The Libor Market Model: from theory to calibration

This thesis is focused on the financial model for interest rates called the LIBOR Market Model. In the appendixes, we provide the necessary mathematical theory. In the inner chapters, firstly, we define the main interest rates and financial instruments concerning with the interest rate models, then, we set the LIBOR market model, demonstrate its existence, derive the dynamics of forward LIBOR rates and justify the pricing of caps according to the Black’s formula. Then, we also present the Swap Market Model, which models the forward swap rates instead of the LIBOR ones. Even this model is justified by a theoretical demonstration and the resulting formula to price the swaptions coincides with the Black’s one. However, the two models are not compatible from a theoretical point. Therefore, we derive various analytical approximating formulae to price the swaptions in the LIBOR market model and we explain how to perform a Monte Carlo simulation. Finally, we present the calibration of the LIBOR market model to the markets of both caps and swaptions, together with various examples of application to the historical correlation matrix and the cascade calibration of the forward volatilities to the matrix of implied swaption volatilities provided by the market.

Contratos de futuros sobre taxas de juro : estudo de caso sobre a Euribor a 3 meses

Mestrado em Contabilidade e Análise Financeira

Understanding Liquidity and Credit Risks in the Financial Crisis

This paper develops a structured dynamic factor model for the spreads between London Interbank Offered Rate (LIBOR) and overnight index swap (OIS) rates for a panel of banks. Our model involves latent factors which reflect liquidity and credit risk. Our empirical results show that surges in the short term LIBOR-OIS spreads during the 2007-2009 fi nancial crisis were largely driven by liquidity risk. However, credit risk played a more signifi cant role in the longer term (twelve-month) LIBOR-OIS spread. The liquidity risk factors are more volatile than the credit risk factor. Most of the familiar events in the financial crisis are linked more to movements in liquidity risk than credit risk.

Transmission of macro-liquidity shocks to liquidity-sorted stock portfolios’ returns: The role of the financial crisis

This study examines the impact of macro-liquidity shocks on the returns of UK stock portfolios sorted on the basis of a series of micro-liquidity measures. The macro-liquidity shocks are extracted on the meeting days of the Bank of England Monetary Policy Committee relative to market expectations embedded in futures contracts on the 3-month LIBOR during the period June 1999- December 2009. We report definitive evidence that these shocks are transmitted to the cross-section of liquidity-sorted portfolios, with most liquid stocks playing a very active role. Our results emphatically document that the shocks-returns relationship has reversed its sign during the recent financial crisis; the standard inverse relationship between interest rate surprises and portfolios’ returns before the crisis has turned into positive during the crisis. This finding confirms the inability of interest rate cuts to boost returns in the shortrun during the crisis, because these were perceived by market participants as a signal of a deteriorating economic outlook.

Stock Market Liquidity and Macro-Liquidity Shocks: Evidence from the 2007-2009 Financial Crisis

We develop an empirical framework that links micro-liquidity, macro-liquidity and stock prices. We provide evidence of a strong link between macro-liquidity shocks and the returns of UK stock portfolios constructed on the basis of micro-liquidity measures between 1999-2012. Specifically, macro-liquidity shocks, which are extracted on the meeting days of the Bank of England Monetary Policy Committee relative to market expectations embedded in 3-month LIBOR futures prices, are transmitted in a differential manner to the cross-section of liquidity-sorted portfolios, with liquid stocks playing the most active role. We also find that there is a significant increase in shares’ trading activity and a rather small increase in their trading cost on MPC meeting days. Finally, our results emphatically document that during the recent financial crisis the shocks-returns relationship has reversed its sign. Interest rate cuts during the crisis were perceived by market participants as a signal of deteriorating economic prospects and reinforced “flight to safety” trading.

Determination of anti-cancer drug emodin using a silica-gel-modified carbon paste electrode

In this paper, a silica-gel-modified carbon paste electrode (Si-gel/CPE) was used to determine the anti-cancer drug emodin by anodic stripping differential pulse voltammetry (ASDPV). The effects of the silica-gel content, the pH of the supporting electrolyte, and the scan rate on the oxidation current of emodin were investigated. The oxidation currents of emodin obtained from ASDPV measurements were linearly correlated with the concentration in the range of 5.0 × 10-9 to 300.0 × 10-9 mol L-1. The limit of detection was determined to be 1.5 × 10-9 mol L-1. The current method was successfully applied to determine emodin in a knotweed root sample, with recovery rate of 92.5% to 98.3%.

