# Pricing Asian options for NIG and VG Levy markets

## TL;DR

This paper compares two methods for pricing Asian options in incomplete exponential Levy markets, specifically NIG and VG models, and finds they generally yield similar prices.

## Contribution

It introduces and compares two approaches for constructing risk-neutral measures in NIG and VG Levy markets for Asian options.

## Key findings

- Both methods produce similar option prices in numerical experiments.
- The study focuses on incomplete markets with exponential Levy models.
- Results support the equivalence of the two pricing approaches.

## Abstract

In this work, we study the value of an Asian option in the case of exponential Levy markets. More specifically, we are interested in the NIG (normal inverse Gaussian) the VG (variance gamma) models. The exponential Levy models produce incomplete markets. There are therefore an infinite number of equivalent martingale measures. We are interested in two methods of constructing of the risk-neutral measures. The first is based on the Esscher transform, and the other consists of bringing a risk-neutral correction on the dynamics of the trajectories. It turns out, according to the numerical results obtained, that the two methods generally produce the same prices.