Recent Work

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) parametrization 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 calls 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 portfolio returns compared to forecasts based on functional Random Walk model.
Forthcoming in Journal of Business & Economic Statistics, 2023
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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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Publication List

Peer-Reviewed Articles

  • 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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Work in Progress

  • Spectral Networks for Times Series with Scale-specific Factors Adjustment

  • Oblique Trees for Forecasting Single-Stock Options Implied Volatility Surfaces

  • Common Factors in Large Panels of Option Prices

  • Group Factors in Single Stock Options

  • FuncBART: Bayesian Additive Regression Trees with Splits on Functional Covariates

  • The Block-Autoregressive Model in Non-Standard Bases

  • Text Analysis of Public Communication Strategies during the COVID-19 Pandemic

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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