Research Statement
Summary
I have strong research interests in derivatives pricing. The 1987 crash and particularly the 2007+ financial crisis transformed the landscape of derivatives pricing and financial risk management. This research field is important for financial institutions, governments and other actors on the financial scene – it has great potential for research and is receiving a lot of attention and funding from government agencies. For instance, The Montreal Structured Finance and Derivatives Institute will receive funding of $15 million over a 10-year period. Moreover, I have a passion for risk management and I am particularly interested in option pricing. Thus my Ph.D. thesis focuses on various aspects of derivatives pricing. I have two completed articles for my thesis, a third one in progress, and I already have ideas for future papers. I have experience in the management of a financial institution through my involvement in Desjardins Group and I also have professional experience in Information Technology Risk Management. In my research I combine this experience with my passion for derivatives pricing, and I strive to make my research accessible and relevant for practitioners.
Past research
My first article, “Refining the Least-Square Monte Carlo Method by Imposing Structure”, was submitted to Quantitative Finance in May 2012. The least squares Monte Carlo method of Longstaff and Schwartz (2001) has become a standard numerical method for option pricing with many potential risk factors. The method requires choosing a number of regressors; and I noticed the potential stability problem when implementing the method to replicate the results in the aforementioned article. I had the idea to impose structure in order to improve the method. The challenge was to find a suitable regression technique to which constraints could be imposed in a multivariate setting. In this paper we show that by imposing structure in the regression problem, we can improve the method by reducing the bias. This is important for practitioners using this method to price complex options.
My second article, “The Cap Market, the Term Structure and the Unspanned Factors: Taking care of non-linearity”, started out as a comparative study of interest rate derivative pricing models. It is known that practitioners use different models to price financial derivatives that all depend on the interest rate (Bonds, options on interest rates, options on SWAPs, etc.) and that is theoretically wrong. After discussing the issue with professionals at a conference, my research was realigned towards the risk factors and the disintegration between different interest rate markets. We extend the existing literature by showing how factors outside the yield curve still help predict variations in interest rate option prices in a non-linear framework. That explains why classical models have difficulties pricing interest rate derivatives, and justifies why practitioners use market-specific models. We also contribute to the literature by showing that one of the external factors is, in fact, independent from the interest rate. A better knowledge of the interactions between different risk factors and the cap market is important for traders and for portfolio managers using those derivatives to hedge their interest rate risk. The project is supported by a Quebec government research fund (Fond Québécois de recherche sur la société et la culture: FQRSC). Future research on that subject should look at how hedging interest rate risk with options is affected by our findings.
Current research
In the third article in my thesis, I examine an important step in pricing derivatives – the estimation. We focus on GARCH models in continuous time, more specifically the NGARCH specification that exhibits asymmetry and fits well the returns observed on the stock market. The continuous time NGARCH model, as opposed to the discrete time specification, profits from a second source of randomness and is thus more flexible. One can infer the model parameters from the discrete time NGARCH estimation or estimate the model in continuous time using particle filters. Particle filters are used because the model does not have a nice closed form solution. Once both discrete and continuous time estimation methods are performed, we compare them in terms of their ability to price derivatives out-of-sample. To do so, the model will be estimated solely on stock returns. Then, both set of parameters are used to price options. A goodness-of-fit gauges the discrepancy between model prices with actual option prices. It has been shown that the continuous time model performs well in this application. In this paper, we investigate whether estimating the model in continuous time provides an advantage in terms of out-of-sample fitting. This is important, not only for practitioners, but also for researchers using GARCH models in their analyses.
Future research
Among several ideas for future research, I am mainly concerned with the identification of the risk premium in derivatives pricing. Recent literature in asset pricing suggests the risk premium is time varying. This directly affects option traders who need to recalibrate their model every time the risk premium changes significantly. Furthermore, investors can have expectations about future risk premiums that can be different for short-term and long-term options. If that is the case, the risk premium might be a function of maturity. Option pricing models would, therefore, need to account for it. One direction of this research would involve estimating a GARCH model with a time varying risk premium. I have various modelling alternatives, and tests must be conducted to select a proper one. The research can easily be broken down in smaller projects for Master students and early findings could lead to new research ideas which can be shared with colleagues or Ph.D. students.
Conclusion
My research interests focus on derivatives pricing and financial risk management. My past and current research shows that I can carry on research projects and communicate them effectively. My future research will build on my current experience; and I plan to address different topics, like credit risk and integrate new techniques, like copulas. I look forward to bringing my experiences and my ideas to a new research group.
