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V. Black-Scholes model: Derivation and solution

Model: Derivation and solutionBe ta Stehl kov Financial derivatives, winter term 2014/2015 Faculty of Mathematics, Physics and InformaticsComenius University, BratislavaV. Black-Scholes model: Derivation and solution Black-Scholes model: Suppose that stock priceSfollows a geometricBrownian motiondS= Sdt+ Sdw+ other assumptions (in a moment) We derive apartial differential equation for the price ofa derivative Two ways of derivations: due toBlack and scholes due toMerton Explicit solution for European call and put optionsV. Black-Scholes model: Derivation and solution Further assumptions (besides GBP): constant riskless interest rater no transaction costs it is possible to buy/sell any (also fractional) number ofstocks; similarly with the cash no restrictions onshort selling option is of European type Firstly, let us consider the case of anon-dividend payingstockV.

Content • Black-Scholes model: Suppose that stock price S follows a geometric Brownian motion dS = µSdt+σSdw + other assumptions (in a moment) We derive a partial differential equation for the price of a derivative • Two ways of derivations: due to Black and Scholes due to Merton • Explicit solution for European call and put options V. Black …

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