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The Bandwidth Selection in Connection to Option Implied Volatility Extraction
Tichý, T.; Kopa, Miloš; Vitali, S.
2015 - English
Among various kinds of options we can found at the market, some are traded at organized exchanges and therefore are quite liquid, while others are traded only between particular parties. Whereas there is no need to look for a model to price liquid exchange traded options, since their price is generally accepted by the demand and supply, for illiquid or even exotic options new efficient models are still developed. The current market practice is to obtain the implied volatility of liquid options as based on Black-Scholes type (BS hereafter) models. The focus of this paper is to study the behavior of IV and SPD for several kernel functions and with respect to different choices of bandwidth parameter h. Specifically, we show several interesting implications of the change of h on the violation of no arbitrage condition and the total area of SPD under zero.
Keywords:
implied volatility; state price density; arbitrage opportunity
Fulltext is available at external website.
The Bandwidth Selection in Connection to Option Implied Volatility Extraction
Among various kinds of options we can found at the market, some are traded at organized exchanges and therefore are quite liquid, while others are traded only between particular parties. Whereas there ...
Influence diagrams for speed profile optimization" computational issues
Vomlel, Jiří; Kratochvíl, Václav
2015 - English
Influence diagrams were applied to diverse decision problems. However, the general theory is still not sufficiently developed if the variables are continuous or hybrid and the utility functions are nonlinear. In this paper, we study computational problems related to the application of influence diagrams to vehicle speed profile optimization and suggest an approximation of the nonlinear utility functions by piecewise linear functions.
Keywords:
influence diagram; speed profile; optimization
Fulltext is available at external website.
Influence diagrams for speed profile optimization" computational issues
Influence diagrams were applied to diverse decision problems. However, the general theory is still not sufficiently developed if the variables are continuous or hybrid and the utility functions are ...
Scenario Generation via L-1 Norm
Kaňková, Vlasta
2015 - English
Optimization problems depending on a probability measure correspond to many economic and financial situations. It can be very complicated to solve these problems, especially when the underlying probability measure belongs to continuous type. Consequently, the underlying continuous probability measure is often replaced by discrete one with finite number of atoms (scenario). The aim of the contribution is to deal with the above mentioned approximation in a special form of stochastic optimization problems with an operator of the mathematical expectation in the objective function. The stability results determined by the help of the Wasserstein metric (based on the L_1 norm) are employed to generate approximate distributions
Keywords:
One-stage stochastic programming problems; multistage stochastic problems; L_1 norm; Wasserstein metric
Fulltext is available at external website.
Scenario Generation via L-1 Norm
Optimization problems depending on a probability measure correspond to many economic and financial situations. It can be very complicated to solve these problems, especially when the underlying ...
On Linear Probabilistic Opinion Pooling Based on Kullback-Leibler Divergence
Sečkárová, Vladimíra
2015 - English
In this contribution we focus on the finite collection of sources, providing their opinions about a hidden (stochastic) phenomenon, that is not directly observable. The assumption on obtaining opinions yields a decision making process commonly referred to as opinion pooling. Due to the complexity of the space of possible decisions we consider the probability distributions over this set rather than single values, exploited before, e.g., in [2]. The final decision (result of pooling) is then a combination of probability distributions provided by sources.
Keywords:
linear opinion pooling; minimum cross-entropy principle; expected Kullback-Leibler divergence
Fulltext is available at external website.
On Linear Probabilistic Opinion Pooling Based on Kullback-Leibler Divergence
In this contribution we focus on the finite collection of sources, providing their opinions about a hidden (stochastic) phenomenon, that is not directly observable. The assumption on obtaining ...
Blind Separation of Mixtures of Piecewise AR(1) Processes and Model Mismatch
Tichavský, Petr; Šembera, Ondřej; Koldovský, Zbyněk
2015 - English
Modeling real-world acoustic signals and namely speech signals as piecewise stationary random processes is a possible approach to blind separation of linear mixtures of such signals. In this paper, the piecewise AR(1) modeling is studied and is compared to the more common piecewise AR(0) modeling, which is known under the names Block Gaussian SEParation (BGSEP) and Block Gaussian Likelihood (BGL). The separation based on the AR(0) modeling uses an approximate joint diagonalization (AJD) of covariance matrices of the mixture with lag 0, computed at epochs (intervals) of stationarity of the separated signals. The separation based on the AR(1) modeling uses the covariances of lag 0 and covariances of lag 1 jointly. For this model, we derive an approximate Cram´er-Rao lower bound on the separation accuracy for estimation based on the full set of the statistics (covariance matrices of lag 0 and lag 1) and covariance matrices with lag 0 only. The bounds show the condition when AR(1) modeling leads to significantly improved separation accuracy.
