## Research

**Research Area**

Empirical Asset Pricing, Nonlinear Programming, Equity Derivatives and Mathematical Finance

**Current Work**

I am currently a third-year PhD student in finance at Durham University. My research area is in asset pricing and my key interest at the moment is on empirical implementation and extensions to the Recovery Theorem and extracting the higher dimensional risk neutral correlations from large option prices panel.

My future research will lie in two strands. One is to extend the current work on the Recovery Theorem in the following two areas. First is further estimating the validation of applying the Recovery Theorem with various standard asset pricing models and build a full econometric diagnostic test for the identification conditions. Second, I am also working on extracting pricing factors from the recovered results for a large cross-sectional option panel dataset, which can be plugged into forecasting models for the spot markets. Part of this work will focus on how to extract useful information from single name stocks traded as American options.

Another research interest is on the estimation of the variance and higher order swaps for both the market index options, such as the S&P 500 index options, and also the single-name equity options, FX options and Bond caps and floors. At present I have developed architecture for extracting moment swaps (starting with variance and vol swaps for FX) and estimated the preliminary models using equity option data and FXOs. Part of this work intends to develop new theoretical insights specifically by linking the variance swap analysis with the Recovery Theorem.

In terms of technology, I have collaborated with the data scientists at the University of Trento data lab in Italy to build the infrastructure for analyzing the large quantity of intraday option prices. Their experience with the LISA gravity experiment has helped me gain insight and experience in processing multi terabyte data sets (for instance in Hadoop and openMP). I am developing a line of research in High Performance Computing (HPC) computations for asset pricing models using high frequency data as a side interest.

My future research will lie in two strands. One is to extend the current work on the Recovery Theorem in the following two areas. First is further estimating the validation of applying the Recovery Theorem with various standard asset pricing models and build a full econometric diagnostic test for the identification conditions. Second, I am also working on extracting pricing factors from the recovered results for a large cross-sectional option panel dataset, which can be plugged into forecasting models for the spot markets. Part of this work will focus on how to extract useful information from single name stocks traded as American options.

Another research interest is on the estimation of the variance and higher order swaps for both the market index options, such as the S&P 500 index options, and also the single-name equity options, FX options and Bond caps and floors. At present I have developed architecture for extracting moment swaps (starting with variance and vol swaps for FX) and estimated the preliminary models using equity option data and FXOs. Part of this work intends to develop new theoretical insights specifically by linking the variance swap analysis with the Recovery Theorem.

In terms of technology, I have collaborated with the data scientists at the University of Trento data lab in Italy to build the infrastructure for analyzing the large quantity of intraday option prices. Their experience with the LISA gravity experiment has helped me gain insight and experience in processing multi terabyte data sets (for instance in Hadoop and openMP). I am developing a line of research in High Performance Computing (HPC) computations for asset pricing models using high frequency data as a side interest.

**Working Papers**

**Working Paper 1**

Empirical Recovery: Hansen-Scheinkman Factorization and Ross Recovery from High Frequency Option Prices

Empirical Recovery: Hansen-Scheinkman Factorization and Ross Recovery from High Frequency Option Prices

**Currently being revised**

Recent research has shown that the Perron-Frobenius eigenfunction of a Markov risk neutral state price transition matrix has an interesting economic interpretation. Yet, the application to actual market prices presents significant challenge. For instance, even at the intraday frequency market data, has lots of gaps and can contain unpredictable levels of noise. As a consequence, the identification of the risk neutral state transition matrix often results in a matrix that violates the basic properties of the Markov chain presumed to be driving the evolution of asset prices. We provide a fast non-linear programming approach to the Recovery Theorem such that the attained minimum formally satisfies the desired mathematical and economical constraints (e.g. the de-facto discount factor being smaller than unity and unimodality of the transition matrix). We demonstrate the empirical effectiveness of the methodology on S&P 500 index options and appeal to recent theoretical results to extend this approach to individual stocks.

**Working Paper 2**

Extracting Risk Neutral Higher Moment and Comoment Structure of Asset Prices From Very High Dimensional Panels

Extracting Risk Neutral Higher Moment and Comoment Structure of Asset Prices From Very High Dimensional Panels

**Currently in preparation**

A cottage industry has built up around computing and forecasting average correlations since the Chicago Board of Exchange (CBOE) released the S&P 500 implied correlation index in 2009. The S&P 500 implied correlation is defined as the average pair-wise correlations among the 50 largest component companies in the S&P 500 index and calculated based on the S&P 500 index option and the corresponding single-name equity options, using simple Black-Scholes at the money implied volatilities. The CBOE S&P 500 implied correlation index measures changes in the relative premium between index options and single-stock options at the second moments and provides a risk neutral measure of the volatility diversification in the market. The risk neutral second moment of a single name option reflects the market’s expectation of the future volatility of the equity’s price while the implied second moment from the index option gives the market’s expectation of the movement of the whole market.

Following in a similar spirit, we introduce innovative measures of risk neutral higher order correlations based on the higher order moment swaps and recover the quadratic, cubic and quartic average co- moments of the cross section of asset prices. Specifically, we derive the exact expression of the average risk neutral cubic and quartic correlations for the S&P 500 index by borrowing the super symmetric structure from standard tensor algebra. This allows us to reduce the number of individual operations for, for instance, the quartic correlation contract to about 5% of those requires for its nia ̈ıve calculation. Using our high frequency option prices panel, we document the term structure of the higher dimensional risk neutral correlations implied by the S&P 500 index and all the components companies through 1996 to the end of 2014.

**Working Paper 3**

Operator Methods For Measuring Systemic Risk Using High Frequency Options Panels Submitted to 2017 Conference on ”Banks, Systemic risk, Measurement and Mitigation”

Operator Methods For Measuring Systemic Risk Using High Frequency Options Panels Submitted to 2017 Conference on ”Banks, Systemic risk, Measurement and Mitigation”

Eigenfunction and quadrature methods have been extensively used in asset pricing to define forward looking pricing measures. In contrast, their use in generating systemic risk measures has been limited. Most uses of forward looking volatility models in systemic risk calculations have focused on using at-the-money Black-Scholes implied volatilities or eschewed derivatives based measures completely for parametric and semi-parametric models such as those from the GARCH family. With the advent of high frequency options panels we document a battery of measures that could be constructed and applied to the measurement of systemic risk, these include computationally intensive measures of cubic and quartic correlations. We outline the calculation of each measure and then present a useful library of statistical properties and stylized facts to allow macro-prudential policy makers to complement their existing risk measures.

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