Modelling Interest Rate Dynamics: A Flexible and Efficient Nonparametric Likelihood Approach

Lead Research Organisation: University of Liverpool
Department Name: Management School

Abstract

Interest rates are a part of everyday life. They are fundamental in the allocation of financial resources in the economy and hence have profound implications on almost every aspect of its operation, from consumer spending to firm production to financial investments, as well as on employment, inflation, and growth.

Interest rates on debt instruments having maturities of less than one year are known as short term interest rates. In the context of financial markets, the dynamics of short term interest rates are central to the valuation of all economic and financial assets whose values crucially depend on them. Therefore, understanding short term interest rate dynamics is now a major concern of both academics and practitioners.

The greatest challenge in modeling short term interest rates is the dilemma between the quest for flexibility in capturing complex features of interest rate dynamics and the desire for tractability and efficiency in the implementation of the model. Existing methods in the literature generally either fail to account for short rate dynamics adequately or lack efficiency in drawing inferences from data in a manner that is convenient and informative.

Thus the overall objective of this project is to develop a flexible and efficient new likelihood based approach for modeling interest rate dynamics. Specifically, this project aims to propose a flexible nonparametric specification for a class of stochastic differential equations and develop likelihood based inferential procedures and investigate nonparametric efficiency in that context. It also intends to extend the approach to multivariate case and test the applicability and suitability of the new methodology in a range of substantive empirical problems in which interest rates feature.

This project, with its range of innovative methodological, theoretical and empirical proposals, promises new advances on the interest rate modeling front. Crucially, the approaches advocated here for using nonparametric RSDEs are completely new, and fill a substantial gap in a literature still dominated by parametric approaches. The use of Empirical Likelihood in this context is also novel. The methodology developed in this proposal will also provide extensive scope for significant empirical contributions to the discipline, given the wide range of empirical problems in which interest rates are concerned.

Although the proposed approach is developed in the context of interest rate modeling, it is general enough to have a methodological impact in the broad realm of stochastic analysis, with substantial applicability to non-economic disciplines such as statistics, physics, engineering, chemistry, medical science, and so on.

Planned Impact

The proposed research has potential significant impacts on a wide range of non-academic sectors both in UK and worldwide. Potential beneficiaries of this research include people from economic and financial sectors, management and business sectors, governmental sectors (including central banks, health sectors, public services sector, etc), as well as various international organizations.

General Non-academic Beneficiaries:
This project promises innovative methodological and empirical contributions in the theory and practice in the broad realm of statistics. Statistics is a vital tool for understanding and managing data and uncertainties arising from every aspect of life. As such, in the most general way, this project has potential significant impacts on our society through its contributions and benefits to a wide range of sectors and communities whose business routinely depend on statistical analysis.

Specific Non-academic Beneficiaries:
Since this project also spans across a number of fields of research, specific benefits, justifications, and potential non-academic beneficiaries are detailed below.

[1] Users concerned with interest rates dynamics:
This project promises a new approach and empirical contributions for modelling interest rate dynamics. This new approach offers additional flexibility and efficiency than that of existing models. Empirical applications will concern practical issues such as estimating term structure of interest rates and valuing interest rate derivatives. Economic, financial and business sectors, central banks, and other governmental sectors may all benefit from the methodological and empirical contributions of this research in modelling interest rates.

[2] Users concerned with economic policies:
In the realm of multivariate analysis which mainly concerns the dependency among variables and their dynamic interactions, this research offers an additional tool for understanding and predicting the effects of government policies on the reaction and performance of the economy in both short and longer terms. Economic, financial, business sectors, central banks, and other policy makers are obvious beneficiaries. For example, better understanding of the dynamic effects of interest rates on other major economic indicators such as inflation, unemployment, and growth will help policy makers (e.g. national central banks, International Monetary Funds, World Bank) in their monetary decisions.

[3] Users concerned with forecasting:
In the realm of time series analysis, the proposed model, with its enhanced effectiveness, potentially helps to improve forecast accuracy. This will yield enormous benefits for people from various sectors whose decisions depend on the prediction of stochastic quantities. Forecasts that have profound implications on our society include economic and business forecasts, weather forecasts, forecasts of spread of diseases, as well as many others.

