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In this thesis, three popular option pricing models, Black and Scholes Model, Heston Model and Bates Model are compared to each other in economic crises situation. We carry out a comparison between different option pricing models based on S&P500 Index options during 2008. First these data are classified regarding to moneyness and maturity time in nine categories and then the performance of the models, exerting two indexes, In Sample performance and Out Of Sample performance are compared in every category. To reach the prices via In Sample performance index, structural parameters of each model are estimated with the data of each day. Then, daily prices are computed by models and compared with... 

In this thesis, we are going to prove the fundamental theorem of asset pricing and then define option and use the binomial option pricing model to for pricing the option. Afterwards, we explain the recovery theorem which gives the relationship between real and risk neutral measure. Moreover, we present an introduction to financial mathematics and state the generalized Black-Scholes model for option pricing.Then, we prove a theorem for options which reveals a relationship between option prices and real measure  

Till today types of demand response program have been identified as one of the most effective and usefull programs in order to the energy efficient consumption and followed by, improving the network's reliability. Also some of these plans have reduced the risk of the retailers and as much as possible prevent the likely loss of these companies at the high energy tariffs times. The required for doing some of these types of plans is investing on various parts like infrastructure mutual relationships between retailers and customer and also smart meters which will require valuation. Till now so many various ways have been done for valuation on types of demand response program plans. This thesis... 

In the past decades, option pricing has become one of the major areas in modern financial theory and practice. The Black-Scholes-Merton method is a type of option pricing, which is an appropriate and very important model in financial markets due to the pricing process under the assumption of no arbitrage and the recognition of the appropriate discount rate.Inspite of its advantages, this model is not appropriate for pricing the options which need to be investigated before the maturity.To overcome this limitation, some discrete extension of Black Scholes model were introduced such as binomial and trinomial trees.In all of these models during the contract period, volatility is considered...