Improving value at risk calculations

Assignment Help Dissertation
Reference no: EM134818 , Length: 50

Dissertation writing help - Improving Value at Risk Calculations by Using Copulas and Non-Gaussian Margins

Custom Dissertation Writing Service - Financial risk management

Value at risk (VaR) is of central importance in modern financial risk management. Of the various methods that exist to compute the VaR, the most popular are historical simulation, the variance-covariance method and Monte Carlo (MC) simulation. While historical simulation is not based on particular assumptions as to the behavior of the risk factors, the two other methods assume some kind of multinomial distribution of the risk factors. Therefore the dependence structure between different risk factors is described by the covariance or correlation between these factors.

It is shown in [1, 2] that the concept of correlation entails several pitfalls. As a consequence, copulas are proposed to describe the dependence between n variables with arbitrary marginal distributions. A copula is a function C : [0, 1] n -> [0, 1] with certain special properties [3], so that the joint distribution can be written as IP(R1 ≤ r1, . . . ,Rn ≤ rn) = C (F1(r1), . . . , Fn(rn)). F1, . . . , Fn denote the cumulative probability functions of the n variables. In general, a copula C depends on one or more parameters p1, . . . , pk that determine the dependence between the variables r1, . . . , rn. In this sense, these parameters assume the role of correlations.

The second pitfall that arises from the multinomial distribution ansatz is the fat tail problem of the margins [4, 5]. One way of taking extreme values better into account is to assume that the risk factors obey Student distribution patterns instead of Gaussian patterns.
In this thesis we investigate two risk factors only. We model each risk factor independently using a Student distribution and describe their dependence by both the Frank copula [6] and the Gumbel-Hougaard copula. We present algorithms to estimate the parameters of the margins and the copulas and to generate pseudo random numbers due to copula dependence.

Making use of historical data spanning a period of nineteen years, we compute the VaR using a copula-modi?ed MC algorithm. To see the advantage of this method, we compare our results with VaR results obtained from the three standard methods mentioned at the beginning. Based on backtesting results, we Find that the copula method is more reliable than both traditional MC simulation and the variance-covariance method and about as good as historical simulation.

Reference no: EM134818

Questions Cloud

Dissertation writing help - carbon trading : Carbon Trading - In this study we first begin a trading platform for a two-company development in a multi-period setting and derive an equilibrium carbon spot price.
The hidden correlation of collateralized debt obligations : Advise a model for the correlation structure of reference portfolios of collateralized debt obligations - The Hidden Correlation of Collateralized Debt Obligations
Semi-analytic lattice integration of a markov model : This dissertation defines the semi-analytic Lattice Integration of a Markov Functional Term Structure Model. Markov functional models is to estimated LIBOR market models and to avoid complications the terminal forward measure is naturally used.
Nonlinear black scholes modelling - fdm vs fem : In the classical Black-Scholes model, the financial parameters, like the volatilities and correlations, are assumed to be known. These are very strong assumptions that are unrealistic in the real world.
Improving value at risk calculations : Value at risk (VaR) is of central importance in modern financial risk management. Of the various methods that exist to compute the VaR, the most popular are historical simulation, the variance-covariance method and Monte Carlo (MC) simulation.
Exercise strategies by monte carlo techniques : Monte-Carlo simulation methods are used to investigate (standardized) Swing options. In a first approach, this is done by an algorithm which is based on the Long-staff Schwartz technique for American and Bermudan options.
Simulating the dynamics of the risk neutral distribution : Knowledge about the dynamics of the risk neutral distribution is necessary for the valuation of complex options on financial assets. We present and discover a formalism (the twin formalism) that allows simulating how the risk neutral probability d..
Two-regime markov-chain model : LIBOR Market Model- the parameterization of the forward rate volatility term structure is presented and it is shown how this relates to swap rates.
Pricing inflation-indexed derivatives : The purpose of this thesis is to review the framework for pricing inflation-indexed derivatives using the two currency Heath-Jarrow-Morton approach introduced by Yildirim and Jarrow.

Reviews

Write a Review

Dissertation Questions & Answers

  Parsimonious model for the joint evolution of yield curves

Counterparty credit risk management and validation of out-of-the-money hedges require risk factor evolution models that are capable of reproducing essential statistical properties of historical time-series.

  Dissertation writing help on immortal picture stories

Whose Immortal Picture Stories?: Amar Chitra Katha and the Construction of Indian Identities

  Optimal time domain equalization design

Optimal Time Domain Equalization Design for Maximizing Data Rate of Discrete Multi-Tone Systems

  Exercise strategies by monte carlo techniques

Monte-Carlo simulation methods are used to investigate (standardized) Swing options. In a first approach, this is done by an algorithm which is based on the Long-staff Schwartz technique for American and Bermudan options.

  A critical appraisal of npt: trends and challenges

This is a thesis, focused upon the Trends and Challenges of Nuclear Power Treaty. It is a very serious issue that need to be studied in depth.

  Write an essay on marketing design innovation

Write an essay on Marketing Design innovation

  Predictive model for aqueous potassium carbonate

A Predictive Model for Aqueous Potassium Carbonate/Piperazine/Ethanolamine for Carbon Dioxide Removal from Flue Gas

  Higher education faculty: satisfaction with online teaching

Higher Education Faculty: Satisfaction with Online Teaching

  An empirical study of product functional families

Dissertation writing help on An Empirical Study of Product Functional Families

  Electrical stimulation frequencies for motor recovery

High vs. Low Electrical Stimulation Frequencies for Motor Recovery in Hemiplegia

  Dissertation writing help - oil futures term structure model

Dissertation focuses on the stochastic evolution of the stochastic system shown by the oil futures term structure (FTS). In particular, given its crucial role in a wide range of financial applications, such as in derivatives pricing or in risk mana..

  Pricing inflation-indexed derivatives

The purpose of this thesis is to review the framework for pricing inflation-indexed derivatives using the two currency Heath-Jarrow-Morton approach introduced by Yildirim and Jarrow.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd