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Option Pricing
Moravec, Radek ; Hurt, Jan (advisor) ; Cipra, Tomáš (referee)
Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1
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Pricing Options Using Monte Carlo Simulation
Dutton, Ryan ; Dědek, Oldřich (advisor) ; Červinka, Michal (referee)
Monte Carlo simulation is a valuable tool in computational finance. It is widely used to evaluate portfolio management rules, to price derivatives, to simulate hedging strategies, and to estimate Value at Risk. The purpose of this thesis is to develop the mathematical foundation and an algorithmic structure to carry out Monte Carlo simulation to price a European call option, investigate Black-Scholes model to look into the parallel between Monte Carlo simulation and Black-Scholes model, provide a solution for Black-Scholes model using Lognormal distribution of a stock price rather than solving Black-Scholes original partial differential equation, and finally compare the results of Monte Carlo simulation with Black- Scholes closed-form formula. Author's contribution can be best described as developing the mathematical foundation and the algorithm for Monte Carlo simulation, comparing the simulation results with the Black-Scholes model, and investigating how path-dependent options can be implemented using simulation when closed-form formulas may not be available. JEL Classification C02, C6, G12, G17 Keywords Monte Carlo simulation, Option pricing, Black-Scholes model Author's e-mail ryandutton4@gmail.com Supervisor's e-mail oldrich.dedek@fsv.cuni.cz
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Option Pricing
Moravec, Radek ; Hurt, Jan (advisor)
Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1
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Pricing Options Using Monte Carlo Simulation
Dutton, Ryan ; Dědek, Oldřich (advisor) ; Červinka, Michal (referee)
Monte Carlo simulation is a valuable tool in computational finance. It is widely used to evaluate portfolio management rules, to price derivatives, to simulate hedging strategies, and to estimate Value at Risk. The purpose of this thesis is to develop the mathematical foundation and an algorithmic structure to carry out Monte Carlo simulation to price a European call option, investigate Black-Scholes model to look into the parallel between Monte Carlo simulation and Black-Scholes model, provide a solution for Black-Scholes model using Lognormal distribution of a stock price rather than solving Black-Scholes original partial differential equation, and finally compare the results of Monte Carlo simulation with Black- Scholes closed-form formula. Author's contribution can be best described as developing the mathematical foundation and the algorithm for Monte Carlo simulation, comparing the simulation results with the Black-Scholes model, and investigating how path-dependent options can be implemented using simulation when closed-form formulas may not be available. JEL Classification C02, C6, G12, G17 Keywords Monte Carlo simulation, Option pricing, Black-Scholes model Author's e-mail ryandutton4@gmail.com Supervisor's e-mail oldrich.dedek@fsv.cuni.cz
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The arbitrage inconsistencies of implied volatility extraction in connection to calendar bandwidth
Vitali, Sebastiano ; Tichý, Tomáš ; Kopa, Miloš
Options are often priced by Black and Scholes model by using artificial (and unobserved) volatility implied by option market prices. Since many options do not have their traded counterparts with the same maturity and moneyness, it is often needed to interpolate the volatility values. The general procedure of implied volatility extraction from market prices and subsequent smoothing can, however, lead to inconsistent values or even arbitrage opportunities. In this paper, a potential arbitrage area is studied in connection with the calendar bandwidth construction.
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Artificial Neural Networks in Option Pricing
Vach, Dominik ; Gapko, Petr (advisor) ; Červinka, Michal (referee)
This thesis examines the application of neural networks in the context of option pricing. Throughout the thesis, different architecture choices and prediction parameters are tested and compared in order to achieve better performance and higher accuracy in option valuation. Two different volatility forecast mechanisms are used to compare neural networks performance with Black Scholes parametric model. Moreover, the performance of a neural network is compared also to more advanced modular neural networks. A new technique of adding rational prediction assumptions to neural network prediction is tested and the thesis shows the importance of adding virtual options fulfilling these assumptions in order to achieve better training of the neural network. This method comes out to increase the prediction power of the network significantly. The thesis also shows the neural network prediction outperforms the traditional parametric methods. The size and number of hidden layers in a neural network is tested with an emphasis to provide a benchmark and a structured way how to choose neural network parameters for future applications in option pricing. JEL Classification C13, C14, G13 Keywords Option pricing, Neural networks, Modular neu- ral networks, S&P500 index options Author's e-mail vach.dominik@gmail.com...
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Option Pricing
Moravec, Radek ; Hurt, Jan (advisor)
Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1
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Option Pricing
Moravec, Radek ; Hurt, Jan (advisor) ; Cipra, Tomáš (referee)
Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1
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