Selected Work

Based on options and realized returns, we analyze risk premia in the Bitcoin market through the lens of the Pricing Kernel (PK). We identify that: 1) The projected PK into Bitcoin returns is W-shaped and steep in the negative returns region; 2) Negative Bitcoin returns account for 33% of the total Bitcoin index premium (BP) in contrast to 70% of S&P500 equity premium explained by negative returns. Applying a novel clustering algorithm to the collection of estimated Bitcoin risk-neutral densities, we find that risk premia vary over time as a function of two distinct market volatility regimes. In the low-volatility regime, the PK projection is steeper for negative returns and has a more pronounced W-shape than the unconditional one, implying particularly high BP for both extreme positive and negative returns and a high Variance Risk Premium (VRP). In high-volatility states, the BP attributable to positive and negative returns is more balanced, and the VRP is lower. Overall, Bitcoin investors are more worried about variance and downside risk in low-volatility states.
Working Paper, 2024
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This paper introduces the analysis of factor models in the frequency domain to the corporate bond pricing literature using the spectral factor model developed by Bandi, Chaudhuri, Lo, and Tamoni (2021). We decompose the bond market factor into orthogonal frequency-specific components, where the spectral betas capture frequency-specific systematic risk. Our findings show that an annual cycle component of the bond market factor, which spans 8 to 16 months, enhances the bond CAPM. In earlier literature, a liquidity risk factor adds incremental cross-sectional pricing power beyond the bond market factor. We show that when the bond market factor is substituted by its annual cycle component, the liquidity risk factor loses its incremental pricing power. Supported by additional evidence, we conclude that the yearly cycle component can be interpreted as the liquidity cycle of the bond market factor. Moreover, the results indicate that dimensionality reduction in factor models can be achieved by separating signal from noise in the frequency domain.
Working Paper, 2024
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Forecasting implied volatility across different levels of moneyness and maturity is crucial yet challenging due to the high dimensionality of the Implied Volatility Surface (IVS) and the nonlinearity that characterizes its temporal dependence. We adopt a Nonlinear Functional Autoregressive (NFAR) framework to a sequence of IVS and employ neural networks that admit a Neural Tangent Kernel (NTK) parameterization to capture nonlinear interactions between surfaces. We illustrate the theoretical and numerical advantages of the proposed functional NTK (fNTK) estimator and establish a link to functional kernel regression. Our empirical analysis includes over 6 million European call and put options from the S&P 500 Index, covering January 2009 to December 2021. The results confirm the superior forecasting accuracy of the fNTK across different time horizons. When applied to short delta-neutral straddle trading, the fNTK achieves a Sharpe ratio ranging from 1.30 to 1.83 on a weekly to monthly basis, translating to 90% to 675% relative improvement in mean returns compared to forecasts based on functional Random Walk model.
Journal of Business & Economic Statistics, Published online: 03 Jun 2025
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We propose two methods based on the functional principal component analysis (FPCA) to estimate smooth derivatives for a sample of observed curves with a multidimensional domain. We apply the eigendecomposition to a) the dual covariance matrix of the derivatives; b) the dual covariance matrix of the observed curves, and take derivatives of their eigenfunctions. To handle noisy and discrete observations, we rely on local polynomial regression. We show that if the curves are contained in a finite-dimensional function space, the second method performs better asymptotically. We apply our methodology in simulations and an empirical study of option implied state price density surfaces. Using call data for the DAX 30 stock index between 2002 and 2011, we identify three components that are interpreted as volatility, skewness and tail factors, and we find evidence of term structure variation.
Statistica Sinica, 2018: 28, 2469-2496
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Supported by several recent investigations, the empirical pricing kernel (PK) puzzle might be considered as a stylized fact. Based on an economic model with reference-dependent preferences for the financial investors, we emphasize a microeconomic view that explains the puzzle via state-dependent aggregate preferences. We also investigate how the shape of the PK estimated from option and stock market index returns changes in relation to the volatility risk premium.
Review of Finance, 2017: 21 (1), 269-298
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Several empirical studies reported that pricing kernels exhibit a common pattern across different markets. The main interest in pricing kernels lies in validating the presence of the peaks and their variability in location among curves. Motivated by this observation we investigate the problem of estimating pricing kernels based on the shape invariant model, a semi-parametric approach used for multiple curves with shape-related nonlinear variation. This approach allows us to capture the common features contained in the shape of the functions and at the same time characterize the nonlinear variability with a few interpretable parameters. These parameters provide an informative summary of the curves and can be used to make a further analysis with macroeconomic variables. Implied risk aversion function and utility function can also be derived. The method is demonstrated with the European options and returns values of the German stock index DAX.
Journal of Financial Econometrics, 2013: 11 (2), 370-399
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Publication List

Peer-Reviewed Articles

  • Risk Premia in the Bitcoin Market
    Working Paper, 2024

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  • Spectral Factor Model for Corporate Bonds
    Working Paper, 2024

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  • Neural Tangent Kernel in Implied Volatility Forecasting: A Nonlinear Functional Autoregression Approach
    Journal of Business & Economic Statistics, Published online: 03 Jun 2025

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  • Functional Principal Component Analysis for Derivatives of Multivariate Curves
    Statistica Sinica, 2018: 28, 2469-2496

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  • Reference-Dependent Preferences and the Empirical Pricing Kernel Puzzle
    Review of Finance, 2017: 21 (1), 269-298

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  • Shape Invariant Modeling of Pricing Kernels and Risk Aversion
    Journal of Financial Econometrics, 2013: 11 (2), 370-399

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Working Papers

  • Dynamic Analysis of Multivariate Time Series Using Wavelet Dependence Graphs
    Working Paper, 2017

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  • Option Implied Stock Return Distribution
    Working Paper, 2016

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Book Chapters

  • Nonparametric Estimation of Risk-Neutral Densities
    In Handbook of Computational Finance, Jin-Chuan Duan, James E. Gentle, and Wolfgang Härdle (eds). Springer Verlag, 2011, 277-305

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  • Parametric Estimation of Risk Neutral Density Functions
    In Handbook of Computational Finance, Jin-Chuan Duan, James E. Gentle, and Wolfgang Härdle (eds), Springer Verlag, 2011, 253-275

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