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This paper provides a methodology for fast and accurate pricing of thelong-dated contracts that arise as the building blocks of insurance and pensionfund agreements. It applies the recursive marginal quantization (RMQ) and jointrecursive marginal quantization (JRMQ) algorithms outside the framework oftraditional risk-neutral methods by pricing options under the real-worldprobability measure, using the benchmark approach. The benchmark approach isreviewed, and the real-world pricing theorem is presented and applied tovarious long-dated claims to obtain less expensive prices than suggested bytraditional risk-neutral valuation. The growth-optimal portfolio (GOP), thecentral object of the benchmark approach, is modelled using the time-dependentconstant elasticity of variance model (TCEV). Analytic European option pricesare derived and the RMQ algorithm is used to efficiently and accurately priceBermudan 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 andzero-coupon bond options, highlighting the departure from risk-neutral pricing.

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