author={Aleksandar Mijatovi{\'c} and Martijn Pistorius},
  journal={Mathematical Finance},
In this paper, we present an algorithm for pricing barrier options in one‐dimensional Markov models. The approach rests on the construction of an approximating continuous‐time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, including a local Lévy process and a local volatility jump‐diffusion. We also provide a convergence proof and error estimates for this algorithm. 
Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing
The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques, also elegantly connected to partial differential equation (PDE) approaches.
A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models
  • D. Nguyen
  • Mathematics
    International Journal of Financial Engineering
  • 2018
We develop a unified hybrid valuation framework for computing option values under stochastic volatility (SV) models with a jump component. The proposed method originates from the tree method and
Convergence Analysis for Continuous-Time Markov Chain Approximation of Stochastic Local Volatility Models: Option Pricing and Greeks
This paper establishes the precise second order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing options and calculating its Greeks under the general
Stochastic Processes in Finance
Stochastic processes arising in the description of the risk-neutral evolution of equity prices are reviewed. Starting with Brownian motion, I review extensions to Levy and Sato processes. These
Pricing exotic options under regime switching: A Fourier transform method
This paper considers the valuation of exotic options (i.e. digital, barrier, and lookback options) in a Markovian, regime-switching, Black-Scholes model. In Fourier space, analytical expressions for
A General Approach for Lookback Option Pricing under Markov Models
We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage
Markov Chain Approximation Method for Pricing Barrier Options with Stochastic Volatility and Jump
The purpose of this paper is to provide an efficient pricing method for barrier option with stochastic volatility and jump risk. First, by constructing a nonuniform variance grid and using local
Pricing Discretely Monitored Barrier Options under Markov Processes through Markov Chain Approximation
The authors propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options with an underlying asset that evolves according to a
American Option Valuation under Continuous-Time Markov Chains
This paper is concerned with the solution of the optimal stopping problem associated to the value of American options driven by continuous-time Markov chains. The value-function of an American option
Pricing Discretely Monitored Barrier Options Under Markov Processes Using a Markov Chain Approximation
We propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options whose underlying asset evolves according to a generic one-dimensional


Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing
This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly
Pricing Discretely Monitored Barrier Options by a Markov Chain
Barrier options have become commonplace in the option market, and a variety of other financial contracts may also be thought of in terms of barrier options. But the existence of a price barrier can
Valuation of Continuously Monitored Double Barrier Options and Related Securities
In this article we apply Carr's randomization approximation and the operator form of the Wiener-Hopf method to double barrier options in continuous time. Each step in the resulting backward induction
A Stochastic Volatility Model for Risk-Reversals in Foreign Exchange
It is a widely recognized fact that risk-reversals play a central role in the pricing of derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary
From local volatility to local Lévy models
We define the class of local Lévy processes. These are Lévy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level
Integro-differential equations for option prices in exponential Lévy models
Abstract.We explore the precise link between option prices in exponential Lévy models and the related partial integro-differential equations (PIDEs) in the case of European options and options with
Pricing Options With Curved Boundaries
This paper provides a general valuation method for the European options whose payoff is restricted by curved boundaries contractually set on the underlying asset price process when it follows the
A Jump-Diffusion Model for Option Pricing
  • S. Kou
  • Economics
    Manag. Sci.
  • 2002
A double exponential jump-diffusion model is proposed, for the purpose of option pricing, which is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options.
The fine structure of asset returns: an empirical investigation
We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and
Analytical Pricing of Double-Barrier Options under a Double-Exponential Jump Diffusion Process: Applications of Laplace Transform
We derive explicit formulas for pricing double (single) barrier and touch options with time-dependent rebates assuming that the asset price follows a double-exponential jump diffusion process. We