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View article: The design of optimal re-insurance contracts when losses are clustered
The design of optimal re-insurance contracts when losses are clustered Open
This paper investigates the form of optimal reinsurance contracts in the case of clusters of losses. The underlying insured risk is represented by a marked Hawkes process, where the intensity of the jumps depends not only on the occurrence…
View article: The rough Hawkes Heston stochastic volatility model
The rough Hawkes Heston stochastic volatility model Open
We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes‐…
View article: A dam management problem with energy production as an optimal switching problem
A dam management problem with energy production as an optimal switching problem Open
We consider an optimal stochastic control problem for a dam. Electrical power production is operating under an uncertain setting for electricity market prices and water level which has to be kept under control. Indeed, the water level insi…
View article: Interest Rates Term Structure Models Driven by Hawkes Processes
Interest Rates Term Structure Models Driven by Hawkes Processes Open
This paper includes a marked Hawkes process in the original Heath–Jarrow–Morton (HJM) setup and investigates the impact of this assumption on the pricing of the popular vanilla fixed-income derivatives. Our model exhibits a smile that can …
View article: The rough Hawkes Heston stochastic volatility model
The rough Hawkes Heston stochastic volatility model Open
We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-…
View article: Is the variance swap rate affine in the spot variance? Evidence from S&P500 data
Is the variance swap rate affine in the spot variance? Evidence from S&P500 data Open
We empirically investigate the functional link between the variance swap rate and the spot variance. Using S\&P500 data over the period 2006-2018, we find overwhelming empirical evidence supporting the affine link analytically found by Kal…
View article: Is the variance swap rate affine in the spot variance? Evidence from S&P500 data
Is the variance swap rate affine in the spot variance? Evidence from S&P500 data Open
We empirically investigate the functional link between the variance swap rate and the spot variance. Using S\&P500 data over the period 2006-2018, we find overwhelming empirical evidence supporting the affine link analytically found by Kal…
View article: The Alpha-Heston Stochastic Volatility Model
The Alpha-Heston Stochastic Volatility Model Open
We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by $α$-stable processes with $α\in(1,2]$. In this framework, we examine the implied volatility and its asymptotic beh…
View article: Stochastic Evolution of Distributions - Applications to CDS indices
Stochastic Evolution of Distributions - Applications to CDS indices Open
We use mixture of percentile functions to model credit spread evolution, which allows to obtain a flexible description of credit indices and their components at the same time. We show regularity results in order to extend mixture percentil…
View article: Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling Open
We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-stable L{é}vy process and preserving the branching property. This model allows to describ…
View article: Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling Open
We introduce a class of interest rate models, called the $\alpha$-CIR model, which gives a natural extension of the standard CIR model by adopting the $\alpha$-stable L{\'e}vy process and preserving the branching property. This model allow…