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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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Interest rate options and their valuation in binomial model
Ondruš, Martin ; Slámová, Lenka (advisor) ; Hurt, Jan (referee)
This work discusses about binomial pricing model, which is the basic principle for pricing of any kind of financial assets. We define its brief definition and show its main characteristics. Next, this work discusses about models of the short rate, especially to their discrete versions. From this set of models, we choose one of the most important interest rate models, which is Ho-Lee model and we look at it in details. According to its basis we interpret calibrating of binomial tree. Finally, we perform how to price different kinds of interest rate options such as caps or barrier options according to Ho-Lee model as well. We use mathematical software Mathematica for pricing options and calibrating of binomial tree.
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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 financial derivatives
Chudáček, Petr ; Hurt, Jan (advisor) ; Dostál, Petr (referee)
This bachelor thesis deals with selected methods of pricing of fi- nancial derivatives. It begins with introduction to financial derivatives, simple methods of pricing them and establishing terminology. It follows with summary of mathematical definitions and theorems necessary for deriving selected models for option pricing. In chapter dealing with diffusion models, there are introduced Black-Scholes Model, Binomial Model, and CEV model. The following chapters deal with Merton's Jump-Diffusion Model, i.e., a diffusion model enriched with jumps, and Variance-Gamma Model as the representative of (pure) jump models. This thesis is interspersed with numerical examples. 1
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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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Interest rate options and their valuation in binomial model
Ondruš, Martin ; Slámová, Lenka (advisor) ; Hurt, Jan (referee)
This work discusses about binomial pricing model, which is the basic principle for pricing of any kind of financial assets. We define its brief definition and show its main characteristics. Next, this work discusses about models of the short rate, especially to their discrete versions. From this set of models, we choose one of the most important interest rate models, which is Ho-Lee model and we look at it in details. According to its basis we interpret calibrating of binomial tree. Finally, we perform how to price different kinds of interest rate options such as caps or barrier options according to Ho-Lee model as well. We use mathematical software Mathematica for pricing options and calibrating of binomial tree.
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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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Option strategies and currency options pricing
Coufalík, Jan ; Sedláček, Jiří (advisor) ; Brázdil, Jiří (referee)
The aim of this diploma thesis is to analyze and implement selected option pricing models using statistical software. The first chapter introduces theoretical basics of options as financial instruments ideal for hedging and speculation. The second chapter constitutes the core part of this thesis since it unveils theoretical concepts of risk-neutral pricing and at the same time analyze some basic, as well as highly sophisticated option pricing models. In addition, each model is accompanied by a practical example of their effective implementation. The final chapter characterize the most widely used option trading strategies and defines the ideal expected market development linked to each strategy.
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Option Pricing and Variance Gamma Process
Moravec, Radek ; Málek, Jiří (advisor) ; Paholok, Igor (referee)
The submitted work deals with option pricing. Mathematical approach is immediately followed by an economic interpretation. The main problem is to model the underlying uncertainities driving the stock price. Using two well-known valuation models, binomial model and Black-Scholes model, we explain basic principles, especially risk neutral pricing. Due to the empirical biases new models have been developped, based on pure jump process. Variance gamma process and its special symmetric case are presented.
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Comparison of binomial and Black-Scholes option pricing models
Šigut, Jiří ; Málek, Jiří (advisor)
This work aims to describe binomial and Black-Scholes model. Options and their features are described in first parts of the work. Then assumptions and theory of both models are presented. The last chapter of theoretical part of this thesis is devoted to describe convergence of both models. Empirical part deals with convergence of pricing models.
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