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In this paper, we price European Call three different option pricing models, where the volatility is dynamically changing i.e. non constant. In stochastic volatility (SV) models for option pricing a closed form approximation technique is…
We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility…
The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
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…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the…
We introduce the Local Occupied Volatility (LOV) model that sits between Dupire's local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the…
We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…
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…
The Local Volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide…
This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared…
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…
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure,…
We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…