Key to the paper and social wasps of Central Europe (Hymenoptera: Vespidae)

A determination key to the Central European paper wasps (Polistinae – Polistes Latreille, 1802 – eight species) and social wasps (Vespinae – 11 species: Vespa Linnaeus, 1758 – one species, Vespula Thomson, 1869 – four species, Dolichovespula Rohwer, 1916 – six species) is given. Distribution and biotope requirements of all species in the Czech Republic and Slovakia are briefly mentioned. All social wasps occur more or less regularly in both countries. Four paper wasps are relatively common but four other species (Polistes atrimandibularis Zimmermann, 1930, P. sulcifer Zimmermann, 1930, P. associus Kohl, 1898, and P. gallicus (Linnaeus, 1767)) are very rare with the Czech Republic and/or Slovakia at the northern edge of their range.

Hedging effectiveness of total returns swaps: application to the Japanese market

The development of the real estate swap market offers many opportunities for investors to adjust the exposure of their portfolios to real estate. A number of OTC transactions have been observed in markets around the world. In this paper we examine the Japanese commercial real estate market from the point of view of an investor holding a portfolio of properties seeking to reduce the portfolio exposure to the real estate market by swapping an index of real estate for LIBOR. This paper explores the practicalities of hedging portfolios comprising small numbers of individual properties against an appropriate index. We use the returns from 74 properties owned by Japanese Real Estate Investment Trusts over the period up to September 2007. The paper also discusses and applies the appropriate stochastic processes required to model real estate returns in this application and presents alternative ways of reporting hedging effectiveness. We find that the development of the derivative does provide the capacity for hedging market risk but that the effectiveness of the hedge varies considerably over time. We explore the factors that cause this variability.

Emissões de eurobonds tem impacto no cupom cambial?

Este estudo tem por objetivo estimar o impacto do fluxo de emissões corporativas brasileiras em dólar sobre o cupom cambial. Podemos entender o cupom cambial, sob a ótica da Paridade Coberta da Taxa de Juros, como resultado de dois componentes: Taxa de juros externa (Libor) e Risco País. Desvios adicionais sobre a Paridade podem ser explicados por diversos fatores como custos de transação, liquidez, fluxos em transações de arbitragem de empresas financeiras ou não-financeiras, etc. Neste contexto, os fluxos de arbitragem ocorrem quando é possível para uma empresa brasileira captar recursos no mercado externo e internar estes recursos no Brasil encontrando uma taxa final de captação em reais inferior à de sua captação local (via debêntures, notas financeiras, empréstimos, CDB’s, etc) incluindo todos os custos. Quando há condições necessárias a este tipo de operação, o efeito pode ser visto no mercado de FRA de cupom cambial da BM&F, através de um fluxo anormal de doadores de juros. Testes não-paramétricos (Wilcoxon-Mann-Whitney, Kruskal-Wallis e Van der Waerden) e a metodologia de estudo de eventos detectaram comportamento anormal no mercado de FRA de cupom cambial frente aos eventos aqui considerados como emissões de eurobonds de empresas brasileiras, excluindo o efeito do risco soberano, medido pelo CDS Brasil e considerando nulo o risco de conversibilidade no período, após análise do diferencial entre NDF onshore e offshore. Para estimação do impacto das emissões sobre o FRA de cupom cambial foram utilizados dois modelos, AR-GARCH e OLS com correção de Newey-West, e os resultados mostraram que as emissões causam fechamento de 2 a 5 bps no FRA de cupom cambial, dependendo do vencimento da emissão e do modelo avaliado. Sob a mesma metodologia, concluímos de cada USD 100 milhões de emissões são responsáveis por, em média, 1 bps de fechamento no FRA de cupom cambial, tudo mais constante.

Os determinantes macroeconômicos da estrutura a termo das taxas de juros em dólar no Brasil

Este trabalho propõe o desenvolvimento de um modelo de três fatores em que os movimentos da Estrutura a Termo da Taxa de Juros em Dólar, o Cupom Cambial, são determinados por variáveis macroeconômicas observáveis. O estudo segue a metodologia elaborada por Huse (2011), que propõe um modelo baseado nos estudos de Nelson e Siegel (1987) e Diebold e Li (2006). Os fatores utilizados são: taxa de câmbio em real por dólar, spread do Credit Default Swap (CDS) Brasil de cinco anos, índice de preço de commodities, taxa de cupom cambial futura com vencimento em três meses, taxa futura de juros em dólar com cupom zero (Libor), volatilidade implícita da taxa de câmbio esperada pelo mercado de hoje até um ano, e inflação implícita de um ano no Brasil. O modelo foi capaz de explicar 95% das mudanças na estrutura a termo do cupom cambial. Aumentos no spread do CDS, na taxa de cupom cambial de três meses, na Libor, no índice de preço de commodities, e na volatilidade implícita do câmbio com vencimento em um ano estão diretamente relacionados com aumento na curva de juros em dólar. Por sua vez, a depreciação cambial tem correlação positiva com as maturidades mais curtas, até 2.5 anos, e negativo com a parte longa, até cinco anos. Choques na inflação implícita têm um pequeno impacto positivo para vencimentos curtos, mas levemente negativo para vencimentos mais longos.