Keywords:
Autoregressive processes; Cramer-Rao bound; Blind source separation
Fulltext is available at external website.
Blind Separation of Mixtures of Piecewise AR(1) Processes and Model Mismatch
Modeling real-world acoustic signals and namely speech signals as piecewise stationary random processes is a possible approach to blind separation of linear mixtures of such signals. In this paper, ...
Model of Risk and Losses of a Multigeneration Mortgage Portfolio
Šmíd, Martin
2015 - English
During the last decades, Merton-Vasicek factor model (1987), later generalize by Frye at al. (2000), became standards in credit risk management. We present a generalization of these models allowing multiple sub-portfolios of loans possibly starting at different times and lasting more than one period. We show that, given this model, a one-to-one mapping between factors and the overall default rate and the charge-off rate exists, is differentiable and numerically computable.
Keywords:
risk management; loan portfolio; default rate; charge off rate
Fulltext is available at external website.
Model of Risk and Losses of a Multigeneration Mortgage Portfolio
During the last decades, Merton-Vasicek factor model (1987), later generalize by Frye at al. (2000), became standards in credit risk management. We present a generalization of these models allowing ...
An empirical comparison of popular algorithms for learning gene networks
Djordjilović, V.; Chiogna, M.; Vomlel, Jiří
2015 - English
In this work, we study the performance of different algorithms for learning gene networks from data. We consider representatives of different structure learning approaches, some of which perform unrestricted searches, such as the PC algorithm and the Gobnilp method and some of which introduce prior information on the structure, such as the K2 algorithm. Competing methods are evaluated both in terms of their predictive accuracy and their ability to reconstruct the true underlying network. A real data application based on an experiment performed by the University of Padova is also considered. We also discuss merits and disadvantages of categorizing gene expression measurements.
Keywords:
Bayesian networks; Gene networks; Biological pathways
Fulltext is available at external website.
An empirical comparison of popular algorithms for learning gene networks
In this work, we study the performance of different algorithms for learning gene networks from data. We consider representatives of different structure learning approaches, some of which perform ...
Algorithms for single-fault troubleshooting with dependent actions
Lín, Václav
2015 - English
We study the problem of single-fault troubleshooting with dependent actions. We propose a binary integer programming formulation for the problem. This can be used to solve the problem directly or to compute lower bounds of optima using linear programming relaxation. We present an optimal dynamic programming algorithm, and three greedy algorithms for computing upper bounds of optima.
Keywords:
single-fault troubleshooting; algorithms; linear programming relaxation
Fulltext is available at external website.
Algorithms for single-fault troubleshooting with dependent actions
We study the problem of single-fault troubleshooting with dependent actions. We propose a binary integer programming formulation for the problem. This can be used to solve the problem directly ...
The arbitrage inconsistencies of implied volatility extraction in connection to calendar bandwidth
Vitali, Sebastiano; Tichý, Tomáš; Kopa, Miloš
2015 - English
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.
Keywords:
Option pricing; implied volatility; arbitrage opportunity; calendar bandwidth; bandwidth size
Fulltext is available at external website.
The arbitrage inconsistencies of implied volatility extraction in connection to calendar bandwidth
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 ...
Bimodality testing of the stochastic cusp model
Voříšek, Jan
2015 - English
Multimodal distributions are popular in many areas: biology (fish and shark population), engineering (material collapse under pressure, stability of ships), psychology (attitude transitions), physics (freezing of water) etc. There were a few attempts to utilize multimodal distributions in financial mathematics as well. Cobb et al. described a class of multimodal distributions belonging to the exponential family, which has unique maximum likelihood estimators and showed a connection to the stationary distribution of the stochastic cusp catastrophe model. Moreover was shown, how to identify bimodality for given parameters of the stochastic cusp model using the sign of Cardans discriminant. A statistical test for bimodality of the stochastic cusp model using maximum likelihood estimates is proposed in the paper as well as the necessary condition for bimodality which can be used for s simplified testing to reject bimodality. By proposed methods is tested the bimodality of exchange rate between USD and GBP in the periods within the years 1975 - 2014.
Keywords:
multimodal distributions; stochastic cusp model; statistical bimodality test
Fulltext is available at external website.
Bimodality testing of the stochastic cusp model
Multimodal distributions are popular in many areas: biology (fish and shark population), engineering (material collapse under pressure, stability of ships), psychology (attitude transitions), physics ...
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