ARM: The Analytic Recovery Method

Abstract

The analytic recovery method (ARM) recovers arbitrage-free density functions from a given set of option prices with maximum accuracy and speed. For arbitrage-free option prices, ARM provides extremely fast convergence and arbitrary accuracy. In the presence of noise, the closest arbitrage-free approximation is identified. Option prices and densities, as well as their moments and other parameters, are easy-to-handle analytic functions defined for arbitrary strike prices. ARM reveals inconsistencies between quoted option prices, particularly for longer durations. ARM is essentially based on the no-arbitrage assumptions; it is not related to a specific model. It has been tested for a selection of S&P 500, EuroStoxx 50, and DAX data. Excellent no-arbitrage fit to call and put prices is obtained; extrapolations are in line with the market.