A Non-Gaussian Pricing Model for Structured Products

Abstract

The paper aims to reconstruct the empirical premia of the structured products with two underlying assets. We apply various models that differ in probability distributions of the underlying price processes.

Pricing techniques, currently worldwide accepted, are based on the Black-Scholes model modifications with Gaussian distributions. Conventionally a correlation between underlying price processes is not considered. In order to achieve the overall objective the paper suggests a pricing model of structured products. The model considers a non-Gaussian realistic market framework for pricing the underlying assets and takes into account their correlation.

The theoretical and methodological basis of our research is quantitative finance, evolutionary equations, dynamical systems and field theory.

The paper presents an example of pricing a range of structured products.

We find that the approach to the theoretical premium valuation of the complex financial instrument is interrelated bijectively with statistical properties of the underlying assets. In particular, the paper presents the effectiveness of our model with regard to the structured derivatives with the correlated assets that obey non-Gaussian distributions. The fair value of the structured product evaluated using our model outperforms estimates obtained by means of other methods as it allows lower fair price of the derivatives.

The results of our research may be beneficial to academics, market participants including market analysts, risk-managers and developers of financial products.

We have concluded that market participants carry extra costs due to the simple models of the structured products' fair value pricing they apply.

The proposed model looks especially promising within the context of the complex derivatives market which growth has been accompanied by low liquidity and high premia, in the absence of a unique framework for pricing the structured products that would be consistent with financial market practice.

Keywords: fair value, non-Gaussian joint probability density function with skew, payout function, structured derivatives market, structured product, structured products pricing methodology

JEL Classification: G12, G13