Related papers: Option pricing in bilateral Gamma stock models
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…
We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent…
We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path…
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…
The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distribution. However, when the problem exhibits certain kind of…
We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. 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…
We present a method based on optimal transport to remove arbitrage opportunities within a finite set of option prices. The method is notably intended for regulatory stress-tests, which require applying significant local distortions to…
This paper focus on pricing exchange option based on copulas by MCMC algorithm. Initially, we introduce the methodologies concerned about risk-netural pricing, copulas and MCMC algorithm. After the basic knowledge, we compare the option…
In this article, we investigate the behavior of long-term options. In many cases, option prices follow an exponential decay (or growth) rate for further maturity dates. We determine under what conditions option prices are characterized by…
We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We present an approximation method based on the mixing formula (Hull & White 1987, Romano & Touzi 1997) for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option…
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the "curse of dimensionality" can be alleviated for the computation of Bermudan option prices with the Monte…
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are…
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…
The pricing of currency options is largely dependent on the dynamic relationship between a pair of currencies. Typically, the pricing of options with payoffs dependent on multi-assets becomes tricky for reasons such as the non-Gaussian…