Continuous Time - Black Scholes Revisited

# Continuous Time - Black Scholes Revisited - 1 Temple...

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Unformatted text preview: 1 Temple University Continuous Time Finance Black-Scholes Revisted 2 Continuous Time Finance Revisited … Discrete Option Pricing 3 Long Call Profit from buying one European call option: option price = \$2, strike price = \$21, option life = 3 months 15 10 5 5 10 15 21 25 30 35 Profit (\$) Terminal stock price (\$) 4 Expectation Pricing -- =- = = ∫ ∞ ∞- 2 2 2 rT- 2 ) ( exp 2 1 ) ( ) ( ) 21 * 20 , max( e Call deviation standard and mean with d distribute normally is ~ ) ~ exp( σ μ πσ σ μ x x f dx x f e X X S S X T Paul Samuelson Nobel Memorial Prize in Economic Sciences in 1970 5 Original Derivation Fischer Black 1938-1995 Myron Scholes Nobel Prize 1997 Robert Merton Nobel Prize 1997 6 Stock Price = \$22 Option Price = \$1 Stock Price = \$18 Option Price = \$0 Stock price = \$20 Option Price=? CRR: One-Step Binomial Model A 3-month call option on the stock has a strike price of 21. What can be said about the current worth of the option? John Cox Stephen Ross Mark Rubinstein 7 Consider the Portfolio: long ∆ shares (future price 22 or 18) short 1 call option (future price 1 or 0) Portfolio is riskless when: 22 ∆ – 1 = 18 ∆ ∆ = 0.25 22 ∆ – 1 18 ∆ Homemade Riskless Position...
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Continuous Time - Black Scholes Revisited - 1 Temple...

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