Meixner Model Research Articles

Cliquet option pricing with Meixner processes

We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner--L\'{e}vy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the cliquet option price by using the probability distribution function of the driving Meixner--L\'{e}vy process and by an application of Fourier transform techniques. In an introductory section, we compile various facts on the Meixner distribution and the related class of Meixner--L\'{e}vy processes. We also propose a customized measure change preserving the Meixner distribution of any Meixner process.

Barrier style contracts under Lévy processes once again

In this paper we present new pricing formulas for some Barrier style contracts of European type when the underlying process is driven by an important class of Levy processes, which includes CGMY model, generalized hyperbolic Model and Meixner Model, when no symmetry properties are assumed, complementing in this way previous findings in Fajardo (J Bank Financ 53:179–187, 2015). Also, we show how to implement our new formulas.

Evaluation of new flux attribution methods for mapping N 2 O emissions at the landscape scale

Abstract The spatial variability of soil nitrous oxide (N 2 O) fluxes is large − regardless of the study scale − resulting in very large uncertainties in soil N 2 O emission assessments. The objectives of this study were to assess the N 2 O flux at the landscape scale by coupling the results of measurements performed at different scales and to propose a method for obtaining emission maps based on these results. During a 2-month campaign (mid-March to mid-May 2015), N 2 O fluxes were measured in a small cropland area (∼km 2 ) (i) continuously at the plot scale using automatic chambers in a wheat field, (ii) punctually on a group of 16 plots including different types of soils and crops using a mobile chamber (fast-box), and (iii) continuously at the landscape scale by eddy covariance using a 15-m height mast. The soil properties were measured at all sites to provide a better understanding of the factors controlling the variability of the N 2 O flux. To map the N 2 O emissions of the entire area, two flux attribution methods were evaluated which allowed estimating the N 2 O flux of each field during the whole period. These methods used a footprint model in combination with fast-box measurements over each crop type to determine the contribution of each field to the flux measured at the eddy covariance mast. Two footprint models were compared (the FIDES, and the Kormann and Meixner models) and two hypotheses on the dependency of N 2 O emissions on crop distribution and soil nitrate contents were tested. Automatic chambers were used to evaluate the attribution methods. The N 2 O fluxes measured by the different methods showed good agreement in magnitude and temporal dynamics, especially when the automatic chambers were in the eddy covariance mast footprint. Overall, the mean measured N 2 O emission was 53 ± 6 μg N N 2 O m −2 h −1 for the automatic chambers, 45 ± 7 N N 2 O m −2 h −1 for the eddy covariance system and 37 ± 9 N N 2 O m −2 h −1 for the fast-box, for periods when both automatic measurement systems were functioning. The N 2 O fluxes measured by the automatic chambers and the fast-box were positively correlated with soil humidity (p 2 O than wheat and rapeseed fields, and much more than forests. Over the whole area during the 2-month experimental period, the N 2 O flux varied from 0.18 to 0.44 kg N N 2 O ha −1 month −1 depending on the attribution method and footprint model. The simplest flux attribution method, taking only land use into account, showed very good agreement with the field measurements provided by the automated chambers (10%–13% difference on the mean flux). Our study demonstrates the potential of flux attribution methods for catching spatial variability of soil N 2 O emission at the landscape scale and reducing uncertainties in its evaluation.

Cliquet Option Pricing with Meixner Processes

We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner-Levy process yielding Meixner distributed log-returns. In this setting, we infer semi-analytic expressions for the cliquet option price by using the probability distribution function of the driving Meixner-Levy process and by an application of Fourier transform techniques. In an introductory section, we compile various facts on the Meixner distribution and the related class of Meixner-Levy processes. We also propose a customized measure change preserving the Meixner distribution of any Meixner process.

PARAMETRIC COMPLEXITY REDUCTION OF DISCRETE-TIME LINEAR SYSTEMS HAVING A SLOW INITIAL ONSET OR DELAY

This paper is concerned with an optimal expansion of linear discrete time systems on Meixner functions. Many orthogonal functions have been widely used to reduce the model parameter number such as Laguerre functions, Kautz functions and orthogonal basis functions. However, when the system has a slow initial onset or delay, Meixner functions, which have a slow start, are more suitable in terms of providing a more accurate approximation to the system. The optimal approximation of Meixner model is ensured once the pole characterizing the Meixner functions is set to its optimal value. In this paper, a new recursive representation of Meixner model is proposed. Further we propose, from input/output measurements, an iterative pole optimization algorithm of the Meixner pole functions. The method consists in applying the Newton-Raphson’s technique in which their elements are expressed analytically by using the derivative of the Meixner functions. Simulation results show the effectiveness of the proposed optimal modeling method.

