Related papers: American options in time-dependent one-factor mode…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
The solution of option-pricing problems may turn out to be computationally demanding due to non-linear and path-dependent payoffs, the high dimensionality arising from multiple underlying assets, and sophisticated models of price dynamics.…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume…
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these…
We propose a general framework of European power option pricing under two different market assumptions about extended Vasic\v{e}k interest rate process and exponential Ornstein-Uhlenbeck asset process with continuous dividend as underlying,…
Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show…
Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices. The formulas are given via…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow…
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium…
Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…
The correlated stochastic volatility models constitute a natural extension of the Black and Scholes-Merton framework: here the volatility is not a constant, but a stochastic process correlated with the price log-return one. At present,…
We present new numerical schemes for pricing perpetual Bermudan and American options as well as $\alpha$-quantile options. This includes a new direct calculation of the optimal exercise barrier for early-exercise options. Our approach is…
We study the binomial, trinomial, and Black-Scholes-Merton models of option pricing. We present fast parallel discrete-time finite-difference algorithms for American call option pricing under the binomial and trinomial models and American…
Developments in finance industry and academic research has led to innovative financial products. This paper presents an alternative approach to price American options. Our approach utilizes famous \cite{heath1992bond} ("HJM") technique to…
This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…
We study the valuation of an American put option with a random time horizon given by the last exit time of the underlying asset from a fixed level. Since this random time is not a stopping time, the problem falls outside the classical…
This paper develops general approaches for pricing various types of American-style Parisian options (down-in/-out, perpetual/finite-maturity) with general payoff functions based on continuous-time Markov chain (CTMC) approximation under…