Explicit option valuation in the exponential NIG model

TL;DR

This paper derives explicit, quickly convergent pricing formulas for various path-independent options within the exponential NIG model, facilitating efficient valuation in financial markets.

Contribution

It introduces closed-form series formulas for option pricing under the exponential NIG model, applicable to both symmetric and asymmetric cases, with convergence and error bounds.

Findings

Formulas are simple and rapidly convergent.

Validation through numerical comparisons shows high accuracy.

Provides bounds for convergence speed and truncation error.

Abstract

We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and take the form of simple and quickly convergent series, under some condition involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff, and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier and Fast Fourier transforms, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.