A Fast Option Valuation Method in the Stochastic Multi-state Economic Model: CP2022

Abstract

Dutch pension funds are under the supervision by De Nederlandsche Bank (DNB) and they must adhere to the Financial Assessment Framework (FTK), which outlines the methods for calculating liabilities, buffer reserves, and risk factors. As part of the FTK, a feasibility test must be performed, which is a scenario-based analysis of pension funds' investment strategies and their pension policies based on economic scenario sets projected 100 years into future. Every quarter, DNB publishes these economic scenarios (P-scenarios) and equivalent risk-neutral scenarios (Q-scenarios) are used to calculate the effects of the pension fund reform in the Netherlands. These scenarios are generated by a stochastic model, which is revised every 5 years by a commission appointed by the Dutch government, called the Commission Parameters. The model currently in use is based on Commission Parameters 2022 and is referred to as CP2022.

The CP2022 model is an affine and arbitrage-free model framework for correlated interest rate, inflation rate, stock index and consumer price index, each being driven by Heston's stochastic volatility process. To generate realistic economic scenarios, the model is calibrated quarterly using bond and option market data. Currently, as part of the calibration process, option prices are computed under the dynamics stated by CP2022 using a Monte Carlo-based approach. As an alternative, we resort to a Fourier method called the COS method, which relies on the availability of the characteristic function of the state factors. We propose an efficient option valuation scheme for pricing European call and put options, and cliquet options under CP2022. Compared to the Monte Carlo method, our scheme demonstrates superior accuracy and computational efficiency.