Related papers: Higher order approximation of call option prices u…
In this paper we present a new method to compute the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility of Fouque \textit{et al.} (2011, CUP). It provides an alternative…
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is…
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…
In this paper an improved Cuckoo Search Algorithm is developed to allow for an efficient and robust calibration of the Heston option pricing model for American options. Calibration of stochastic volatility models like the Heston is…
Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able…
This paper investigates asymptotically optimal importance sampling (IS) schemes for pricing European call options under the Heston stochastic volatility model. We focus on two distinct rare-event regimes where standard Monte Carlo methods…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise…
We price American options using kernel-based approximations of the Volterra Heston model. We choose these approximations because they allow simulation-based techniques for pricing. We prove the convergence of American option prices in the…
We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random…
We propose a convolution-FFT method for pricing European options under the Heston model that leverages a continuously differentiable representation of the joint characteristic function. Unlike existing Fourier-based methods that rely on…
This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and…
Two novel closed-form formulas for the price of barrier options in stochastic volatility models with zero interest rate and dividend yield but nonzero correlation between the asset and its instantaneous volatility are derived. The first is…
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…
In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the…
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…
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…
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and…
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…
For the Barndorff-Nielsen and Shephard model, we present approximate expressions of call option prices based on the decomposition formula developed by Arai (2021). Besides, some numerical experiments are also implemented to make sure how…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…