Model Dependency of the Digital Option Replication – Replication under an Incomplete Model (in English)

The paper focuses on the replication of digital options under an incomplete model. Digital options are regularly applied in the hedging and static decomposition of many path-dependent options. The author examines the performance of static and dynamic replication. He considers the case of a market agent for whom the right model of the underlying asset-price evolution is not available. The observed price dynamic is supposed to follow four distinct models: (i) the Black and Scholes model, (ii) the Black and Scholes model with stochastic volatility driven by Hull and White model, (iii) the variance gamma model, defined as time changed Brownian motion, and (iv) the variance gamma model set in a stochastic environment modelled as the rate of time change via a Cox-Ingersoll-Ross model. Both static and dynamic replication methods are applied and examined within each of these settings. The author verifies the independence of the static replication on underlying processes.digital options, dynamic and static replication, internal time, Lévy models, replication error, stochastic environment, stochastic volatility, variance gamma process

Description of the twelfth species of the genus Thermistis Pascoe, 1867 (Coleoptera: Cerambycidae: Lamiinae: Saperdini)

Web of Science4750115014

Posouzení metody částečného hedgingu na případu řízení měnového rizika nefinanční instituce

Financial risk management is an inherent part of each business activity. The analysis of available hedging strategies, theirs interconnection with efficient market and firm value theories, as well as various empirical studies are regular theme of scientific papers. In this study we focus on an alternative approach to hedging of financial risk of non-financial institutions – the partial hedging approach with shortfall acceptation. This approach initiates from Föllmer and Leukert (1999) method of quantile hedging. It is also related to cashflow at risk approach of Stein et al. (2001). The approach to hedging presented in this paper is based on a combined option position, so that a substantial decrease in initial capital needs can be achieved by accepting of some probability of shortfall. The strategy is studied under various circumstances given e.g. by risk neutral and real market probabilities. Simultaneously, it is compared to more standard strategies of hedging. Finally, we present two interesting findings: (i) real world probability of shortfall significantly differs from the risk neutral one, (ii) at first sight insignificant error in simulation results can have important influence on the interpretation of partial hedging strategies

Replication Methods in the Pricing and Hedging of Barrier Options

This paper considers various options replication methods. Firstly, a specific type of barrier option, an up-and-out call, is considered. Other barrier options are briefly also described, and various types of barriers are considered. Secondly, a general definition of replication methods is provided. Two methods are thus examined in detail: The first one, based on ever-changing positions in replicating portfolio, is referred to as a dynamic replication method. The second one is denoted as a static replication method ? its aim is to create a static basket of simple assets that will replicate the option payoff. However, in the real world it is difficult to attain perfect replication; therefore, the expected replication error of both methods is studied via simulation technique.Options; barrier options; replication methods; dynamic and static replication; replication error

Efficiency analysis of several EU stock markets: mean-risk efficient portfolios

Web of Science29571069

The impact of association measures within the portfolio dimensionality reduction problem

The dependency structure of random sources plays a crucial role in portfolio theory and in several pricing and risk management problems. In this paper, we discuss the possible usage of alternative association measures in portfolio problems. Among association measures, we highlight those that are consistent with the choices of risk-averse investors and we characterise semidefinite positive association measures. Additionally, we propose new portfolio selection problems that optimise the association between the portfolio and market benchmarks and follow a dimensionality reduction problem. Finally, by carrying out an empirical analysis, we show the impact of selected association measures within the portfolio problem. This analysis proves that the proper usage of both a risk measure and an association measure can increase the portfolio performance substantially

DGM for real options valuation: Options to change operating scale

summary:The real options approach interprets a flexibility value, embedded in a project, as an option premium. The object of interest is to valuate real options to change operating scale, typical for natural resources industry. The evolution of the project as well as option prices is decribed by partial differential equations of the Black-Scholes type, linked through a payoff function given by a type of the flexibility provided. The governing equations are discretized by the discontinuous Galerkin method over a finite element mesh and they are integrated in temporal variable by an implicit Euler scheme. The special attention is paid to the treatment of early exercise feature that is handled by additional penalty term. The capabilities of the approach presented are documented on the selected individual real options from the reference experiments using real market data

Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

Výkonnost replikace digitálních opcí při neúplném modelu

Digital options are financial derivatives allowing the trader to decompose the payoff of more complicated derivatives. The payoff of these contracts is all or nothong. Therefore, contracts of this type are suitable especially to hedge exotic derivatives with any discontinuity in the payoff function. The paper provides the two most common ways to replicate the payoff of these contracts - static and dynamic replication. Both methods are compared in discrete environment and subsequently studied for the case of incomplete model. To be more exact, we suppose stochastic volatility of underlying assent returns and the negative skewness plus positive excess kurtosis of underlying returns