Yannick Dillschneider

Asset Pricing | Financial Econometrics

Functional Estimation of Option Pricing Models (with Evgenii Vladimirov)

March 26, 2025 SSRN
Abstract: In this paper, we develop a novel estimation procedure for parametric option pricing models specified under the risk-neutral measure. We set up our estimation strategy to minimize the distance in a functional sense between the option-implied and model-implied logarithm of conditional characteristic functions. Within a broad class of option pricing models, for which the characteristic function is marginally affine, the model's latent state vector can be concentrated out in closed form. As a result, our estimation procedure is computationally fast and easy to implement, while at the same time exploiting all distributional information contained in an option panel about the risk-neutral dynamics of the underlying asset price. We establish the asymptotic properties of the parameter and state estimators and investigate the finite-sample performance of our method in Monte Carlo simulations. In an empirical application, we illustrate the usefulness of our estimation procedure based on by far the largest option panel, both in the time-series and cross-sectional dimensions, considered in the related literature.
Presented at: FinEML 2024 (Lugano) (poster), EWMES 2024 (Mallorca), Financial Risks International Forum 2025 (Paris), University of Amsterdam, Erasmus University Rotterdam

What can you really tell from option prices? (with Oleg Bondarenko, Paul Schneider, and Fabio Trojani)

January 26, 2024
Abstract: Recent theoretical and empirical work exploits option-implied information to constrain the conditional moments of asset returns. In this paper, we characterize the information content that can be reliably used for this purpose considering the market incompleteness inherent to option markets. Our analysis relies on novel model-free bounds for a large class of risk-neutral moments built from a given option cross-section. We show the non-robustness of several risk-neutral moments in the literature, form new robust versions of them, and develop associated model-free bounds constraining the conditional moments of asset returns. These bounds deviate substantially, both quantitatively and qualitatively, from those associated with non-robust risk-neutral moments.
Presented at: QFFE 2024 (Marseille), SoFiE 2024 (Rio), ESEM 2024 (Rotterdam), CDI Conference 2024 (Montreal), FinEML 2024 (Lugano), EWMES 2024 (Mallorca)

Standard Transform Analysis for Asset Pricing and Parameter Estimation

June 11, 2022 SSRN
Abstract: This paper provides tractable expressions for broad classes of standard transforms for the case of affine jump diffusions. Extending and unifying existing results, these include expressions for exponential, polynomial-log-linear, and polynomial transforms of a state vector in both conditional and unconditional form. We cover the usual single-period setting, but also extensions to multi-period settings, non-stationarity, and time-inhomogeneous state dynamics. Using these standard transforms, we discuss applications in asset pricing and parameter estimation.

Pricing Dividend Derivatives in Reduced-Form and Structural Models

May 14, 2022 SSRN
Abstract: In this paper, we develop a general pricing framework for dividend derivatives, which covers different specifications for state-space models, pricing kernels, and dividends. For certain special cases within an affine jump-diffusion setting, we derive transform-based pricing formulas for general dividend derivatives. Using our framework, we then obtain specific pricing formulas for dividend futures and options within both reduced-form and structural models.

A Machine Learning Framework for Asset Pricing

May 5, 2022 SSRN
Abstract: This paper introduces a unified machine learning framework for solving general asset pricing problems. Building on representations of asset prices in discrete-time and continuous-time models, we develop a solution strategy using neural networks and further machine learning techniques to determine asset prices. We exemplify and numerically study our methodology for consumption-based asset pricing models.

Generalized Transform Analysis for Asset Pricing and Parameter Estimation

May 25, 2021 SSRN
Abstract: In this paper, we extend the existing generalized transform analysis in a way that allows us to propose a novel GMM approach for estimating asset pricing models. Our methodology is capable of incorporating a broad class of assets within both reduced-form and structural models, while avoiding the drawbacks of competing approaches. To formulate moment conditions, we derive expressions for moments involving transform-based asset prices. Our theory yields analytically tractable expressions for exact moments and an additionally computationally efficient strategy to obtain approximate moments, whose convergence we establish under standard conditions. Exact and approximate moments induce exact and approximate GMM estimators, respectively, for which we discuss asymptotic properties. Finally, we exemplify our methodology with a worked-out estimation problem involving equity options.
Presented at: University of Amsterdam, Esade Business School, AFFI 2021, SoFiE 2021 Pre-Conference, IAAE 2021, AMES 2021, CMES 2021, ESEM 2021

GMM Estimation of Stochastic Volatility Models Using Transform-Based Moments of Derivatives Prices (with Raimond Maurer)

