Pricing under the Benchmark Approach
Eckhard Platen

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.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Complex Systems and Time Series Analysis
MethodsFocus