Power Style Contracts Under Asymmetric LLvy Processes

In this paper we present new pricing formulas for some Power style contracts of European type when the underlying process is driven by an important class of L´evy processes, which includes CGMY model, generalized hyperbolic Model and Meixner Model, when no symmetry properties are assumed, extending and complementing in this way previous findings in the literature. Also, we show how to implement our new formulas.

Exchange Rates Forecasting: Can Jump Models Combined with Macroeconomic Fundamentals Help?

Connection between macroeconomic variables and foreign exchange (FX) rates evaluated in the context of out-of-sample forecasting is a well-known problem in economics. We propose a method that utilizes stochastic models based on jump processes (namely the normal inverse Gaussian and Meixner models), combines them with macroeconomic fundamentals, and using a moving (rolling or recursive) regularized estimation procedure produces forecasts of FX rates. These are compared to benchmark models, namely the direct forecast and the Gauss model forecast. Empirical out-of-sample experiments are performed on EUR/USD and USD/DKK currencies.

A bootstrapping market implied moment matching calibration for models with time-dependent parameters

This paper extends the moment matching market implied calibration procedure (Guillaume and Schoutens 2012) to Markov models with piecewise constant parameters between successive quoted option maturities. The Markov property allows us to determine the parameter set of each subprocess by a bootstrapping moment matching calibration. This sequential calibration arises naturally due to the additive property of cumulants of independent random variables and consists in solving M independent moment matching systems of N equations, where M and N denote the number of quoted maturities and the number of parameters, respectively. As shown in Guillaume and Schoutens (2012), for popular Lévy processes, these systems can be transformed into M systems of algebraic equations which give directly the N model parameters of each subprocess in terms of the second to the (N+1)th standardized moments of the log asset return process between successive maturity times. For the numerical study, we work out the bootstrapping moment matching calibration under two popular Lévy models with piecewise constant parameters, namely the VG and Meixner models and compare its performance with existing calibration procedures for term structure models.

Pricing Perpetual American Option Under L evy Process: A Mellin Transform Approach

We propose a Mellin transform method to numerically compute the prices and greeks of American option driven by a class of Levy processes under incomplete market with Follmer Schweizer minimal measure. We develop a partial integro-differential l equation(PIDE) for American option and applied Mellin transform on it. Subsequently we perform the inversion of these Mellin transform to construct an approximation of the prices and sensitivities of American options in a class of Levy models. The class includes many of the Levy process employed in quantitative finance such as the NIG, CGMY and Meixner models.

Mellin Transform Approach for Pricing of Lookback Option under Levy Process with Minimal Martingle Measure

We propose a Mellin transform method to numerically compute the prices and greeks of Lookback options driven by a class of Levy processes under incomplete market with Follmer Schweizer minimal measure. We develop a partial integro-differential equation (PIDE) for Lookback option and applied Mellin transform on it. Subsequently we perform the Inversion of these Mellin transform to construct an approximation of the prices and sensitivities of Lookback options in a class of Levy models. The class includes many of the Levy models employed in quantitative finance such as the NIG, CGMY and Meixner models.

A moment matching market implied calibration

This paper provides a new market implied calibration based on a moment matching methodology where the moments of the risk-neutral density function are inferred from at-the-money and out-the-money European vanilla option quotes. In particular, we derive a model-independent risk-neutral formula for the moments of the asset log-return distribution function by expanding power returns as a weighted sum of vanilla option payoffs (based on results of Breeden and Litzenberger and Carr and Madan). For the numerical study, we develop different popular exponential Lévy models, namely the VG, NIG and Meixner models. The new calibration methodology rests on closed-form formulae only: it is shown that the moment matching system can be transformed into a system of algebraic equations that computes directly the optimal value of the model parameters in terms of the second to the th market standardized moments under the different Lévy models under investigation. Hence, the proposed calibration can be performed almost instantaneously. Furthermore, for the models considered in this paper, the method does not require any search algorithm and hence any starting value for the model parameters and avoids the problem of becoming stuck in local minima.

