Related papers: Heat modulated affine stochastic volatility models…
We introduce the Volterra Stein-Stein model with stochastic interest rates, where both volatility and interest rates are driven by correlated Gaussian Volterra processes. This framework unifies various well-known Markovian and non-Markovian…
In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…
We study the forward price dynamics in commodity markets realized as a process with values in a Hilbert space of absolutely continuous functions defined by Filipovi\'c. The forward dynamics are defined as the mild solution of a certain…
This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous.…
Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.
Let $\sigma_t(x)$ denote the implied volatility at maturity $t$ for a strike $K=S_0 e^{xt}$, where $x\in\bbR$ and $S_0$ is the current value of the underlying. We show that $\sigma_t(x)$ has a uniform (in $x$) limit as maturity $t$ tends to…
In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process…
Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two…
Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to…
This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo…
This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts…
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…
For a commodity spot price dynamics given by an Ornstein-Uhlenbeck process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and…
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with…
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how…
We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterized by the affine form of their cumulant…
We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions…
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic.…
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for…
In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…