Pricing under the Benchmark Approach

TL;DR

This paper explores the benchmark approach to pricing financial derivatives, demonstrating that benchmark-neutral prices are minimal and often lower than traditional risk-neutral prices, with applications to extreme-maturity options.

Contribution

It introduces a benchmark-neutral pricing framework and applies it to extreme-maturity options, showing these prices are theoretically minimal compared to risk-neutral prices.

Findings

Benchmark-neutral prices are minimal and theoretically optimal.

Risk-neutral prices are significantly higher.

Application to extreme-maturity European put options.

Abstract

The paper summarizes key results of the benchmark approach with a focus on the concept of benchmark-neutral pricing. It applies these results to the pricing of an extreme-maturity European put option on a well-diversified stock index. The growth optimal portfolio of the stocks is approximated by a well-diversified stock portfolio and modeled by a drifted time-transformed squared Bessel process of dimension four. It is shown that the benchmark-neutral price of a European put option is theoretically the minimal possible price and the respective risk-neutral put price turns out to be significantly more expensive.