A multivariate Lévy process model with linear correlation

Kawai, Reiichiro

doi:10.1080/14697680902744729

Cited by 19 publications

(13 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2 This model can also, at least to some extent, be considered as a generalization to the multidimensional case of the model proposed in Corcuera et al [17] and the parameter σ j in (4) can then be interpreted as the Lévy space (implied) volatility of stock j. The idea of building a multivariate asset model by taking a linear combination of a systematic and an idiosyncratic process can also be found in Kawai [26] and Ballotta and Bonfiglioli [3].…”

Section: The Modelmentioning

confidence: 99%

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Linders

Schoutens

2016

Innovations in Derivatives Markets

View full text Add to dashboard Cite

In this paper we employ a one-factor Lévy model to determine basket option prices. More precisely, basket option prices are determined by replacing the distribution of the real basket with an appropriate approximation. For the approximate basket we determine the underlying characteristic function and hence we can derive the related basket option prices by using the Carr-Madan formula. We consider a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several Lévy models are calibrated to market data and basket option prices are determined. In the last part we show how our newly designed basket option pricing formula can be used to define implied Lévy correlation by matching model and market prices for basket options. Our main finding is that the implied Lévy correlation smile is flatter than its Gaussian counterpart. Furthermore, if (near) atthe-money option prices are used, the corresponding implied Gaussian correlation estimate is a good proxy for the implied Lévy correlation.

show abstract

Section: The Modelmentioning

confidence: 99%

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Linders

Schoutens

2016

Innovations in Derivatives Markets

View full text Add to dashboard Cite

show abstract

“…The multivariate V G process in [27] uses n-dimensional Brownian motion as its subordinate and a univariate gamma process as its subordinator, which gives it a restrictive dependence structure, where components cannot have idiosyncratic time changes and must have equal kurtosis when there is no skewness. Models based on linear combinations of independent Lévy processes [19,23] also do not account for both common and idiosyncratic time changes. These deficiencies are addressed by the use of an alphagamma subordinator, resulting in the variance-alpha-gamma (V AG) process which was introduced by Semeraro in [34] and also studied in [18,22].…”

Section: Introductionmentioning

confidence: 99%

Calibration for Weak Variance-Alpha-Gamma Processes

Buchmann

Madan

2018

Methodol Comput Appl Probab

View full text Add to dashboard Cite

The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibration methods for the weak variance-alpha-gamma process, method of moments, maximum likelihood estimation (MLE) and digital moment estimation (DME). We derive a condition for Fourier invertibility needed to apply MLE and show in our simulations that MLE produces a better fit when this condition holds, while DME produces a better fit when it is violated. We also find that the weak variance-alphagamma process exhibits a wider range of dependence and produces a significantly better fit than the variance-alpha-gamma process on an S&P500-FTSE100 data set, and that DME produces the best fit in this situation.

show abstract

“…In traditional studies, it is usually assumed that the two Lévy processes are independent when dealing with the joint characteristic functions (Eberlein and Raible ). Other authors have addressed the correlation between pairs of Lévy processes (Kawai ; Beinhofer et al ). In this paper, we use a different method to deal with the correlated processes.…”

Section: Introductionmentioning

confidence: 99%

Pricing Defaultable Bonds Using a Lévy Jump‐Diffusion Model

Chiang

Tsai

2018

Int Rev Finance

View full text Add to dashboard Cite

This paper uses a reduced‐form approach to derive a closed‐form pricing formula for defaultable bonds. The authors specify the default hazard rate as an affine function of multiple variables which follow the Lévy jump‐diffusion processes. Because such specification allows greater flexibility in the generation of a valid probability of default, their pricing model should be more accurate than the valuation models in traditional studies, which ignore the jump effects. This paper also proposes a new method for estimating the parameters in a Lévy Jump‐diffusion process. The real data from the Taiwanese bond market are used to illustrate how their model can be applied in practical situations. The authors compare the pricing results for the influential variables with no jump effects, with jump magnitudes following the normal distribution, and with jump magnitudes following the gamma distribution. The results reveal that the predictive ability is the best for the model with the jump components. The valuation model shown in this paper should help portfolio managers more accurately price defaultable bonds and more effectively hedge their portfolio holdings.

show abstract

A multivariate Lévy process model with linear correlation

Cited by 19 publications

References 22 publications

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Calibration for Weak Variance-Alpha-Gamma Processes

Pricing Defaultable Bonds Using a Lévy Jump‐Diffusion Model

Contact Info

Product

Resources

About