A General Framework for Pricing Asian Options Under Markov Processes

  title={A General Framework for Pricing Asian Options Under Markov Processes},
  author={Ning Cai and Yingda Song and Steven Kou},
  journal={Oper. Res.},

A General Valuation Framework for SABR and Stochastic Local Volatility Models

A general framework for the valuation of options in stochastic local volatility models with a general correlation structure, which includes the Stochastic alpha beta structure, is proposed.

Moments of integrated exponential Lévy processes and applications to Asian options pricing

We find explicit formulas for the moments of the time integral of an exponential Lévy process. We consider both the cases of unconditional moments and conditional on the Lévy process level at the

A Markov chain approximation scheme for option pricing under skew diffusions

In this paper, we propose a general valuation framework for option pricing problems related to skew diffusions based on a continuous-time Markov chain approximation to the underlying stochastic

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

Analysis of Markov Chain Approximation for Option Pricing and Hedging: Grid Design and Convergence Behavior

A general method for option pricing and hedging in Markovian models with continuous-state spaces and a key issue for its efficiency is how to design the grid for the Markov chain approximation.

An Efficient and Stable Method for Short Maturity Asian Options

In this paper, we develop a Markov chain‐based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a

Single-Transform Formulas for Pricing Asian Options in a General Approximation Framework under Markov Processes

This note analytically invert the Z -transform and the Laplace transform involved in their final results, respectively, for the discretely and the continuously monitored cases, and obtains explicit single Laplace transforms of option prices.

On "A General Framework for Pricing Asian Options Under Markov Processes"

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general

Transform Analysis for Markov Processes and Applications: An Operator-based Approach

We establish a novel duality relationship between continuous and discrete non-negative additive functionals of stochastic (not necessarily Markovian) processes and their right inverses. For general



Markov Processes: Characterization and Convergence

Introduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random

Pricing Discretely Monitored Asian Options by Maturity Randomization

We present a new methodology based on maturity randomization to price discretely monitored arithmetic Asian options when the underlying asset evolves according to a generic Levy process. Our

Pricing discretely monitored Asian options under Levy processes

Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model

A closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model is obtained and it is shown that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense.


An algorithm for pricing barrier options in one-dimensional Markov models based on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given Markov model.

Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models

A closed-form asymptotic expansion approach to pricing discretely monitored Asian options in general one-dimensional diffusion models that is accurate, fast, and easy to implement for a broad range of diffusion models, even including those violating the regularity conditions.

Pricing American options under variance gamma

We derive a form of the partial integro-differential equation (PIDE) for pricing American options under variance gamma (VG) process. We then develop a numerical algorithm to solve for values of

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.