Effective and simple VWAP option pricing model

TL;DR

This paper introduces a simple, gamma process-based model for pricing VWAP options, leveraging empirical volume statistics, and providing an exact analytic solution in an incomplete market setting.

Contribution

The paper proposes a novel, straightforward gamma process model for VWAP option pricing that accounts for market incompleteness and empirical volume data.

Findings

Empirical volume data of ASX equities fit gamma distributions well.

The model enables exact analytic pricing of VWAP options.

It addresses market incompleteness by incorporating volume risk.

Abstract

Volume weighted average price (VWAP) options are a popular security type in many countries, but despite their popularity very few pricing models have been developed so far for VWAP options. This can be explained by the fact that the VWAP pricing problem is set in an incomplete market since there is no underlying with which to hedge the volume risk, and hence there is no uniquely defined price. Any price, which is obtained will include a market price of volume risk which must be determined from the corresponding volume statistics. Our analysis strongly supports the hypothesis that the empirical volume statistics of ASX equities can be described reasonably well by fitted gamma distributions. Based on this observation we suggest a simple gamma process-based model that allows for the exact analytic pricing of VWAP options in a rather straightforward way.