NIG-Levy process in asset price modeling: case of Estonian companies

As an asset is traded at fair value, its varying price trace an interesting trajectory reflecting in a general way the asset’s value and underlying economic activities. These trajectory exhibit jumps, clustering and a host of other properties not usually captured by Gaussian based models. Levy processes offer the possibility of distinguishing jumps, diffusion, drift and the laxity to answer questions on frequency, continuity, etc. An important feature of normal inverse Gaussian-Levy (NIGLevy) model is its path richness: it can model so many small jumps in a way that eliminates the need for a Gaussian component; hence, limitations arising from Gaussian based models are almost eliminated. Secondly, the characteristics listed above are reflected in the Levy triplet and are easily introduced in the modeling picture through estimated Levy parameters. Thirdly, knowledge of NIG-Levy parameters enables us to use NIG-Levy models as underlying asset price models for pricing financial derivatives. We use the R open software to calculate Levy parameters for 12 Estonian companies and choose good NIG-Levy asset price models by the method proposed by Käärik and Umbleja (2011). We observe that not all financial data of Estonian companies trading on the Tallinn Stock Exchange between 01 Jan 2008 – 01 Jan 2012 can be effectively modeled by NIG-Levy process, despite having Levy parameters. Those positively modeled are recommended as underlying assets for pricing financial derivatives.