Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities

  title={Pricing methods for $\alpha$-quantile and perpetual early exercise options based on Spitzer identities},
  author={Carolyn E. Phelan and Daniele Marazzina and Guido Germano},
  journal={Quantitative Finance},
  pages={899 - 918}
We present new numerical schemes for pricing perpetual Bermudan and American options as well as α-quantile options. This includes a new direct calculation of the optimal exercise boundary for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener–Hopf method. Our direct calculation of the price of α-quantile options combines for the first time the Dassios–Port–Wendel identity and the Spitzer identities for the extrema of processes… Expand
3 Citations

Topics from this paper

Pricing discretely-monitored double barrier options with small probabilities of execution
A new stochastic simulation-based methodology for pricing discretely-monitored double barrier options and estimating the corresponding probabilities of execution and it is demonstrated clearly that this treatment always outperforms the standard Monte Carlo approach and becomes substantially more efficient when the underlying asset has high volatility and the barriers are set close to the spot price. Expand
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 aExpand
Pricing Discretely-Monitored Double Barrier Options with Small Probabilities of Execution
In this paper, we propose a new stochastic simulation-based methodology for pricing discretely-monitored double barrier options and estimating the corresponding probabilities of execution. We developExpand


Numerical pricing of discrete barrier and lookback options via Laplace transforms
URL: Most contracts of barrier and lookback options specify discrete monitoring policies. However, unlike their continuous counterparts, discrete barrier andExpand
On a new approach to calculating expectations for option pricing
We discuss a simple new approach to calculating expectations of a specific form used for the pricing of derivative assets in financial mathematics. We show that in the ‘vanilla case’, theExpand
Optimal stopping and perpetual options for Lévy processes
  • E. Mordecki
  • Economics, Computer Science
  • Finance Stochastics
  • 2002
A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formulas for perpetual American put options involving the infimum of the after-mentioned process are obtained. Expand
The Wiener–Hopf Technique and Discretely Monitored Path-Dependent Option Pricing
Fusai, Abrahams, and Sgarra (2006) employed the Wiener–Hopf technique to obtain an exact analytic expression for discretely monitored barrier option prices as the solution to the Black–ScholesExpand
Perpetual American Options Under L[e-acute]vy Processes
This work uses Dynkin's formula and the Wiener--Hopf factorization to find the explicit formula for the price of the option for any candidate for the exercise boundary, and by using this explicit representation, selects the optimal solution. Expand
Analyticity of the Wiener-Hopf Factors and Valuation of Exotic Options in Lévy Models
This paper considers the valuation of exotic path-dependent options in Levy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener–HopfExpand
α-Quantile Option in a Jump-Diffusion Economy
In this note, we extend the analysis of the behaviour of the α-quantile option to the case of a contract’s underlying security driven by a Levy process. To this aim, a simulation procedure based onExpand
Fluctuation identities with continuous monitoring and their application to the pricing of barrier options
We present a numerical scheme to calculate fluctuation identities for exponential Levy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper orExpand
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes
In this paper we propose a transform method to compute the prices and Greeks of barrier options driven by a class of Lévy processes. We derive analytical expressions for the Laplace transforms inExpand
Lookback option pricing using the Fourier transform B-spline method
We derive a new, efficient closed-form formula approximating the price of discrete lookback options, whose underlying asset price is driven by an exponential semimartingale process, which includes (Expand