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F B E559f2 Binomial Pricing

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uichong

The document discusses binomial pricing models for pricing American options. It introduces a binomial model where the underlying asset price can move up or down between time periods. It shows how to price a European call option in this framework by constructing a replicating portfolio. The price of the option is set so that this portfolio replicates the payoffs. It then extends this to multiple time periods and discusses how to price early exercise features of American options.

BusinessEconomy & Finance
1 of 23
Binomial Pricing Pricing of American Options
Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object]
Binomial Setting ,[object Object],[object Object],S uS dS
Binomial Setting (cont.) ,[object Object],[object Object],[object Object],[object Object],S=100 S = 125 S = 80
Binomial Setting (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object]
Option Pricing ,[object Object],[object Object],[object Object],S=100 uS = 125 dS = 80 S C (X=110) C u = 15 C d = 0
Option Pricing (cont.) ,[object Object],[object Object],[object Object],[object Object]
Option Pricing (cont.) ,[object Object],[object Object],[object Object],[object Object]
Option Pricing (cont.) ,[object Object],[object Object],[object Object]
Option Pricing (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Risk Neutral Pricing ,[object Object],[object Object],[object Object]
Risk Neutral Pricing (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Risk Neutral Pricing (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object]
Multiperiod Setting ,[object Object],[object Object],S uS dS u 2 S udS d 2 S
Multiperiod Setting (cont.) ,[object Object],[object Object]
Multiperiod Setting (cont.) ,[object Object],[object Object],[object Object]
Binomial Pricing ,[object Object],[object Object],[object Object],[object Object]
Binomial Pricing (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object]
American Options ,[object Object],[object Object],[object Object],[object Object],[object Object]
American Options (cont.) 100 Call Payoff 90 (82) 90.2 73.8 0 0 110 (102) 112.2 91.8 12.2 0 I II III In parenthesis: ex-dividend
American Options (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object]
American Options (cont.) Value of call:  Solution: exercise and get 10. Replicating portfolio: 110 (102) 112.2 91.8 12.2 0 I
American Options (cont.) ,[object Object],[object Object],[object Object],100 110 90 10 0 III

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F B E559f2 Binomial Pricing

  • 1. Binomial Pricing Pricing of American Options
  • 2.
  • 3.
  • 4.
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  • 11.
  • 12.
  • 13.
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  • 20. American Options (cont.) 100 Call Payoff 90 (82) 90.2 73.8 0 0 110 (102) 112.2 91.8 12.2 0 I II III In parenthesis: ex-dividend
  • 21.
  • 22. American Options (cont.) Value of call:  Solution: exercise and get 10. Replicating portfolio: 110 (102) 112.2 91.8 12.2 0 I
  • 23.