Related papers: Multiscale Stochastic Volatility Model for Derivat…
In this paper we derive a efficient Monte Carlo approximation for the price of path-dependent derivatives under the multiscale stochastic volatility models of Fouque \textit{et al}. Using the formulation of this pricing problem under the…
We present a stochastic local volatility model for derivative contracts on commodity futures. The aim of the model is to be able to recover the prices of derivative claims both on futures contracts and on indices on futures strategies.…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent.…
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
In this article, we analyze two modeling approaches for the pricing of derivative contracts on a commodity index. The first one is a microscopic approach, where the components of the index are modeled individually, and the index price is…
A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations.…
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…
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…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to…
This dissertation develops and justifies a novel method for deriving approximate formulas to estimate two parameters in stochastic volatility diffusion models with exponentially-affine characteristic functions and single- or two-factor…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
Accurately forecasting the price of oil, the world's most actively traded commodity, is of great importance to both academics and practitioners. We contribute by proposing a functional time series based method to model and forecast oil…
The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the…
We present a new model for commodity pricing that enhances accuracy by integrating four distinct risk factors: spot price, stochastic volatility, convenience yield, and stochastic interest rates. While the influence of these four variables…