1,720,971 research outputs found
An investigation of the Volatility Adjustment
No full textWe use market data to reconstruct the volatility adjustment, a component of the Solvency II framework designed to mitigate the impact of market risk on insurance liabilities, of different countries on a monthly basis. Only partially in agreement with the regulation, we observe that the volatility adjustment, especially the proposed new mechanism, is not affected by credit quality, illiquidity of bonds, and investors' risk appetite, but by turbulence in financial markets and equity market performance. We also show that the new mechanism proposed by EIOPA performs differently with respect to the one in force at the time of writing the current paper, yielding higher and smoother values and providing a relief to insurance companies on the Solvency II capital requirement front
Constructing a class of stochastic volatility models: empirical investigation with VIX data
No full textWe propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the
time-varying higher moments observed in financial series. Three desirable results are obtained. First, we
have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for
option prices as in Heston and Nandi [2000]. Second, we reproduce some features of the VIX Index. Finally,
we derive a simple formula for the VIX index and use it for option pricing
Option pricing in an exponential MixedTS Lévy process
Full text linkIn this paper we present an option pricing model based on the assumption that the underlying asset price is an exponential Mixed Tempered Stable Lévy process. We also introduce a new R package called PricingMixedTS that allows the user to calibrate this model using procedures based on loss or likelihood function
The determinants of lapse rates in the Italian life insurance market
No full textWe investigate the drivers of lapses in life insurance contracts of a large Italian insurance company. We consider both traditional (with profit or participating) and unit-linked policies. We develop two different types of analyses. First of all, we investigate the determinants of lapse decisions by policyholders looking at microdata on each contract and some macroeconomic variables. Then, through a panel study, we investigate the role of macroeconomic variables on lapses at the regional level. We observe that policy features affecting lapses of the two types of contracts are quite different. Only for the contracts stipulated few years before, we find weak evidence supporting the Interest Rate Hypothesis, i.e. a positive correlation between interest and lapse rates. Instead, there is some positive evidence that lapse rates are positively related to personal financial/economic difficulties (emergency fund hypothesis)
A Hawkes model with CARMA(p,q) intensity
Full text linkIn this paper we introduce a new model, named CARMA(p,q)-Hawkes, as the Hawkes model with exponential
kernel implies a strictly decreasing behavior of the autocorrelation function while empirical evidences reject
its monotonicity. The proposed model is a Hawkes process where the intensity follows a Continuous Time
Autoregressive Moving Average (CARMA) process. We also study the conditions for the stationarity and the
positivity of the intensity and the strong mixing property for the increments. Furthermore, we present two
estimation case studies based respectively on the likelihood and on the autocorrelation function
Discrete-Time Approximation of a Cogarch(p,q) Model and its Estimation
Full text linkIn this article, we construct a sequence of discrete-time stochastic processes that converges in the Skorokhod metric to aCOGARCH(p, q) model. The result is useful for the estimation of the COGARCH(p, q) on irregularly spaced time series data.The proposed estimation procedure is based on the maximization of a pseudo log-likelihood function and is implemented inthe yuima package
Portfolio selection with independent component analysis
No full textWe analyze a methodology for portfolio selection based on the independent component analysis. In this paper parametric and non-parametric approaches are used for capturing the behavior of independent components that generate the distribution of asset returns. Although the setup is quite general, we focus mainly on the numerical issues encountered for parametric models and suggest the inclusion of a penalty function in the optimization problem
Sensitivity analysis of Mixed Tempered Stable parameters with implications in portfolio optimization
Full text linkThis paper investigates the use, in practical financial problems, of the Mixed Tempered Stable distribution both in its univariate and multivariate formulation. In the univariate context, we study the dependence of a given coherent risk measure on the distribution parameters. The latter allows to identify the parameters that seem to have a greater influence on the given measure of risk. The multivariate Mixed Tempered Stable distribution enters in a portfolio optimization problem built considering a real market dataset of seventeen hedge fund indexes. We combine the flexibility of the multivariate Mixed Tempered Stable distribution, in capturing different tail behaviors, with the ability of the ARMA-GARCH model in capturing the time dependence observed in the data
Generalized linear models and machine learning for lapse rate estimation : a comparison
No full textLAUREA MAGISTRALEQuesta tesi magistrale è nata durante un periodo di stage che ho svolto presso
una compagnia assicurativa. Ho preso parte ad un gruppo di data scientists per
un periodo di circa sei mesi e la mia principale attività consisteva nell’utilizzo di
statistica multivariata per costruire modelli predittivi.
I Modelli Lineari Generalizzati rappresentano lo stato dell’arte per quanto riguarda
il mondo assicurativo. Sono impiegati per risolvere varie tipologie di problemi come
il calcolo del premio tecnico in differenti tipi di polizza o la stima della probabilità
di mantenere un cliente o acquisirne uno nuovo. Come accade nei modelli lineari
classici, anche nei Modelli Lineari Generalizzati c’è una variabile risposta e
alcune variabili con funzione di regressori. La differenza fra i due approcci è che,
usando i Modelli Lineari Generalizzati, il modello costruito come combinazione
lineare dei regressori va a modelllizzare una funzione della media della variabile
risposta, non la sua media. Inoltre con i Modelli Lineari Generalizzati, la variabile
risposta ha una distribuzione che fa parte della Famiglia Esponenziale come ad
esempio le distribuzioni Normale, Esponenziale, Binomiale o Poisson. Il principale
svantaggio derivante dall’utilizzo dei Modelli Lineari Generalizzati è che l’ipotesi
sulla distribuzione non è sempre verificata e si ottengono quindi modelli con scarsa
performance.