Spatial representativeness of eddy covariance measurements using footprint analysis in arid areas

Based on data measured by eddy covariance (EC) and the Kormann and Meixner model, footprints of the flux of desert shrub ecosystems were analyzed. The contributions of different land types during the growing season in Fukang station in 2007 were estimated. Spatial distributions of footprint source areas were evaluated to reveal the relative flux contribution to the total flux over the entire observation period. The results indicate that: (1) The applied footprint model provides accurate footprint estimates and the flux data can be used for the shrub flux estimations. The flux contribution from shrub land showed that the observed flux data were able to represent seasonal change in the flux of desert shrub ecosystems. The flux contribution rate of shrub was highest during May to July between 10:00 and 18:00 h. (2) The location of the EC system in Fukang is appropriate for monitoring shrub flux. (3) Footprint analysis is necessary because it assesses the contribution of the target land-use type to the total flux for any user-defined period. The flux contribution rate was affected significantly by wind direction and the source region.

A Bootstrapping Market Implied Moment Matching Calibration for Models with Time-Dependent Parameters

This paper extends the moment matching market implied calibration procedure to Markov models with piecewise constant parameters between successive quoted option maturities. The Markov property allows us to determine the parameter set of each subprocess by a bootstrapping moment matching calibration. This sequential calibration arises naturally due to the additive property of cumulants of independent random variables and consists in solving M independent moment matching systems of N equations, where M and N denote the number of quoted maturities and the number of parameters, respectively. For popular Levy processes, these systems can be transformed into M systems of algebraic equations which give directly the N model parameters of each subprocess in terms of the second to the (N+1)th standardized moments of the log asset return process between successive maturity times. For the numerical study, we work out the bootstrapping moment matching calibration under two popular Levy models with piecewise constant parameters, namely the VG and Meixner models and compare its performance with existing calibration procedures for term structure models.

Barrier style contracts under Lévy processes: An alternative approach

Abstract In this paper we present new pricing formulas for some single barrier style contracts of the European type when the underlying process is driven by an important class of Levy processes, which includes the CGMY model, generalized hyperbolic model and Meixner model, frequently used in the literature. To achieve this goal we first assume that a symmetry property holds, i.e., we assume that under a change of numeraire the risk neutral distribution does not change, and then we analyze the most realistic asymmetric case.

A Moment Matching Market Implied Calibration

This paper provides a new market implied calibration based on a moment matching methodology where the moments of the risk-neutral density function are inferred from at-the-money and out-the-money European vanilla option quotes. In particular, we derive a model independent risk-neutral formula for the moments of the asset log-return distribution function by expanding power returns as a weighted sum of vanilla option payo s (based on results of Breeden, D. and Litzenberger, R. (1978) and Carr, P. and Madan, D.B. (2002)). For the numerical study, we work out di erent popular exponential Levy models, namely the VG, NIG and Meixner models. The new calibration methodology rests on closed-form formulae only: it is shown that the moment matching system can be transformed into a system of algebraic equations which computes directly the optimal value of the N model parameters in terms of the second to the (N 1)th market standardized moments under the di erent Levy models under investigation. Hence, the proposed calibration can be performed almost instantaneously. Furthermore, the method is not requiring a starting value for the model parameters and avoids the problem of getting stuck in local minima.

The [formula omitted]-Meixner model

We propose to approximate the Meixner model by a member of the β-family introduced by Kuznetsov (2010) in [2]. The advantage of the approximation is the semi-explicit formulae for the running extrema under the β-family processes which enables us to produce more efficient algorithms for pricing path dependent options through the Wiener–Hopf factors. We will explore the performance of the approximation both in an equity framework and in the credit risk setting, where we use the approximation to calibrate a surface of credit default swaps. The paper follows the approach of the study made by Schoutens and Damme (2010) in [1], where the aim was to approximate the variance gamma. We will contextualize the results by Schoutens and Damme (2010) in [1] and the ones here with respect to the approach taken by Jeannin and Pistorius (2010) in [15]. An asymptotic expression for the rate of convergence of the approximation is derived.

The Longstaff–Schwartz algorithm for Lévy models: Results on fast and slow convergence

We investigate the Longstaff--Schwartz algorithm for American option pricing assuming that both the number of regressors and the number of Monte Carlo paths tend to infinity. Our main results concern extensions, respectively, applications of results by Glasserman and Yu [Ann. Appl. Probab. 14 (2004) 2090--2119] and Stentoft [Manag. Sci. 50 (2004) 1193--1203] to several L\'{e}vy models, in particular the geometric Meixner model. A convenient setting to analyze this convergence problem is provided by the L\'{e}vy--Sheffer systems introduced by Schoutens and Teugels.