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We study short-maturity (\"weekly\") S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer-dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always \"signaled\" by the level of market volatility and elude standard asset pricing models.

We develop a new parametric estimation procedure for option panels observed with error. We exploit asymptotic approximations assuming an ever increasing set of option prices in the moneyness (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We also provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and one constructed nonparametrically from high-frequency data on the underlying asset. Furthermore, we develop new tests for the day-by-day model fit over specific regions of the volatility surface and for the stability of the risk-neutral dynamics over time. A comprehensive Monte Carlo study indicates that the inference procedures work well in empirically realistic settings. In an empirical application to S& P 500 index options, guided by the new diagnostic tests, we extend existing asset pricing models by allowing for a flexible dynamic relation between volatility and priced jump tail risk. Importantly, we document that the priced jump tail risk typically responds in a more pronounced and persistent manner than volatility to large negative market shocks.

We provide a general valuation approach for capital budgeting decisions involving the modularization in the design of a system. Within the framework developed by Baldwin and Clark (Baldwin, C. Y., K. B. Clark. 2000. Design Rules: The Power of Modularity . MIT Press, Cambridge, MA), we implement a valuation approach using a numerical procedure based on the least-squares Monte Carlo method proposed by Longstaff and Schwartz (Longstaff, F. A., E. S. Schwartz. 2001. Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. 14 (1) 113–147). The approach is accurate, general, and flexible.

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

We develop parametric inference procedures for large panels of noisy option data in a setting, where the underlying process is of pure-jump type, i.e., evolves only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across the observation times. We consider an asymptotic setting in which the cross-sectional dimension of the panel increases to infinity, while the time span remains fixed. The information set is augmented with high-frequency data on the underlying asset. Given a parametric specification for the risk-neutral asset return dynamics, the option prices are nonlinear functions of a time-invariant parameter vector and a time-varying latent state vector (or factors). Furthermore, no-arbitrage restrictions impose a direct link between some of the quantities that may be identified from the return and option data. These include the so-called jump activity index as well as the time-varying jump intensity. We propose penalized least squares estimation in which we minimize the L2 distance between observed and model-implied options. In addition, we penalize for the deviation of the model-implied quantities from their model-free counterparts, obtained from the high-frequency returns. We derive the joint asymptotic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vector exhibit different rates of convergence, depending on the relative (asymptotic) informativeness of the high-frequency return data and the option panel.

In the existing literature on barrier options much effort has been exerted to ensure convergence through placing the barrier in close proximity to, or directly onto, the nodes of the tree lattice. For a variety of barrier option types we show that such a procedure may not be a necessary pre-requisite to achieving accurate option price approximations. Using a trinomial tree model we show that with a suitable transition probability adjustment our \"probability adjusted\" model exhibits convergence to the barrier option price. We study the convergence properties of several option types, including exponential barrier options, single linear time-varying barrier options, double linear time-varying barrier options, and Bermuda options. For options whose strike prices are close to the barrier we are able to obtain numerical results where other models and techniques typically fail. Furthermore, we show that it is possible to calculate accurate option price approximations with minimal effort for options with complicated barriers that defeat standard techniques. In no single case does our method require a repositioning of the pricing lattice nodes. [PUBLICATION ABSTRACT]

Working Paper No. 21491 We study short-term market risks implied by weekly S&P 500 index options. The introduction of weekly options has dramatically shifted the maturity profile of traded options over the last five years, with a substantial proportion now having expiry within one week. Economically, this reflects a desire among investors for actively managing their exposure to very short-term risks. Such short-dated options provide an easy and direct way to study market volatility and jump risks. Unlike longer-dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment, i.e., changes in the investment opportunity set. Adopting a novel general semi-nonparametric approach, we uncover variation in the shape of the negative market jump tail risk which is not spanned by market volatility. Incidents of such tail shape shifts coincide with serious mispricing of standard parametric models for longer-dated options. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events on the market that are not always \"signaled\" by the level of market volatility and elude standard asset pricing models.

Options with maturities below one week, hereafter \"ultra-short-term\" options, have seen a sharp increase in trading activity in recent years. Yet, these instruments are difficult to price jointly using classical pricing models due to the pronounced oscillations observed in the at-the-money implied-volatility term structure across ultra-short-term tenors. We propose Edgeworth++, a parsimonious jump-diffusion model featuring a nonparametric stochastic volatility component, which provides flexibility in capturing implied-volatility smiles for each tenor, combined with a deterministic shift extension, which allows the model to fit rich at-the-money implied-volatility shapes across tenors. We derive a local (in tenor) expansion of the process characteristic function suited to value ultra-short-term options. The expansion leads to fast and accurate option pricing in closed form via standard Fourier inversion. We discuss the benefits of the proposed approach relative to benchmarks.

We develop a new parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness- maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained nonparametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model fit for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time. A large-scale Monte Carlo study indicates the inference procedures work well for empirically realistic specifications and sample sizes. In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying jump risk premia and a flexible relation between risk premia and the level of risk. Both extensions lead to an improved characterization of observed option prices.