Quantization Under the Real-world Measure: Fast and Accurate Valuation of Long-dated Contracts

TL;DR

This paper introduces a fast, accurate method for pricing long-dated insurance and pension contracts using the benchmark approach and recursive quantization algorithms under the real-world measure, offering cost-effective alternatives to traditional risk-neutral methods.

Contribution

It develops a novel framework combining the benchmark approach with recursive marginal quantization to efficiently price long-dated claims under the real-world measure, extending beyond traditional risk-neutral valuation.

Findings

Less expensive prices than traditional risk-neutral valuation.

Efficient pricing of Bermudan options on the growth-optimal portfolio.

Application of the TCEV model with RMQ to price bonds and options.

Abstract

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional risk-neutral methods by pricing options under the real-world probability measure, using the benchmark approach. The benchmark approach is reviewed, and the real-world pricing theorem is presented and applied to various long-dated claims to obtain less expensive prices than suggested by traditional risk-neutral valuation. The growth-optimal portfolio (GOP), the central object of the benchmark approach, is modelled using the time-dependent constant elasticity of variance model (TCEV). Analytic European option prices are derived and the RMQ algorithm is used to efficiently and accurately price Bermudan options on the GOP. The TCEV model is then combined with a $3/2$ stochastic short-rate model and RMQ is used to price zero-coupon bonds and zero-coupon bond options, highlighting the departure from risk-neutral pricing.