Related papers: Superposition of COGARCH processes
The problem of European-style option pricing in time-changed L\'{e}vy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
Cascades of events and extreme occurrences have garnered significant attention across diverse domains such as financial markets, seismology, and social physics. Such events can stem either from the internal dynamics inherent to the system…
The tail behavior of aggregates of heavy-tailed random vectors is known to be determined by the so-called principle of "one large jump'', be it for finite sums, random sums, or, L\'evy processes. We establish that, in fact, a more general…
We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of…
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…
In this paper we estimate the conditional value-at-risk by fitting different multivariate parametric models capturing some stylized facts about multivariate financial time series of equity returns: heavy tails, negative skew, asymmetric…
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset…
An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically…
Conditional independence and graphical models are crucial concepts for sparsity and statistical modeling in higher dimensions. For L\'evy processes, a widely applied class of stochastic processes, these notions have not been studied. By the…
The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log…
We show that the quotient of Levy processes of jump-diffusion type has a fat-tailed distribution. An application is to price theory in economics. We show that fat tails arise endogenously from modeling of price change based on an excess…
We study the behavior of a real-valued and unobservable process (Y_t) under an extreme event of a related process (X_t) that is observable. Our analysis is motivated by the well-known GARCH model which represents two such sequences, i.e.…
Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…
We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated L\'evy flight recently introduced by us and (ii) the…
Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous…
The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…
We introduce an algorithm for the pricing of finite expiry American options driven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm…