On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance

Asmussen, Søren

doi:10.1007/s00780-022-00482-x

Cited by 5 publications

(1 citation statement)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(ii) Skewness and kurtosis [8]; (iii) Formal statistical tests including Kolmogorov-Smirnov test [9], Cramervon Mises test [10], Shapiro-Wilks test, and Jarque-Bera test [11]. The results are shown in figure 2, table 3 and table 4, respectively.…”

Section: Model Diagnosticsmentioning

confidence: 97%

Validity Testing of Classical Asset Allocation Models: An Empirical Study

Gao,

2023

AEMPS

View full text Add to dashboard Cite

This paper uses a 20 years of daily total return data for the S&P 500 Index (ticker symbol SPX) and 10 stocks, make all the necessary calculations to plot a portfolio area that gather an efficient boundary, a minimum risk or variance boundary, and a minimum return boundary together for a given set of constraints. Analyze all the outcomes in order to compare the various restrictions for each optimization issue (MM and IM), as well as the two solutions to the same optimization problem. The Excel solver was the primary tool utilized during calculation to resolve optimization issues for each point on the minimal risk or variance border. Also, this paper use an Excel solution table to calculate a large number of multipoints on any desired boundary. Through calculation and research, we found that, Markowitz model makes full use of covariance matrix to generate excellent portfolio. However, the results are numerically unstable. At the same time, the hypothesis of normality, stationarity and mean square error are verified. The exponential model simplifies the Markowitz model and produces more robust results. However, it introduces additional assumptions about the independence, normality, and homoscedasticity of the regression residuals, which are also invalid. The reduction (CDaR) model is hypothesis-free. The numerical stability can be obtained by transforming the nonlinear optimization problem into a linear programming problem.

show abstract

Section: Model Diagnosticsmentioning

confidence: 97%

Validity Testing of Classical Asset Allocation Models: An Empirical Study

Gao,

2023

AEMPS

View full text Add to dashboard Cite

show abstract

Remarks on Lévy Process Simulation

Asmussen

2022

Advances in Modeling and Simulation

View full text Add to dashboard Cite

On the number of terms in the COS method for European option pricing

Junike

2024

Numer. Math.

View full text Add to dashboard Cite

The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number of terms N to approximate the truncated density by a cosine series. How to choose the truncation range is already known. Here, we are able to find an explicit and useful bound for N as well for pricing and for the sensitivities, i.e., the Greeks Delta and Gamma, provided the density of the log-returns is smooth. We further show that the COS method has an exponential order of convergence when the density is smooth and decays exponentially. However, when the density is smooth and has heavy tails, as in the Finite Moment Log Stable model, the COS method does not have exponential order of convergence. Numerical experiments confirm the theoretical results.

show abstract

On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance

Cited by 5 publications

References 36 publications

Validity Testing of Classical Asset Allocation Models: An Empirical Study

Validity Testing of Classical Asset Allocation Models: An Empirical Study

Remarks on Lévy Process Simulation

On the number of terms in the COS method for European option pricing

Contact Info

Product

Resources

About