Un problema che ha recentemente guadagnato interesse nel mondo assicurativo
è la stima del tasso di abbandono. Quest’ultimo rappresenta la probabilità che,
per qualche ragione, un cliente abbandoni la polizza sottoscritta con la compagnia
assicurativa.
Lo scopo di questa tesi è capire se i Modelli Lineari Generalizzati rimangono il
metodo più adatto anche per questo problema. I risultati ottenuti con i Modelli
Lineari Generalizzati per la stima del tasso di abbandono vengono quindi confrontati
con quelli ricavati tramite una delle più recenti tecniche di Machine Learning,
vale a dire l’algoritmo eXtreme Gradient Boosting (XGBoost). Il paragone
ci permette di concludere che l’approccio basato sul Machine Learning raggiunge
una perfomance migliore del Modello Lineare Generalizzato sull’insieme test considerato.
La tesi è organizzata come segue:
Nel Capitolo 1, vengono descritti i principali tratti della normativa che attualmente
regola i requisiti di solvibilità delle compagnie di assicurazione: la direttiva Solvency II.
Nel Capitolo 2, sono invece presentate in dettaglio la struttura e le caratteristiche
dei Modelli Lineari Generalizzati.
Il Capitolo 3 contiene un primo esempio di tecnica di Machine Learning: gli alberi
di classificazione e regressione (CARTs).
Nel Capitolo 4, consideriamo il passaggio dai CARTs all’apprendimento ensemble,
illustrando vari esempi di quest’ultimo tra cui l’algoritmo eXtreme Gradient
Boosting (XGBoost) in quanto verrà poi utilizzato nel nostro specifico caso.
Nel Capitolo 5, consideriamo alcune metriche utili per valutare la performance di
un modello e confrontare i risultati raggiunti con modelli diversi.
Il Capitolo 6 rappresenta il nucleo di questa tesi: viene qui presentato il caso di
studio definendo nel dettaglio il problema considerato. Inoltre viene descritto il
data set utilizzato per l’analisi.
Nel Capitolo 7, l’output generato da un Modello Lineare Generalizzato per la
stima del tasso d’abbandono viene confrontato con il risultato ottenuto dall’utilizzo
dell’algoritmo eXtreme Gradient Boosting. Per il paragone, vengono sfruttate le
metriche introdotte nel Capitolo 5.
Infine, il Capitolo 8, presenta le conclusioni del lavoro svolto e suggerimenti per
possibili lavori futuri.This master thesis was born while working as an intern in an insurance company.
I joined a team of data scientists for a period of six months and my main activity
was exploiting multivariate statistics to build predictive models.
Generalized Linear Models (GLMs) are the state-of-the-art techniques commonly
used in the insurance world. They are employed to solve different kind of problems
such as the definition of the technical premium of different warranties or the
estimation of the probability of retention and conversion of an insurance policy.
As with the classic Linear Models, also in Generalized Linear Models there is a
response variable and some predictor variables. The difference is that using GLMs,
we model a function of the mean of the response variable (not its mean) as a linear
combination of the features. With GLMs, the response variable comes from an exponential
family distribution such as Normal, Exponential, Binomial or Poisson.
The main drawback of using GLMs is that sometimes this hypothesis may not
hold resulting in poor models’ performances.
A problem that has recently gained interest in the insurance world is the estimation
of the Lapse Rate. It represents the probability that, for some reasons, a
customer will drop the contract with the insurance company.
We want to understand whether GLMs are still the most suitable models for this
problem.
In this thesis, the results obtained with Generalized Linear Models for the estimation
of the Lapse Rate are compared with the ones given by the eXtreme
Gradient Boosting (XGBoost) algorithm, one of the most recent Machine Learning
techniques. We conclude that the Machine Learning-based approach is able to
perform better than Generalized Linear Models on the available test set.
The thesis is organized as follows:
In Chapter 1, we describe the main characteristics of the directive that nowadays
regulates solvency requirements for insurance companies: Solvency II directive.
In Chapter 2, the structure and the characteristics of Generalized Linear Models
are presented in details.
In Chapter 3, we focus on the first example of a Machine Learning technique: Classification and Regression Trees.
In Chapter 4, we consider the development of CARTs to Ensemble Methods. We
illustrate different instances of ensemble methods concluding with the eXtreme
Gradient Boosting algorithm (XGBoost) since it is the one used in our specific
case.
In Chapter 5, we consider some evaluation metrics useful to asses the performance
of a model and to compare results achieved with different methods.
Chapter 6 represents the core of the thesis: here the case study is reported along
with the definition of the considered problem. We also give a brief description of
the data set used for our purpose.
In Chapter 7, we compare the results obtained with Generalized Linear Models
against the ones coming from eXtreme Gradient Boosting algorithm. To do this,
we exploit the metrics introduced in Chapter 5.
Finally, in Chapter 8, we report the conclusions and possible future works that
can be done
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