Related papers: Option prices in stochastic volatility models

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…

We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…

We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…

The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the…

We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston…

We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this…

Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…

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…

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…

Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of…

This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and…

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…

In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options…

It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work…

This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the…

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…

Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the…

We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation…