A Stochastic Volatility Model With Realized Measures for Option Pricing

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options

Measuring price impact and information content of trades in a time-varying setting

The estimation of market impact is crucial for measuring the information content of trades and for transaction cost analysis. Hasbrouck's (1991) seminal paper proposed a Structural-VAR (S-VAR) to jointly model mid-quote changes and trade signs. Recent literature has highlighted some pitfalls of this approach: S-VAR models can be misspecified when the impact function has a non-linear relationship with the trade sign, and they lack parsimony when they are designed to capture the long memory of the order flow. Finally, the instantaneous impact of a trade is constant, while market liquidity highly fluctuates in time. This paper fixes these limitations by extending Hasbrouck's approach in several directions. We consider a nonlinear model where we use a parsimonious parametrization allowing to consider hundreds of past lags. Moreover we adopt an observation driven approach to model the time-varying impact parameter, which adapts to market information flow and can be easily estimated from market data. As a consequence of the non-linear specification of the dynamics, the trade information content is conditional both on the local level of liquidity, as modeled by the dynamic instantaneous impact coefficient, and on the state of the market. By analyzing NASDAQ data, we find that impact follows a clear intra-day pattern and quickly reacts to pre-scheduled announcements, such as those released by the FOMC. We show that this fact has relevant consequences for transaction cost analysis by deriving an expression for the permanent impact from the model parameters and connecting it with the standard regression procedure. Monte Carlo simulations and empirical analyses support the reliability of our approach, which exploits the complete information of tick-by-tick prices and trade signs without the need for aggregation on a macroscopic time scale

A realized volatility approach to option pricing with continuous and jump variance components

Stochastic and time-varying volatility models typically fail to correctly price out-of-the-money put options at short maturity. We extend realized volatility option pricing models by adding a jump component which provides a rapidly moving volatility factor and improves on the fitting properties under the physical measure. The change of measure is performed by means of an exponentially affine pricing kernel which depends on an equity and two variance risk premia, associated with the continuous and jump components of realized volatility. Our choice preserves analytical tractability and offers a new way of estimating variance risk premia by combining high-frequency returns and option data in a multicomponent pricing model

Coupling news sentiment with web browsing data improves prediction of intra-day price dynamics

The new digital revolution of big data is deeply changing our capability of understanding society and forecasting the outcome of many social and economic systems. Unfortunately, information can be very heterogeneous in the importance, relevance, and surprise it conveys, affecting severely the predictive power of semantic and statistical methods. Here we show that the aggregation of web users' behavior can be elicited to overcome this problem in a hard to predict complex system, namely the financial market. Specifically, our in-sample analysis shows that the combined use of sentiment analysis of news and browsing activity of users of Yahoo! Finance greatly helps forecasting intra-day and daily price changes of a set of 100 highly capitalized US stocks traded in the period 2012-2013. Sentiment analysis or browsing activity when taken alone have very small or no predictive power. Conversely, when considering a news signal where in a given time interval we compute the average sentiment of the clicked news, weighted by the number of clicks, we show that for nearly 50% of the companies such signal Granger-causes hourly price returns. Our result indicates a "wisdom-of-the-crowd" effect that allows to exploit users' activity to identify and weigh properly the relevant and surprising news, enhancing considerably the forecasting power of the news sentiment

Comment on: Price Discovery in High Resolution

This note is commenting on Hasbrouck (2018). The paper investigates the problem of price discovery on markets with trades recorded at sub-millisecond frequencies. The application of the popular information share measure of Hasbrouck (1995) to such data faces several difficulties, as the underlying vector error correction models would need a huge number of lags to capture dynamics at different time-scales. The problem is handled by imposing a set of restrictions on parameters inspired by the Heterogeneous Autoregressive model for realized volatility. We illustrate some potential drawbacks of the information share measure adopted in the paper and propose a modeling strategy aimed at dealing with such limitations. In particular, we introduce a structural multi-market model with a lagged adjustment mechanism describing lagged absorption of information across markets. The advantages of the method are shown in simulations

Accounting for risk of non linear portfolios: a novel Fourier approach

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur. Phys. J.

Pricing Exotic Options in a Path Integral Approach

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances.Comment: 21 pages, LaTeX, 3 figures, 6 table

A Jump and Smile Ride: Jump and Variance Risk Premia in Option Pricing

We introduce a discrete-time model for log-return dynamics with observable volatility and jumps. Our proposal extends the class of realized volatility heterogeneous auto-regressive gamma (HARG) processes adding a jump component with time-varying intensity. The model is able to reproduce the temporary increase in the probability of occurrence of a jump immediately after an abrupt large movement of the asset price. Belonging to the class of exponentially affine models, the moment generating function under the physical measure is available in closed form. Thanks to a flexible specification of the pricing kernel compensating for equity, volatility, and jump risks, the generating function under the risk-neutral measure inherits analytical tractability too. An application of the leveraged HARG model with dynamic jump intensity to the pricing of a large sample of S&P500 Index options assesses its superior performances with respect to state-of-the-art benchmark models

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics

The analysis of the intraday dynamics of covariances among high-frequency returns is challenging due to asynchronous trading and market microstructure noise. Both effects lead to significant data reduction and may severely affect the estimation of the covariances if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering the covariances, (ii) market microstructure noise is taken into account, (iii) estimation is performed by standard maximum likelihood. Our empirical analysis, performed on 1-sec NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for high-frequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons