An Approximate Model for Total Amount of Non-life Insurance Claims using Generalized Gamma Distribution and H-Function

This article proposes an analytical method to approximate the probability density function (PDF) and the cumulative distribution function (CDF) of the total amount of non-life claims to be paid by the insurer over a financial period considered. The individual claims amounts are independent positive random variables following the generalized gamma distribution (GGD) and distributed in a non-identical manner. The analytical approach suggested relies on the Fox H-function. The Fox H-function has various applications available in the literature. The method developed has demonstrated its performance both in respect of the result obtained (in comparison to the Monte-Carlo method) and in respect of simplicity (easily accessible for the most common claims amount distributions). The resulting PDF expression can be directly used to estimate the technical benefit, total cost, and ruin probability of the non-life insurance company

Polynomial models in finance

This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for which the conditional moments are analytic. The first half of this thesis is concerned with modelling the fluctuations in the volatility of stock prices, and with the valuation of options on the stock. A new stochastic volatility model for which the squared volatility follows a Jacobi process is presented in the first chapter. The stock price volatility is allowed to continuously fluctuate between a lower and an upper bound, and option prices have closed-form series representations when their payoff functions depend on the stock price at finitely many dates. Truncating these series at some finite order entails accurate option price approximations. This method builds on the series expansion of the ratio between the log price density and an auxiliary density, with respect to an orthonormal basis of polynomials in a weighted Lebesgue space. When the payoff functions can be similarly expanded, the method is particularly efficient computationally. In the second chapter, more flexible choices of weighted spaces are studied in order to obtain new series representations for option prices with faster convergence rates. The option price approximation method can then be applied to various stochastic volatility models. The second half of this thesis is concerned with modelling the default times of firms, and with the pricing of credit risk securities. A new class of credit risk models in which the firm default probability is linear in the factors is presented in the third chapter. The prices of defaultable bonds and credit default swaps have explicit linear-rational expressions in the factors. A polynomial model with compact support and bounded default intensities is developed. This property is exploited to approximate credit derivatives prices by interpolating their payoff functions with polynomials. In the fourth chapter, the joint term structure of default probabilities is flexibly modelled using factor copulas. A generic static framework is developed in which the prices of high dimensional and complex credit securities can be efficiently and exactly computed. Dynamic credit risk models with significant default dependence can in turn be constructed by combining polynomial factor copulas and linear credit risk models

Signed path dependence in financial markets: Applications and implications

Despite decades of studies, there is still no consensus on what type of serial dependence, if any, might be present in risky asset returns. The serial dependence structure in asset returns is complex and challenging to study, it varies over time, it varies over observed time resolution, it varies by asset type, it varies with liquidity and exchange and it even varies in statistical structure. The focus of the work in this thesis is to capture a previously unexplored notion of serial dependence that is applicable to any asset class and can be both parameteric or non-parameteric depending on the modelling approach preferred. The aim of this research is to develop new approaches by providing a model-free definition of serial dependence based on how the sign of cumulative innovations for a given lookback horizon correlates with the future cumulative innovations for a given forecast horizon. This concept is then theoretically validated on well-known time series model classes and used to build a predictive econometric model for future market returns, which is applied to empirical forecasting by means of a profit seeking trading strategy. The empirical experiment revealed strong evidence of serial dependence in equity markets, being statistically and economically significant even in the presence of trading costs. Subsequently, this thesis provides an empirical study of the prices of Energy Commodities, Gold and Copper in the futures markets and demonstrates that, for these assets, the level of asymmetry of asset returns varies through time and can be forecast using past returns. A new time series model is proposed based on this phenomenon, also empirically validated. The thesis concludes by embedding into option pricing theory the findings of previous chapters pertaining to signed path dependence structure. This is achieved by devising a model-free empirical risk-neutral distribution based on Polynomial Chaos Expansion and Stochastic Bridge Interpolators that includes information from the entire set of observable European call option prices under all available strikes and maturities for a given underlying asset, whilst the real-world measure includes the effects of serial dependence based on the sign of previous returns. The risk premium behaviour is subsequently inferred from the two distributions using the Radon-Nikodym derivative of the empirical riskneutral distribution with respect to the modelled real-world distribution

The information in the yield curve

The term structure of interest rates as described by yield curves has the potential to contain information about the course of future nominal and real interest rates, inflation and economic activity. The link between the yield curve and these economic variables is formalised via capital asset pricing models. The information in yield curves is examined in a systematic manner using two new term structure data sets. The first one is an extended version of the McCulloch yield data for the United States for the period 1947-91 and the second one is a new highly detailed data set for the United Kingdom supplied by the Bank of England for this study, which consists of daily observations on yields for the period 4th January 1983 to 30th November 1993.Empirical evidence for the United States for the period 1952-91 shows that inflation and real interest rate changes tend to offset each other so that there is no useful information about nominal interest rates. Information about the real term structure is sometimes obscured by the offsetting effects of real interest rates and term premiums. Evidence is presented that shows yield spreads may give more unambiguous signals about economic activity if such activity is measured in relative terms. The better predictive power of UK term structures with regard to nominal interest rates is due to inflation and real interest rates moving together in the same direction. The phenomenon of disinflation can produce highly significant information about the real term structure. For the US and, more particularly, the UK, the predictive power of the yield curve is subject to significant change. The main conclusion reached is that over-reliance certainly should not be placed on the yield curve as a leading economic indicator

Short-termism : an investigation of some UK evidence

The aim of this thesis is to undertake an empirical investigation into the assertion that UK investors display short-term behaviour. The thesis starts by reviewing the existing literature which comprises a diverse set of explanations of the concept of short-termism. This survey results in, firstly, a more concise definition of short-termism and, secondly, a framework into which the various theories may be placed. The various approaches to short-termism are categorised into two effects: the numerator effect and the denominator effect. The former refers to the underestimation of future cash flows while the latter refers to those cases in which an excessively high discount rate is used. Both these effects result in the present value of a proposed project being reduced. therefore causing the project to be rejected when it might otherwise have been accepted. Although the literature covers many different approaches to short-termism this thesis concentrates only on one aspect of short-termism. namely the denominator effect. Such an approach is advantageous in that it allows the consideration, and possible elimination, of a particular type of short-termism. thus giving direction to future research. By decomposing the discount rate into the following components: a time value of money, a liquidity premium, an equity risk premium and an exchange rate risk premium it becomes possible to distinguish between "true" short-term ism and "general" short-termism. "True" short-termism refers to the existence ofa high time value of money whilst "general" short-termism refers to the use of a high discount rate for whatever reason. whether it be a high time value of money, liquidity premium or equity risk premium. A preliminary investigation into the existence of both types of short-termism is carried out by the comparison of international real rates of return and risk premia as a means of testing for differences in the behaviour of investors across countries. The results of this investigation lend little support to the assertion that UK investors are short-termist, but suggest that if short-termism is present it is in the form of "true" short-termism. Following these results, further empirical analysis is carried out into the issue of "true" short-termism. A key feature of this analysis is the relaxation of the assumption of the rational expectations in both the interest rate and foreign exchange market. The effect of this is two-fold: firstly, ex post and ex ante rates need no longer only differ by a random error, and secondly, a non-zero exchange rate risk premium may exist. Therefore the thesis also derives an ex ante interest rate series and an exchange rate volatility series using the methodology of Mishkin(1984a,b) and a Generalised Autoregressive Conditional Heteroscedasticity framework respectively. Throughout the thesis a parallel hypothesis is considered of whether a distinction could be drawn between investor behaviour in countries with capital market-based financial systems and those with bank-based financial systems. The thesis finds little support, given the assumptions made and dataset used, for the assertion that UK investors are more short-termist than elsewhere and no evidence to support a distinction between investor behaviour across countries

An empirical investigation of technical analysis in fixed income markets

The aim of this thesis is to evaluate the effectiveness of technical analytic indicators in the fixed income markets. Technical analysis is a widely used methodology by investors in the equity and foreign exchange markets, but the empirical evidence on the profltability of technical trading systems in the bond markets is sparse. Therefore, this thesis serves as a coherent and systematic examination of technical trading systems in the government bond futures and bond yield markets. We investigate three aspects of technical analysis. First, we evaluate the profitability of 7,991 technical trading systems in eight bond futures contracts. Our results provide mixed conclusions on the profitability these technical systems, since the results vary across different futures markets, even adjusting for data snooping effects and transaction costs. In addition, we find the profitability of the trading systems has declined in recent periods. Second, we examine the informativeness of technical chart patterns in the government benchmark bond yield and yield spread markets. We apply the nonparametric regression methodology, including the Nadaraya-Watson and local polynomial regression, to identify twelve chart patterns commonly taught by chartists. The empirical results show no incremental information are contained within these chart patterns that investors can systematically exploit to earn excess returns. Furthermore, we find that bond yield spreads are fundamentally different to price series such as equity prices or currencies. Lastly, we categorize and evaluate five type of price gaps in the financial markets for the first time. We apply our price gap categorisation to twenty-eight futures contracts. Our results support the Gap- Fill hypothesis and find that some price gaps may provide additional information to investors by exhibiting returns that are statistically different to the unconditional returns over a short period of time. ՝In conclusion, this thesis provides empirical evidence that broadly support the usage of technical analysis in the financial markets

The Barcelona International Conference on Advances in Statistics (BAS 2012) : Abstracts of communications

Conferència Organitzada per l'Escola Politècnica Superior, Universitat de Vic en col·laboració amb Servei d'Estadística de la Universitat Autònoma de Barcelona i CosmoCaixa Barcelona. Celebrada del 18 al 22 de juny de 2012 a Barcelon

A Comparative Analysis of 30 Bonus-Malus Systems

The automobile third party insurance merit-rating systems of 22 countries are simulated and compared, using as main tools the stationary average premium level, the variability of the policyholders\u27 payments, their elasticity with respect to the claim frequency, and the magnitude of the hunger for bonus. Principal components analysis is used to define an “Index of Toughness” for all systems