1,721,014 research outputs found
Forecasting vital rates by a trimodal extension of the flexible generalized skew normal probability density function
No full textModelling the Chinese crude oil futures returns through a skew‐geometric Brownian motion correlated with the market volatility index process for pricing financial options
No full textIn this paper we model the dynamics of the Chinese crude oil futures returns by using a skew-geometric Brownian motion correlated with the market volatility, which is taken as a square-root stochastic process. We use the OVX index data as proxy for market volatility. We validate the proposed model in terms of accuracy of its calibrations through an in-sample simulation. Instead, out-of-sample simulations are used to show that a correlated skew-geometric Brownian motion is more appropriate for modelling the Chinese returns compared to a single skew-geometric Brownian motion in terms of forecasts. Furthermore, we price an American call option on the Chinese futures by using a recursively scheme based on a closed-form formula, and an alternative Monte Carlo approach, for the related European call option. We show that our call price estimates are very close to market values and our model generally outperforms many benchmarks in literature, such as the Barone-Adesi and Whaley formula and its generalizations
Advanced operator theory for energy market trading: a new framework
No full textThis paper analyzes a parabolic operator L that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with L and derive its explicit analytical representation. The
theoretical framework developed in this study provides a robust foundation for modeling stochastic processes relevant to financial markets. Furthermore, we apply these findings to
energy market trading by developing specialized simulation algorithms and forecasting models. These methodologies were tested across all assets comprising the S&P 500 Energy
Index, evaluating their predictive accuracy and effectiveness in capturing market dynamics.
The empirical analysis demonstrated the practical advantages of employing generalized semigroups in modeling non-Gaussian market behaviors and extreme price fluctuations
Empirical Evidences on the Interconnectedness between Sampling and Asset Returns’ Distributions
Full text linkThe aim of this work was to test how returns are distributed across multiple asset classes, markets and sampling frequency. We examine returns of swaps, equity and bond indices as well as the rescaling by their volatilities over different horizons (since inception to Q2-2020). Contrarily to some literature, we find that the realized distributions of logarithmic returns, scaled or not by the standard deviations, are skewed and that they may be better fitted by t-skew distributions. Our finding holds true across asset classes, maturity and developed and developing markets. This may explain why models based on dynamic conditional score (DCS) have superior performance when the underlying distribution belongs to the t-skew family. Finally, we show how sampling and distribution of returns are strictly connected. This is of great importance as, for example, extrapolating yearly scenarios from daily performances may prove not to be correct
Addressing the financial impact of natural disasters in the era of climate change
No full textThe objective of our study is to predict the financial losses that may result from natural disasters, along with their level of volatility, over a period of 1 to 15 years. Volatility can lead to significant fluctuations in Profit and Loss (P&L) for companies that are affected by unexpected events. To achieve this goal, we created a novel two -factor square -root model that allows us to establish a correlation between the frequency of occurrences and volatility, using correlated Brownian motions. Moreover, we utilized a Generalized Pareto Distribution (GPD) to estimate the maximum potential loss in terms of Value at Risk (VaR) for each specific type of natural disaster. To ensure the reliability of our predictions, we compared our results to those of four reference models and conducted a backtesting analysis. This approach is particularly suitable for insurance companies seeking to maintain stable reserves, but it can also be adapted for any other type of business that is vulnerable to extreme events and aims to safeguard a consistent cash flow for their stakeholders
Some extensions of the Black-Scholes and Cox-Ingersoll-Ross models
Full text linkIn this thesis we will study some financial problems concerning the option pricing in complete and incomplete markets and the bond pricing in the short-term interest rates framework. We start from well known models in pricing options or zero-coupon bonds, as the Black-Scholes model and the Cox-Ingersoll-Ross model and study some their generalizations.
In particular, in the first part of the thesis, we study a generalized Black-Scholes equation to derive explicit or approximate solutions of an option pricing problem in incomplete market where the incompleteness is generated by the presence of a non-traded asset. Our aim is to give a closed form representation of the indifference price by using the analytic tool of (C0) semigroup theory.
The second part of the thesis deals with the problem of forecasting future interest rates from observed financial market data. We propose a new numerical methodology for the CIR framework, which we call the CIR# model, that well fits the term structure of short interest rates as observed in a real market
Credit default swap spreads modeling and forecasting with a stochastic square-root three-factor model
No full textIn this study, we consider the CIR3 model, a three-factor stochastic model with correlated trends and volatilities for modeling and forecasting credit default swap (CDS) spreads. After recalling existence and uniqueness results, together with a generalized Feller condition to ensure positivity, we use a Lamperti-type transform to rewrite our SDEs system in a form in which the stochastic part of the leading process is uncorrelated with those of its mean and volatility processes. Finally, we calibrate the model through the estimating function approach for ergodic diffusions and simulate the CDS prices by discretizing our (transformed) system. These findings contribute to a deeper understanding of stochastic models with correlated trends and volatilities, with applications in pricing, trading and risk assessment
Cost and severity of natural catastrophes in extreme events: implications for society and insurances
No full textThis research introduces a novel approach to estimating the economic impact of natural catastrophes (NatCats) by correlating log-loss severity, modeled using a Vasicek process, with the frequency of occurrences following a geometric Brownian motion. The novelty lies in combining these two processes to dynamically capture the relationship between the frequency and severity of catastrophic events, which provides a more comprehensive risk assessment. Unlike traditional models, this approach accounts for the joint dynamics of both losses and occurrences, offering a refined method for pricing tail events in NatCat insurance. The model’s integration of these correlated processes enables more accurate pricing, particularly for extreme events, thus enhancing the ability of the insurance and reinsurance industries to assess and manage catastrophic risks. The model aligns risks with at-risk assets, helping policymakers prepare for and manage the financial challenges of natural disasters. Its parsimony, relying solely on occurrence and severity, allows for efficient and robust risk assessment, making it effective even with limited data
Advanced Operator Theory for Energy Market Trading: A New Framework
No full textThis paper analyzes a parabolic operator (Formula presented.) that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with (Formula presented.) and derive its explicit analytical representation. The theoretical framework developed in this study provides a robust foundation for modeling stochastic processes relevant to financial markets. Furthermore, we apply these findings to energy market trading by developing specialized simulation algorithms and forecasting models. These methodologies were tested across all assets comprising the S&P 500 Energy Index, evaluating their predictive accuracy and effectiveness in capturing market dynamics. The empirical analysis demonstrated the practical advantages of employing generalized semigroups in modeling non-Gaussian market behaviors and extreme price fluctuations
Time series forecasting with the CIR# model: from hectic markets sentiments to regular seasonal tourism
Full text linkThis research aims to propose the so-called CIR#, which takes its cue from the well- known Cox-Ingersoll-Ross (CIR) model originally devised for pricing, as a general econometric model. To this end, we present the results on two very different time series such as Polish interest rates (subject to market sentiments) and seasonal tourism (subject to pandemic lock-down measures). For interest rates, as reference models, we consider an improved version of the CIR model (denoted CIRadj), the Hull and White model, the exponentially weighted moving average (EWMA) which is often adopted whenever no structure is assumed in the data and a popular machine learning model such as the short-term memory network (LSTM). For tourism, as a benchmark, we consider seasonal autoregressive integrated moving average (SARIMA) complemented by the generalized autoregressive conditional heteroskedasticity (GARCH) for modelling the variance, the classic Holt-Winters model and the aforementioned LSTM. Results support the claim that the CIR# performs better than the other models in all considered cases being able to deal with erratic behaviour in data
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