arXiv subjects

Erik Schlögl

Publications and source records attributed to Erik Schlögl.

9 recordsLinked to original sources

arXiv2026

If Not Now, Then When? Model Risk in the Optimal Exercise of American Options

Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style derivatives and the associated optimal stopping problems. This paper analyzes model risk in the optimal exercise of an American put option using the benchmark methodology of Hull and Suo [2002]. The true data-generating process is assumed to follow a Heston stochastic volatility model. We compare the optimal exercise strategy of an investor who correctly uses the Heston model with those of investors who instead use misspecified Black--Scholes or Dupire local volatility models. Optimal exercise boundaries are computed numerically via finite difference methods. Stochastic volatility dynamics and return--volatility correlation are found to have a substantial impact on optimal exercise behavior across models, creating a source of model risk. As this behavior is not transmitted to exercise strategies determined by misspecified models, even if such models are fully calibrated to European option prices, calibration fails to mitigate model risk in this context. This issue persists under frequent recalibration of a misspecified model.

q-fin.MF↗

arXiv2025

Pricing and Calibration of VIX Derivatives in Mixed Bergomi Models via Quantisation

We apply vector quantisation within mixed one- and two-factor Bergomi models to implement a fast and efficient approach for option pricing in these models. This allows us to calibrate such models to market data of VIX futures and options. Our numerical tests confirm the efficacy of vector quantisation, making calibration feasible over daily data covering several months. This permits us to evaluate the calibration accuracy and the stability of the calibrated parameters, and we provide a comprehensive assessment of the two models. Both models show excellent performance in fitting VIX derivatives, and their parameters show satisfactory stability over time.

q-fin.PR↗

arXiv2021

Estimation When Both Covariance And Precision Matrices Are Sparse

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood, subject to the double sparsity constraint. In our method, only a particular class of sparsity pattern is allowed: both the matrix and its inverse must be subordinate to the same chordal graph. Compared to a naive enforcement of double sparsity, our chordal graph approach exploits a special algebraic local inverse formula. This local inverse property makes computations that would usually involve an inverse (of either precision matrix or covariance matrix) much faster. In the context of estimation of covariance matrices, our proposal appears to be the first to find such special pairs of covariance and precision matrices.

stat.ME↗

arXiv2021

Short Rate Dynamics: A Fed Funds and SOFR perspective

The Secured Overnight Funding Rate (SOFR) is becoming the main Risk-Free Rate benchmark in US dollars, thus interest rate term structure models need to be updated to reflect the key features exhibited by the dynamics of SOFR and the forward rates implied by SOFR futures. Historically, interest rate term structure modelling has been based on rates of substantially longer time to maturity than overnight, but with SOFR the overnight rate now is the primary market observable. This means that the empirical idiosyncrasies of the overnight rate cannot be ignored when constructing interest rate models in a SOFR-based world. As a rate reflecting transactions in the Treasury overnight repurchase market, the dynamics of SOFR are closely linked to the dynamics of the Effective Federal Funds Rate (EFFR), which is the interest rate most directly impacted by US monetary policy target rate decisions. Therefore, these rates feature jumps at known times (Federal Open Market Committee meeting dates), and market expectations of these jumps are reflected in prices for futures written on these rates. On the other hand, forward rates implied by Fed Funds and SOFR futures continue to evolve diffusively. The model presented in this paper reflects the key empirical features of SOFR dynamics and is calibrated to futures prices. In particular, the model reconciles diffusive forward rate dynamics with piecewise constant paths of the target short rate.

q-fin.MF↗

arXiv2019

Model Risk Measurement under Wasserstein Distance

The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for equivalent and non-equivalent probability measures and incorporates the economic reality of the fictitious adversary. It provides practically feasible results that overcome the restriction of considering only models implying probability measures equivalent to the reference model. The Wasserstein approach suits for various types of model risk problems, ranging from the single-asset hedging risk problem to the multi-asset allocation problem. The robust capital market line, accounting for the correlation risk, is not achievable with other non-parametric approaches.

q-fin.MF↗

arXiv2018

Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models

We focus on two particular aspects of model risk: the inability of a chosen model to fit observed market prices at a given point in time (calibration error) and the model risk due to recalibration of model parameters (in contradiction to the model assumptions). In this context, we follow the approach of Glasserman and Xu (2014) and use relative entropy as a pre-metric in order to quantify these two sources of model risk in a common framework, and consider the trade-offs between them when choosing a model and the frequency with which to recalibrate to the market. We illustrate this approach applied to the models of Black and Scholes (1973) and Heston (1993), using option data for Apple (AAPL) and Google (GOOG). We find that recalibrating a model more frequently simply shifts model risk from one type to another, without any substantial reduction of aggregate model risk. Furthermore, moving to a more complicated stochastic model is seen to be counterproductive if one requires a high degree of robustness, for example as quantified by a 99 percent quantile of aggregate model risk.

q-fin.RM↗

arXiv2018

A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors

Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. a spread applied to one leg of a swap to exchange one floating interest rate for another of a different tenor in the same currency) arises endogenously. This rollover risk consists of two components, a credit risk component due to the possibility of being downgraded and thus facing a higher credit spread when attempting to roll over short-term borrowing, and a component reflecting the (systemic) possibility of being unable to roll over short-term borrowing at the reference rate (e.g., LIBOR) due to an absence of liquidity in the market. The modelling framework is of "reduced form" in the sense that (similar to the credit risk literature) the source of credit risk is not modelled (nor is the source of liquidity risk). However, the framework has more structure than the literature seeking to simply model a different term structure of interest rates for each tenor frequency, since relationships between rates for all tenor frequencies are established based on the modelled roll-over risk. We proceed to consider a specific case within this framework, where the dynamics of interest rate and roll-over risk are driven by a multifactor Cox/Ingersoll/Ross-type process, show how such model can be calibrated to market data, and used for relative pricing of interest rate derivatives, including bespoke tenor frequencies not liquidly traded in the market.

q-fin.PR↗

arXiv2018

Arbitrage-Free Interpolation in Models of Market Observable Interest Rates

Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.

q-fin.MF↗

arXiv2018

Parameter Learning and Change Detection Using a Particle Filter With Accelerated Adaptation

This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in online sequential filtering does not match the model posterior filtered based on data up to a current point in time. The examples considered encompass parameter regime shifts and stochastic volatility. The filter adapts to regime shifts extremely rapidly and delivers a clear heuristic for distinguishing between regime shifts and stochastic volatility, even though the model dynamics assumed by the filter exhibit neither of those features.

stat.ML↗