Working papers

The Black-Merton-Scholes (BMS) model has become the industry standard for quoting and risk managing option positions. This standard, however, experiences severe stress when dealing with short-dated options, for which the BMS option implied volatility can become explosive in the presence of random price jumps. This paper proposes a new theoretical framework for pricing, quoting, and risk managing short-dated option contracts. The framework subordinates a diffusion process with an unbiased gamma jump process with its characteristic time matching the expiry of the option contracts. Option valuation can be represented as an exponential function with a single volatility input. Given an option price, the option's implied volatility can be solved analytically with a Lambert function. The paper applies the new pricing framework to short-dated NDX options and highlights its effectiveness in matching closer with the empirical return distribution, generating more stable implied volatility quotes, leading to better delta hedging performance, and identifying more uniformly profitable relative value investment opportunities.

This paper proposes a bootstrapping procedure for estimating conditional option return risk and option risk premium. Applying the procedure to currency options shows that mean-variance option investment based on the bootstrapped risk and risk premium generates high risk-adjusted returns. Attributing the bootstrapped risk and risk premium to classic risk factor structures highlights the time-varying contribution of each risk source and identifies highly profitable factor timing investment opportunities. Incorporating the bootstrapped option risk premium in option pricing model estimation enhances statistical dynamics identification and promotes model designs that capture both the option price behavior and the option risk premium variation. 

This paper strives to identify value-based systematic investment opportunities in the U.S. corporate bond market through the joint construction of a bond valuation model and a return factor model. The valuation model explains the cross-sectional variation of bond yields with a flexible local linear functional form in bond risk characteristics. The return factor model embeds the residual yield from the valuation model as a mispricing factor, while accounting for stronger co-movements between bonds from the same industry, similar rating classes, and similar duration segments, as well as differential market pricing for bond return risk, liquidity cost, and optionality exposure. The slope coefficient on the mispricing factor captures the ex post excess return on the value-investing portfolio that targets a unit exposure to the identified mispricing opportunities while being neutral to all systematic risk exposures. 

Investors are averse to risk but love optionality. When a security's embedded optionality increases with its risk level, the entanglement,  combined with the opposite investor preferences, can generate seemingly abnormal market pricing behaviors. This paper frames the bond and stock return behavior within a structural framework and disentangles their directional risk exposure from their optionality exposure via a joint stock-bond return factor model. The factor portfolio targeting a unit exposure to market risk but zero exposure to optionality generates a significantly positive average excess return, consistent with investor risk aversion. By contrast, the factor portfolio targeting a unit exposure to optionality but without directional exposure to firm value variation generates a significantly negative average excess return, reflecting investor penchant for optionality. The separation of risk from optionality sheds light on the distress puzzle in the stock and bond market and helps explain the bet-against-beta and volatility premiums in the stock market.

This paper introduces the concept of cross-sectional mean-variance efficiency in corporate risk-taking decisions. We construct mean-variance ratio forecasts on the asset return of US public companies and examine how much the forecasts can explain the cross-sectional risk-taking variation with a common proportionality coefficient. Estimation shows that cross-sectional mean-variance efficiency explains a large proportion of corporate risk-taking variation at the firm level and almost completely explains the variation at the industry level. Over time, corporations target mean-variance efficient allocations to maintain stable financial leverage. When a firm deviates from mean-variance efficiency, the firm rebalances toward it at a slow speed.

The paper identities the historical variance term structure as a key conditioning variable that differentiates the different phases of a company's information cycle and shows that stock variance dynamics vary strongly through the different phases of the cycle. To predict stock variance over a large and ever-changing universe, the paper replaces time-series dynamics specification per each name with a cross-sectional forecasting relation at each date and develop a two-dimensional conditional pooling estimation that balances the needs for reducing estimation errors and capturing dynamics variation across the cycle. We quantify the economic significance of the approach through an option investment analysis and highlight the classic asset pricing relation variations across the information cycle.