Price risk management in the copper market using commodity derivatives and options strategies

Metals price risk management is a key issue related to financial risk in metal markets because of uncertainty of commodity price fluctuation, exchange rate, interest rate changes and huge price risk either to metals’ producers or consumers. Thus, it has been taken into account by all participants in metal markets including metals’ producers, consumers, merchants, banks, investment funds, speculators, traders and so on. Managing price risk provides stable income for both metals’ producers and consumers, so it increases the chance that a firm will invest in attractive projects. The purpose of this research is to evaluate risk management strategies in the copper market. The main tools and strategies of price risk management are hedging and other derivatives such as futures contracts, swaps and options contracts. Hedging is a transaction designed to reduce or eliminate price risk. Derivatives are financial instruments, whose returns are derived from other financial instruments and they are commonly used for managing financial risks. Although derivatives have been around in some form for centuries, their growth has accelerated rapidly during the last 20 years. Nowadays, they are widely used by financial institutions, corporations, professional investors, and individuals. This project is focused on the over-the-counter (OTC) market and its products such as exotic options, particularly Asian options. The first part of the project is a description of basic derivatives and risk management strategies. In addition, this part discusses basic concepts of spot and futures (forward) markets, benefits and costs of risk management and risks and rewards of positions in the derivative markets. The second part considers valuations of commodity derivatives. In this part, the options pricing model DerivaGem is applied to Asian call and put options on London Metal Exchange (LME) copper because it is important to understand how Asian options are valued and to compare theoretical values of the options with their market observed values. Predicting future trends of copper prices is important and would be essential to manage market price risk successfully. Therefore, the third part is a discussion about econometric commodity models. Based on this literature review, the fourth part of the project reports the construction and testing of an econometric model designed to forecast the monthly average price of copper on the LME. More specifically, this part aims at showing how LME copper prices can be explained by means of a simultaneous equation structural model (two-stage least squares regression) connecting supply and demand variables. A simultaneous econometric model for the copper industry is built: {█(Q_t^D=e^((-5.0485))∙P_((t-1))^((-0.1868) )∙〖GDP〗_t^((1.7151) )∙e^((0.0158)∙〖IP〗_t ) @Q_t^S=e^((-3.0785))∙P_((t-1))^((0.5960))∙T_t^((0.1408))∙P_(OIL(t))^((-0.1559))∙〖USDI〗_t^((1.2432))∙〖LIBOR〗_((t-6))^((-0.0561))@Q_t^D=Q_t^S )┤ P_((t-1))^CU=e^((-2.5165))∙〖GDP〗_t^((2.1910))∙e^((0.0202)∙〖IP〗_t )∙T_t^((-0.1799))∙P_(OIL(t))^((0.1991))∙〖USDI〗_t^((-1.5881))∙〖LIBOR〗_((t-6))^((0.0717) Where, Q_t^D and Q_t^Sare world demand for and supply of copper at time t respectively. P(t-1) is the lagged price of copper, which is the focus of the analysis in this part. GDPt is world gross domestic product at time t, which represents aggregate economic activity. In addition, industrial production should be considered here, so the global industrial production growth that is noted as IPt is included in the model. Tt is the time variable, which is a useful proxy for technological change. A proxy variable for the cost of energy in producing copper is the price of oil at time t, which is noted as POIL(t ) . USDIt is the U.S. dollar index variable at time t, which is an important variable for explaining the copper supply and copper prices. At last, LIBOR(t-6) is the 6-month lagged 1-year London Inter bank offering rate of interest. Although, the model can be applicable for different base metals' industries, the omitted exogenous variables such as the price of substitute or a combined variable related to the price of substitutes have not been considered in this study. Based on this econometric model and using a Monte-Carlo simulation analysis, the probabilities that the monthly average copper prices in 2006 and 2007 will be greater than specific strike price of an option are defined. The final part evaluates risk management strategies including options strategies, metal swaps and simple options in relation to the simulation results. The basic options strategies such as bull spreads, bear spreads and butterfly spreads, which are created by using both call and put options in 2006 and 2007 are evaluated. Consequently, each risk management strategy in 2006 and 2007 is analyzed based on the day of data and the price prediction model. As a result, applications stemming from this project include valuing Asian options, developing a copper price prediction model, forecasting and planning, and decision making for price risk management in the copper market.

Jüdische Augen-Gläser, d.i.: ein in 2 Th. verf. u. d. Juden zur Erkenntnuß d. wahren Glaubens vorgesteltes Buch ...

gegeben durch Eliam Liborium Roblik