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MGTC71-11

# MGTC71-11 - European Options on Stocks Providing a Dividend...

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1 MGTC71-Lecture 11 Options on Stock Indices, Currencies Ata Mazaheri 2 European Options on Stocks Providing a Dividend Yield We get the same probability distribution for the stock price at time T in each of the following cases: 1. The stock starts at price S 0 and provides a dividend yield = q 2. The stock starts at price S 0 e q T and provides no income 3 European Options on Stocks Providing Dividend Yield (Cont’d) We can value European options by reducing the stock price to S 0 e q T and then behaving as though there is no dividend 4 Extension of Chapter 9 Results rT qT Ke e S c - - - 0 Lower Bound for calls: Lower Bound for puts qT rT e S Ke p - - - 0 Put Call Parity qT rT e S p Ke c - - + = + 0 5 Extension of BSM Results T T q r K S d T T q r K S d d N e S d N Ke p d N Ke d N e S c qT rT rT qT σ σ - - + = σ σ + - + = - - - = - = - - - - ) 2 / 2 ( ) / ln( ) 2 / 2 ( ) / ln( ) ( ) ( ) ( ) ( 0 2 0 1 1 0 2 2 1 0 where 6 The Binomial Model S 0 u ƒ u S 0 d ƒ d S 0 ƒ p (1 – p ) f=e -rT [ pf u + (1 -p ) f d ]

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7 The Binomial Model (Cont’d) In a risk-neutral world the stock price grows at r-q rather than at r when there is a dividend yield at rate q The probability, p , of an up movement must therefore satisfy pS 0 u+ ( 1-p ) S 0 d=S 0 e ( r-q ) T so that p e d u d r q T = - - - ( ) 8
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