I have strong research interests in derivatives pricing. The 1987 crash and particularly the 2007+ financial crisis transformed the landscape of derivatives pricing and financial risk management. This research field is important for financial institutions, governments and other actors on the financial scene – it has great potential for research and is receiving a lot of attention and funding from government agencies. For instance, The Montreal Structured Finance and Derivatives Institute will receive funding of $15 million over a 10-year period. Moreover, I have a passion for risk management and I am particularly interested in option pricing. Thus my Ph.D. thesis focuses on various aspects of derivatives pricing. I have two completed articles for my thesis, a third one in progress, and I already have ideas for future papers. I have experience in the management of a financial institution through my involvement in Desjardins Group and I also have professional experience in Information Technology Risk Management. In my research I combine this experience with my passion for derivatives pricing, and I strive to make my research accessible and relevant for practitioners.
Past research
My first article, “Refining the Least-Square Monte Carlo Method by Imposing Structure”, was submitted to Quantitative Finance in May 2012. The least squares Monte Carlo method of Longstaff and Schwartz (2001) has become a standard numerical method for option pricing with many potential risk factors. The method requires choosing a number of regressors; and I noticed the potential stability problem when implementing the method to replicate the results in the aforementioned article. I had the idea to impose structure in order to improve the method. The challenge was to find a suitable regression technique to which constraints could be imposed in a multivariate setting. In this paper we show that by imposing structure in the regression problem, we can improve the method by reducing the bias. This is important for practitioners using this method to price complex options.
My second article, “The Cap Market, the Term Structure and the Unspanned Factors: Taking care of non-linearity”, started out as a comparative study of interest rate derivative pricing models. It is known that practitioners use different models to price financial derivatives that all depend on the interest rate (Bonds, options on interest rates, options on SWAPs, etc.) and that is theoretically wrong. After discussing the issue with professionals at a conference, my research was realigned towards the risk factors and the disintegration between different interest rate markets. We extend the existing literature by showing how factors outside the yield curve still help predict variations in interest rate option prices in a non-linear framework. That explains why classical models have difficulties pricing interest rate derivatives, and justifies why practitioners use market-specific models. We also contribute to the literature by showing that one of the external factors is, in fact, independent from the interest rate. A better knowledge of the interactions between different risk factors and the cap market is important for traders and for portfolio managers using those derivatives to hedge their interest rate risk. The project is supported by a Quebec government research fund (Fond Québécois de recherche sur la société et la culture: FQRSC). Future research on that subject should look at how hedging interest rate risk with options is affected by our findings.
Current research
In the third article in my thesis, I examine an important step in pricing derivatives – the estimation. We focus on GARCH models in continuous time, more specifically the NGARCH specification that exhibits asymmetry and fits well the returns observed on the stock market. The continuous time NGARCH model, as opposed to the discrete time specification, profits from a second source of randomness and is thus more flexible. One can infer the model parameters from the discrete time NGARCH estimation or estimate the model in continuous time using particle filters. Particle filters are used because the model does not have a nice closed form solution. Once both discrete and continuous time estimation methods are performed, we compare them in terms of their ability to price derivatives out-of-sample. To do so, the model will be estimated solely on stock returns. Then, both set of parameters are used to price options. A goodness-of-fit gauges the discrepancy between model prices with actual option prices. It has been shown that the continuous time model performs well in this application. In this paper, we investigate whether estimating the model in continuous time provides an advantage in terms of out-of-sample fitting. This is important, not only for practitioners, but also for researchers using GARCH models in their analyses.
Future research
Among several ideas for future research, I am mainly concerned with the identification of the risk premium in derivatives pricing. Recent literature in asset pricing suggests the risk premium is time varying. This directly affects option traders who need to recalibrate their model every time the risk premium changes significantly. Furthermore, investors can have expectations about future risk premiums that can be different for short-term and long-term options. If that is the case, the risk premium might be a function of maturity. Option pricing models would, therefore, need to account for it. One direction of this research would involve estimating a GARCH model with a time varying risk premium. I have various modelling alternatives, and tests must be conducted to select a proper one. The research can easily be broken down in smaller projects for Master students and early findings could lead to new research ideas which can be shared with colleagues or Ph.D. students.
Conclusion
My research interests focus on derivatives pricing and financial risk management. My past and current research shows that I can carry on research projects and communicate them effectively. My future research will build on my current experience; and I plan to address different topics, like credit risk and integrate new techniques, like copulas. I look forward to bringing my experiences and my ideas to a new research group.