Option Pricing

survival of the fittest Pricing under Stochastic capriciousness with effectual Method of Moments Estimation Supervisors: Prof. Sankarshan Basu (IIM, Bangalore) Prof. S. Dharmaraja (Dept. of Mathematics, IIT Delhi) Options Financial instruments that convey the right, but not the obligation, to take aim in a future achievement on many profound security Basic spoken language : Call Option: Gives the carrier the right to buy contrive Option: Gives the holder the right to buy Strike value (K): Pre-determined wrong at which to execute the excerption Expiration Date: furthermost appointee the option can be exercised Vaibhav Agarwal 2004MT50450 Pricing of Options fateful Scholes linguistic rule Assumes that summation prices follow GBM B.S. Formula(contd.) expenditure of a European Call option as given by B.S. Formula : where St : price of inherent Wt : Wiener process (Brownian Motion) µ : draw (Return) σ : unpredictability (Risk) price c hanges are log-normally distributed where BS Formula is flawed BS Formula is monotonically change magnitude with σ It also assumes σ to be “constant” i.e.

unrelated to S or T It is notice that BS Formula: underprices deep-in-the-money or deep-out-of-themoney options overprices at-the-money options Volatility grin/ reorient and Implied Volatility Implied Volatility σi is the capriciousness that equates the BS Price to the commercialize price : BS( St, K, r, σi, T) = Option market Price Implied volatilities for unalike strikes and maturities are not constant Vo latility make a face/skew is observed Volat! ility term structures + Volatility Smile Volatility Surface Volatility Smile/ reorient and Surface Stochastic Volatility The supra results direct to the view that the volatilities were, in fact, not constant. σ depended on St and T, at least This led to the idea of Stochastic Volatility The name derives from the models intervention of the underlying securitys volatility as a random process, governed by give in variables such as the price level of...If you wishing to write down a full essay, order it on our website: OrderCustomPaper.com

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