May 20, 2021 SSRN
Abstract: Derivatives, especially equity and volatility options, contain valuable and oftentimes essential information for estimating stochastic volatility models. Absent strong assumptions, their typically highly nonlinear pricing dependence on the state vector prevents or at least severely impedes their inclusion into standard estimation approaches. This paper develops a novel and unified methodology to incorporate moments involving derivatives prices into a GMM estimation procedure. Invoking new results from generalized transform analysis, we derive analytically tractable expressions for exact moments and devise a computationally attractive approximation procedure. We exemplify our methodology with an estimation problem that jointly accounts for stock returns as well as prices of equity and volatility options. Finally, we provide numerical results that support the effectiveness of our methodology.
Presented at: EEA 2020, Virtual Derivatives Workshop 2020, SoFiE Summer School 2021, RCEA 2022, ESAM 2022, EWMES 2022 (Berlin), AFFI 2023 (Bordeaux), IAAE 2023 (Oslo), CFE-CMStatistics 2023 (Berlin)

Ross Recovery in Pricing Semigroups

December 29, 2020 SSRN
Abstract: Ross recovery specifies conditions under which it is possible to recover the real-world probability measure as well as the pricing kernel from a family of pricing operators. In this paper, we study Ross recovery theoretically within a semigroup framework using Perron-Frobenius operator theory. Thereby, we derive sufficient conditions guaranteeing existence and uniqueness of a transition independent pricing kernel consistent with the pricing semigroup. Our resultant theory provides a unified perspective on various existing recovery approaches. Building on our theoretical results, we also briefly address the estimation of a pricing semigroup and the corresponding (Markov) transition semigroup from a sample of option prices.
Presented at: AFFI 2019 (Quebec City)

Functional Ross Recovery: Theoretical Results and Empirical Tests (with Raimond Maurer)

Journal of Economic Dynamics and Control, 2019, 108, 103750:1-32
September 13, 2019 SSRN JEDC
Abstract: Recently, Ross (2015) showed that the real-world probability distribution of a discrete Markovian state variable can be recovered from observed option prices. The so-called recovery theorem follows from Perron-Frobenius matrix theory when the pricing kernel is transition independent. In this paper, we generalize the recovery theorem to continuous state spaces using Perron-Frobenius operator theory. Building on our theoretical results, we devise a nonparametric estimation approach to empirically recover the pricing kernel and real-world probability density in closed form. Using S&P 500 index options, we analyze recovered pricing kernels empirically and find evidence that Ross recovery is misspecified.
Presented at: AFFI 2018 (Paris), CDI Conference 2019 (Montreal), DGF 2019 (Essen)

Dynamic Portfolio Choice

Optimal Annuitization Under Stochastic Interest Rates (with Raimond Maurer and Peter Schober)

ASTIN Bulletin, forthcoming
April 25, 2024 SSRN
Abstract: The decision about when and how much to annuitize is an important element of the retirement planning of most individuals. Optimal annuitization strategies depend on the individual's exposure to annuity risk, meaning the possibility of meeting unfavorable personal and market conditions at the time of the annuitization decision. This paper studies optimal annuitization strategies within a life-cycle consumption and portfolio choice model, focusing on stochastic interest rates as an important source of annuity risk. Closing a gap in the existing literature, our numerical results across different model variants reveal several typical structural effects of interest rate risk on the annuitization decision, which may however vary depending on preference specifications and alternative investment opportunities: When allowing for gradual annuitization, annuity risk is temporally diversified by spreading annuity purchases over the whole pre-retirement period, with annuity market participation starting earlier in the life cycle and becoming more extensive with increasing interest rate risk. Ruling out this temporal diversification possibility, as embedded in many institutional settings, incurs significant welfare losses, which are increasing with higher interest rate risk, together with larger overall demand for annuitization.

Generalized Euler Equation Errors for Discrete Time Dynamic Portfolio Choice Models (with Raimond Maurer and Peter Schober)

February 11, 2020 SSRN
Abstract: The solution to dynamic portfolio choice models can be formulated in terms of a value function by the Bellman principle of optimality, which reduces the multi-period optimal policy choice problem to a sequence of one-period maximization problems. For two adjacent periods, economists compute the error of numerically obtained policies by measuring how much these policies violate the intertemporal first order conditions for the optimal policy choice problem --- so-called Euler equation errors. In this paper, we derive generalized Euler equation errors for the solution to a broad class of discrete time dynamic portfolio choice models where the policies are continuous choice variables. Our key precondition is that the gradient of the value function with respect to the state variables can be approximated. This is, for example, the case when a global polynomial basis or B-spline basis functions are used for the approximation of the value function within the discrete time dynamic programming approach. We apply our theoretical results to exemplary, representative dynamic portfolio choice models.

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