Functional Ross recovery: Theoretical results and empirical tests

Dillschneider, Yannick; Maurer, Raimond

doi:10.1016/j.jedc.2019.103750

Cited by 16 publications

(8 citation statements)

References 58 publications

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“…(2016), where they show that recovery holds if the martingale component in the factorization theory is degenerate (i.e., unity). In a recent extensive study, Dillschneider and Maurer (2019) also extend the Ross recovery to the continuous state setup and establish some insightful results clarifying the relationship between the Ross recovery and the Hansen–Scheinkman framework. Qin and Linetsky (2017) further extend the Hansen–Scheinkman framework to the semi‐martingale setting, in which empirical application would require computing the eigenvalues and eigenfunctions of the associated operators.…”

Section: Introductionmentioning

confidence: 86%

“…Fortunately, in the continuous‐state setup, such extensions (e.g., Jentzsch theorem and its extensions) of the Perron‐Probenius theorem have been well established in the mathematical literature (the use of such extensions was first suggested by Ross). Given the empirical focus of this paper, we refer the reader to the elegant Dillschneider and Maurer (2019) for the precise conditions needed to invoke Jentzsch theorem for recovery. We would like to emphasize here that the existing extensions of Ross recovery theory (e.g., Carr & Yu, 2012; Walden, 2017, etc.)…”

Section: A New (Continuous‐state) Methods For Ross Recovery – the Cas...mentioning

confidence: 99%

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Empirical Ross recovery without discretization

Golec

Yao

2022

The Financial Review

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We propose a new continuous-state method for empirically recovering the key objects in the Ross recovery theory which avoids discretization. The new method is based on a key bivariate orthogonal Hermite representation of the state price transition kernel, which leads to an elegant correspondence of the eigenvalue-eigenfunction system of the transition kernel and the eigenvalue-eigenvector system of the expansion coefficient matrix. Using S&P 500 index option prices, we demonstrate how our method can generate wellbehaved state price transition kernels and physical densities.Our method can also be used to compute the key objects in the Hansen and Scheinkman's factorization theory.

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Section: Introductionmentioning

confidence: 86%

Section: A New (Continuous‐state) Methods For Ross Recovery – the Cas...mentioning

confidence: 99%

Empirical Ross recovery without discretization

Golec

Yao

2022

The Financial Review

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“…Jackwerth and Menner (2017) apply Ross's discrete model to S&P 500 call option data, and find that recovered distributions are incompatible with physical probabilities. Similarly, Dillschneider and Maurer (2018), also using S&P options pricing data and assuming a bounded state space, find empirical evidence that the pricing kernel is misspecified under this approach. Our PDE approach complement these papers, by focusing on the numerical implications of truncating the state space.…”

Section: A Regular Sturm-liouville Problemmentioning

confidence: 94%

Numerical Ross Recovery for Diffusion Processes Using a PDE Approach

Sydow

Waldén

2020

Applied Mathematical Finance

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We develop and analyse a numerical method for solving the Ross recovery problem for a diffusion problem with unbounded support, with a transition independent pricing kernel. Asset prices are assumed to only be available on a bounded subinterval B ¼ ½ÀN; N. Theoretical error bounds on the recovered pricing kernel are derived, relating the convergence rate as a function of N to the rate of mean reversion of the diffusion process. Our suggested numerical method for finding the pricing kernel employs finite differences, and we apply Sturm-Liouville theory to make use of inverse iteration on the resulting discretized eigenvalue problem. We numerically verify the derived error bounds on a test bench of three model problems.

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“…Because the option pay-off extends out in time, option prices capture some market sentiment. [15][16][17][18][19][20] This is known as forward-looking information.…”

Section: Extracting Forward-looking Return Distributionsmentioning

confidence: 99%

Determining safe retirement withdrawal rates using forward-looking distributions

Appel

Maré

2022

S. Afr. J. Sci.

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An important topic for retirees is determining how much they can safely withdraw from their retirement savings: draw too much from their retirement fund and risk outliving their retirement savings, or draw too little and live below their means. For retirees to decide on the appropriate withdrawal rate, retirees need to have the tools available to decide on their spending rates. There are many factors that influence withdrawal rates, such as initial wealth, asset allocations, age, life expectancy, and risk tolerances. The topic of safe withdrawal rates aims to optimise spending rates while minimising the risk of running out of retirement savings. The focus of this study was on using forward-looking moments of the risk-neutral and real-world asset distributions in determining safe withdrawal rates for South African retirees. The use of forward-looking information, typically derived from traded derivative securities (rather than historical data), is essential in optimising safe withdrawal rates for retirees. In particular, we extracted the forwardlooking risk-neutral and real-world distributions from option prices on the South African Top 40 index, and used the moments of the distributions as a signal in a simple tactical asset allocation framework. That is, when we expect the growth asset to decrease in value, we hold cash (or short the asset) and, alternatively, when we expect the growth asset to increase in value, we hold the growth asset for the period. Using this approach, we found that we can sustain withdrawal rates of up to 7% compared to the commonly quoted 4% safe withdrawal rate obtained by historical simulations.

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Functional Ross recovery: Theoretical results and empirical tests

Cited by 16 publications

References 58 publications

Empirical Ross recovery without discretization

Empirical Ross recovery without discretization

Numerical Ross Recovery for Diffusion Processes Using a PDE Approach

Determining safe retirement withdrawal rates using forward-looking distributions

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