[Paper Review] Stochastic Deflator for an Economic Scenario Generator with Five Factors

Po−Keng Cheng, Frédéric Planchet|arXiv (Cornell University)|Jun 8, 2018

Stochastic processes and financial applications20 references3 citations

TL;DR

This paper proposes a stochastic deflator model incorporating five economic risk factors—interest rates, market price of risk, stock prices, default intensities, and convenience yields—for use in economic scenario generation. The method ensures consistency in pricing various derivatives, with numerical results confirming its reliability across stocks, bonds, and options under different market conditions.

ABSTRACT

In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero-coupon bonds, vanilla options, and corporate coupon bonds. We find required regularity conditions to implement our stochastic deflator. Our numerical results show the reliability of the deflator approach in pricing financial derivatives.

Motivation & Objective

• To develop a stochastic deflator that integrates five key economic and financial risk factors for use in economic scenario generation.
• To ensure consistency and regularity in derivative pricing across diverse financial instruments such as zero-coupon bonds, vanilla options, and corporate bonds.
• To validate the deflator’s reliability through numerical simulations across multiple asset classes.
• To identify the necessary regularity conditions for the deflator’s mathematical and financial validity.
• To provide a robust framework for risk management and asset-liability modeling in insurance and banking contexts.

Proposed method

• The deflator is constructed as a stochastic process driven by five underlying risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields.
• The model employs a change of measure via a Radon-Nikodym derivative to define the deflator, ensuring it is a martingale under the risk-neutral measure.
• The deflator is calibrated to match observed market prices of benchmark instruments, including zero-coupon bonds and options.
• The model uses a multi-factor affine term structure framework to ensure analytical tractability and computational efficiency.
• Numerical simulations are conducted under the physical measure to generate economic scenarios, with pricing performed under the risk-neutral measure using the deflator.
• The deflator is tested across multiple asset classes to verify its consistency and robustness in derivative valuation.

Experimental results

Research questions

• RQ1 How can a stochastic deflator be constructed to incorporate five distinct economic and financial risk factors in a consistent and mathematically sound way?
• RQ2 What regularity conditions are necessary to ensure the deflator remains a valid martingale and supports consistent derivative pricing?
• RQ3 To what extent does the deflator accurately price complex derivatives such as corporate coupon bonds and vanilla options?
• RQ4 How does the inclusion of default intensities and convenience yields affect the model’s ability to replicate market prices?
• RQ5 Can the deflator approach maintain reliability across diverse financial instruments under various economic scenarios?

Key findings

• The proposed stochastic deflator successfully incorporates five risk factors—interest rates, market price of risk, stock prices, default intensities, and convenience yields—into a unified framework.
• The model satisfies necessary regularity conditions to ensure the deflator is a true martingale under the risk-neutral measure.
• Numerical results confirm the deflator’s reliability in pricing a wide range of derivatives, including zero-coupon bonds, vanilla options, and corporate coupon bonds.
• The deflator approach maintains consistency across different asset classes, demonstrating robustness in diverse market scenarios.
• The inclusion of default intensities and convenience yields enhances the model’s ability to reflect real-world market dynamics in pricing.
• The model’s performance is validated through extensive simulations, showing alignment with observed market prices and consistent risk-neutral valuation.