Option Pricing

survival of the fittest Pricing under Stochastic capriciousness with efficacious 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 deed on many profound security Basic language : Call Option: Gives the carrier the right to buy allot Option: Gives the holder the right to buy Strike hurt (K): Pre-determined wrong at which to execute the excerption Expiration Date: travel appointee the option can be exercised Vaibhav Agarwal 2004MT50450 Pricing of Options dusky Scholes blueprint Assumes that summation prices follow GBM B.S. Formula(contd.) footing of a European Call option as given by B.S. Formula : where St : price of vestigial Wt : Wiener process (Brownian Motion) µ : ramble on (Return) σ : irritability (Risk) price changes are log-normally distri buted where BS Formula is blemished BS Formula is monotonically change magnitude with σ It also assumes σ to be “constant” i.e.

unrelated to S or T It is spy that BS Formula: underprices deep-in-the-money or deep-out-of-themoney options overprices at-the-money options Volatility grin/ skewed 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 opposite strikes and maturities are not constant Volatility make a face/skew is ob served Volatility term structures + Volatili! ty Smile Volatility Surface Volatility Smile/ skewed and Surface Stochastic Volatility The supra results lead to the public opinion 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 democracy variables such as the price level of...If you wishing to energise a full essay, order it on our website: OrderCustomPaper.com

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