• Corpus ID: 15343762

Option Pricing with Levy-Stable Processes

  title={Option Pricing with Levy-Stable Processes},
  author={{\'A}lvaro Cartea and Sam D. Howison},
In this paper we show how to calculate European-style option prices when the log-stock and stock returns processes follow a symmetric Levy-Stable process. We extend our results to price European-style options when the log-stock process follows a skewed Levy-Stable process. 

Figures from this paper

Option pricing with Lévy-Stable processes generated by Lévy-Stable integrated variance

We show how to calculate European-style option prices when the log-stock price process follows a Lévy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter −1 ≤ β ≤ 1. Key to our

The Optimal Hedge Ratio in Option Pricing: The Case of Exponentially Truncated Lévy Stable Distribution

In financial option pricing, the stable Levy framework is a problematic issue because of its (theoretical) infinite invariance. This paper deals with the integration of these processes into option

The practical use of the general formula of the optimal hedge ratio in option pricing: an example of the generalized model of an exponentially truncated Levy stable distribution

  • Bucsa
  • Mathematics, Economics
  • 2013
In financial option pricing, the optimal hedge ratio is a well known concept. This paper uses this concept within the context of an exponentially truncated Lévy stable distribution.

Valuation of Hybrid Capital Instruments using Lévy Processes

This master thesis introduces a pricing procedure for hybrid capital instruments issued by insurance companies when the underlying interest rate process is modeled by α−stable Lévy processes, as

Using Exponential Lévy Models to Study Implied Volatility patterns for Electricity Options

German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after

A Functional Central Limit Theorem for the Realized Power Variation of Integrated Stable Processes

Abstract In this article, we consider the asymptotic behavior of the realized power variation of processes of the form , where S α is an α-stable process with index of stability 0 < α < 2 and u is a

Modeling of financial processes with a space-time fractional diffusion equation of varying order

Abstract In this paper, a new model for financial processes in form of a space-time fractional diffusion equation of varying order is introduced, analyzed, and applied for some financial data. While

Rates for branching particle approximations of continuous-discrete filters

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t → Xt is a Markov process and we wish to

Small noise analysis of time-periodic bistable jump diffusion

Das kontraintuitive Phanomen der Stochastischen Resonanz beschreibt das Verstarken schwacher periodischer Eingangssignale von nicht linearen Systemen durch Hinzufugen von Rauschtermen mit geringer



Distinguished Limits of Levy-Stable Processes, and Applications to Option Pricing

In this paper we derive analytic expressions for the value of European Put and Call options when the stock process follows an exponential Levy-Stable process. It is shown that the generalised

Derivatives in Financial Markets with Stochastic Volatility

1. The Black-Scholes theory of derivative pricing 2. Introduction to stochastic volatility models 3. Scales in mean-reverting stochastic volatility 4. Tools for estimating the rate of mean-reversion

The Pricing of Options on Assets with Stochastic Volatilities

One option-pricing problem which has hitherto been unsolved is the pricing of European call on an asset which has a stochastic volatility. This paper examines this problem. The option price is

Portfolio selection with stable distributed returns

This paper examines empirical differences among the optimal allocations obtained with the Gaussian and the stable non-Gaussian distributional assumption for the financial returns and compares performances among stable multivariate models.

Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type

Stochastic volatility models of the Ornstein‐Uhlenbeck type possess authentic capability of capturing some stylized features of financial time series. In this work we investigate this class of models

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

Continuous Time Finance

This chapter gives a brief survey of continuous time finance. We categorize diffusion models according to the nature of their volatility coefficient. Models whose volatility coefficient does not

The impact of fat tailed returns on asset allocation

Analyzes the asset allocation problem of an investor who can invest in equity and cash when there is time variation in expected returns on the equity and suggests that asset allocation may be up to 20% different depending on the utility function and the risk aversion level of the investor.

Option valuation using the fast Fourier transform

This paper shows how the fast Fourier Transform may be used to value options when the characteristic function of the return is known analytically.