Related papers: SPX, VIX and scale-invariant LSV\footnote{Local St…
Joint calibration to SPX and VIX market data is a delicate task that requires sophisticated modeling and incurs significant computational costs. The latter is especially true when pricing of volatility derivatives hinges on nested Monte…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the strong existence and…
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.…
Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic…
This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are…
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al.…
The Heston stochastic volatility model is arguably, the most popular stochastic volatility model used to price and risk manage exotic derivatives. In spite of this, it is not necessarily easy to calibrate to the market and obtain stable…
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one…
Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…
In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…
We consider an investor who seeks to maximize her expected utility derived from her terminal wealth relative to the maximum performance achieved over a fixed time horizon, and under a portfolio drawdown constraint, in a market with local…
The Bass Local Volatility Model (Bass-LV), as studied in [Conze and Henry-Labordere, 2021], stands out for its ability to eliminate the need for interpolation between maturities. This offers a significant advantage over traditional LV…
The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of…
In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the…
Financial markets are a complex dynamical system. The complexity comes from the interaction between a market and its participants, in other words, the integrated outcome of activities of the entire participants determines the markets trend,…
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is…