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We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time,…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models…
This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional…
We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by…
We extend the approach of Carr, Itkin and Muravey, 2021 for getting semi-analytical prices of barrier options for the time-dependent Heston model with time-dependent barriers by applying it to the so-called $\lambda$-SABR stochastic…
This paper introduces a semi-analytical method for pricing American options on assets (stocks, ETFs) that pay discrete and/or continuous dividends. The problem is notoriously complex because discrete dividends create abrupt price drops and…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform…
The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form…
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…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier…
The paper demonstrates that a pure-diffusion 3/2 model is able to capture the observed upward-sloping implied volatility skew in VIX options. This observation contradicts a common perception in the literature that jumps are required for the…
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…
Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely…
In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in…
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…
Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing…
We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent…