Related papers: A General Approach for Lookback Option Pricing und…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general…
Markovian-regime-switching (MRS) models are commonly used for modelling economic time series, including electricity prices where independent regime models are used, since they can more accurately and succinctly capture electricity price…
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to…
Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a…
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
We propose a general framework to study last passage times, suprema and drawdowns of a large class of stochastic processes. A central role in our approach is played by processes of class Sigma. After investigating convergence properties and…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
In this study, we propose a new formula for spread option pricing with the dependence of two assets described by a copula function. The advantage of the proposed method is that it requires only the numerical evaluation of a one-dimensional…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed…
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…
We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a…
In this article, we study the rate of convergence of prices when a model is approximated by some simplified model. We also provide a method how explicit error formula for more general options can be obtained if such formula is available for…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
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…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
Evaluating moving average options is a tough computational challenge for the energy and commodity market as the payoff of the option depends on the prices of a certain underlying observed on a moving window so, when a long window is…
We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the…
We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates…