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Lecture

# Lecture7.docx

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School
York University
Department
Course
Professor
Nabil Tahani
Semester
Winter

Description
LECTURE 6 An option is a right to buy ( call)/ to sell (put) the underlying asset Styles: - European e.g S&P 500 - American Asian options: Lookback options: you look at the history of the stock for estimating the pay off. Options pay off long call K = \$100, T = 1 year, Premium c = \$10 pay off S T K -10 K = 100 110 ST So that pay off = max (T – K , 0) Short call: pay off -10 110 K = 100 Long put Pay off 60 55 55 60 ST Pay off = max ( k T S , 0) Short put 45 55 K = 60 -55 -60 In the money/ out of money/ instrinsic value - An in the money option is an option that pays off immediately - For call K - OTM ITM 𝐒𝐓 For put ITM OTM Intrinsic value of the call =0S - K For eg. , S0= 790 , K = 760 , C = 46 Intrinsic value = 790 – 760 = 30 The difference between 30 and 46, \$16 is for the time . As such C > intrinsic value Note: time value of the call is difference between c and intrinsic value . For put : S0= 790.77 , K – 810 , p = 19.5 Intrinsic value = K - 0 Which is 810 – 790.77 = 19.23 We may have p < Intrinsic value Notation: - c : European call option price - p: European put option price - C : American call option price - P : American put option price - S : stock price today 0 - K : strike / exercise price - T : life of option - R : risk free rate for maturity T with continuous compounding - σ: volatility of stock price - D : present value of dividends during the option
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