li>Short 1 call, long 1 stock </li></ul><ul><li>Short 1 call, short 1 put </li></ul>
  10. 10. Types of Derivative Strategies Chapter 11 <ul><li>Take a position in the option and the underlying </li></ul><ul><li>Take a position in 2 or more options of the same type (A spread) </li></ul><ul><li>Combination: Take a position in a mixture of calls & puts (A combination) </li></ul>
  11. 11. Positions in an Option & the Underlying (Figure 10.1, page 22 4 ) Profit S T K Profit S T K Profit S T K Profit S T K (a) (b) (c) (d)
  12. 12. Bull Spread Using Calls (Figure 10.2, page 22 5 ) K 1 <ul><ul><li>K 2 </li></ul></ul>Profit S T
  13. 13. Bull Spread Using Puts Figure 10.3, page 22 6 K 1 K 2 Profit S T
  14. 14. Bear Spread Using Puts Figure 10.4, page 22 7 K 1 K 2 Profit S T
  15. 15. Bear Spread Using Calls Figure 10.5, page 2 29 K 1 K 2 Profit S T
  16. 16. Box Spread <ul><li>A combination of a bull call spread and a bear put spread </li></ul><ul><li>If all options are European a box spread is worth the present value of the difference between the strike prices </li></ul><ul><li>If they are American this is not necessarily so . ( S ee Business Snapshot 10.1) </li></ul>
  17. 17. Butterfly Spread Using Calls Figure 10.6, page 23 1 K 1 K 3 Profit S T K 2
  18. 18. Butterfly Spread Using Puts Figure 10.7, page 23 2 K 1 K 3 Profit S T K 2
  19. 19. Calendar Spread Using Calls Figure 10.8, page 23 2 Profit S T K
  20. 20. Calendar Spread Using Puts Figure 10.9, page 23 3 Profit S T K
  21. 21. A Straddle Combination Figure 10.10, page 23 4 Profit S T K
  22. 22. Strip & Strap Figure 10.11, page 23 5 Profit K S T Profit K S T Strip Strap
  23. 23. A Strangle Combination Figure 10.12, page 23 6 K 1 K 2 Profit S T
  24. 24. Standard contracts <ul><li>Straddles </li></ul><ul><li>Strangles </li></ul><ul><li>Risk reversals </li></ul><ul><li>Binary call or put </li></ul><ul><li>Butterfly spread </li></ul>
  25. 25. A general replication formula <ul><li>Prove this formula: </li></ul><ul><li>Try to replicate the terminal payoff that pays ln(S T ) </li></ul><ul><li>If you can replicate, you can price. </li></ul><ul><li>Price variance swap in terms of European options, assuming continuous underlying dynamics. </li></ul>
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