Related papers: European Option Pricing Under Generalized Tempered…
Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on…
This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin…
We present an alternative formula to price European options through cosine series expansions, under models with a known characteristic function such as the Heston stochastic volatility model. It is more robust across strikes and as fast as…
We present a generative framework for pricing European-style basket options by learning the conditional terminal distribution of the log arithmetic-weighted basket return. A Mixture Density Network (MDN) maps time-varying market inputs…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
The paper summarizes key results of the benchmark approach with a focus on the concept of benchmark-neutral pricing. It applies these results to the pricing of an extreme-maturity European put option on a well-diversified stock index. The…
This paper provides evidence that stock returns, after truncation, might be modeled by a special type of continuous mixtures or normals, so-called $q$-Gaussians. Negative binomial distributions might model the counts for extreme returns. A…
A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…
Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…
We consider option pricing using replicating binomial trees, with a two fold purpose. The first is to introduce ESG valuation into option pricing. We explore this in a number of scenarios, including enhancement of yield due to trader…
We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations. We also provide precise boundaries for the…
A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is…
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback.…
This work studies the valuation of currency options in markets suffering from a financial crisis. We consider a European option where the underlying asset is a foreign currency. We assume that the value of the underlying asset is a…
We establish an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology is based on expansions of the mixing representation of the put option…
The Constant Elasticity of Variance (CEV) model significantly outperforms the Black-Scholes (BS) model in forecasting both prices and options. Furthermore, the CEV model has a marked advantage in capturing basic empirical regularities such…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of…
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…
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…