[4] Users concerned with optimal control and risk management:
In the realm of stochastic analysis, the proposed new stochastic model potentially leads to improved ability in the optimal control of stochastic quantities and management of risks. Engineers may benefit from this research in the optimal control process in the design of machineries; Risk managers may benefit from this project in their ability in controlling and managing risks.

[5] Users concerned with asset valuation:
In the realm of asset pricing, the proposed research promises a new continuous-time model for financial variables, which forms the basis for developing new valuation mechanisms for pricing financial assets such as the interest rate derivatives. More effective valuation of financial assets improves the efficiency of financial markets and allocation of resources. Potential beneficiaries include investment banks, hedge funds companies, asset management companies, pension funds, and financial regulation organizations, etc.
 
Description (Overview)
This project aimed to develop new econometric methods for flexibly and efficiently modelling the dynamics of key economic variables such as the short-term interest rates. The project was fruitful in that it successfully generated four research papers, two new research projects, one new research grant, and two new research partnerships.

(New Knowledge and Methods)
We formally established that Reducible Diffusion (RDs), which formed the foundation of our methodology, are a powerful tool for modelling complex dynamics. Since RDs are nonlinear transformations of analytically tractable Underlying Parametric Diffusions (UPDs), they are substantially more flexible than conventional parametric diffusions and sufficiently tractable for making efficient statistical inference. The main achievement of this project is the development of four novel econometric methods for modelling RDs with applications to short-term interest rates.

Firstly, we proposed a new univariate parametric RD model with time-varying transformations. Our time-varying specifications can potentially account for autoregressive, threshold, smooth-transition, and regime-switching types of empirically relevant dynamic effects, which significantly improved the goodness-of-fit to short-rate data.

Secondly, we proposed a novel three-stage procedure for modelling multivariate short-rate series using a combination of univariate RDs and copulas. This approach is extremely flexible as it allows the users to model independently: (i) the time-invariant marginal distribution of individual series, (ii) the time-series dynamics of individual series, and (iii) most importantly the time-varying nonlinear dependence between multiple series. We derived the asymptotic distributions of the three-stage maximum likelihood estimators of model parameters.

Thirdly, we proposed a novel semiparametric univariate RD model which is crucially assumed to be an unknown transformation of a UPD. This approach yields a general class of dynamic models with parametric dynamic copulas and nonparametric marginal distribution. Very rich and complex dynamics can be generated by this model and its implementation is convenient and efficient. We derived the asymptotic distributions of the estimators of the nonparametric transformation function and the parametric component and studied their finite sample properties.

Finally, we proposed a unified framework for modelling multivariate RDs in both parametric and semiparametric settings. This framework crucially assumes that our multivariate RDs are the so-called triangular transformation of tractable multivariate UPDs. This triangular structure induces significant flexibility while preserving substantial tractability. We investigated the issues of identification and likelihood-based inference and examined the finite sample properties of the proposed estimators.

(New Research Questions, Collaborations and Funding Opportunity)
This project opened two important new research questions: (i) How to generalize our model so that the UPD can have latent components (e.g. stochastic volatility) and hence introduce additional empirically relevant flexibility? (ii) How to generalize our model so that the underlying parametric process can be non-stationary and possibly have jump components?

These research questions have created collaborations between the PI and leading experts in this field. Specifically, the PI is collaborating with Prof. Dennis Kristensen (University College London) on Project (i) and with Prof. Jihyun Kim (Toulouse School of Economics) on Project (ii).

Moreover, the PI has secured new funding from British Academy for the next 18 months on Project (ii).

In the last year, the article "A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures" has been accepted for publication in the journal "Econometric Reviews". The article is based on the outcome from this research project supported by this ESRC grant. In this project, We propose a novel distribution-driven nonlinear multi-factor TD model with latent components. Our model is a transformation of a underlying multivariate Ornstein Uhlenbeck (MVOU) process, where the transformation function is endogenously specified by a flexible parametric stationary distribution of the observed variable. Computationally efficient exact likelihood inference can be implemented for our model using a modifed Kalman filter algorithm and the transformed affine structure also allows us to price derivatives in semi-closed form. We compare the proposed multi-factor model with existing TD models for modelling VIX. Our results show that the proposed model outperforms all existing TD models both in the sample and out of the sample consistently across all categories and scenarios of our comparison.

Matlab codes are compiled into packages for implementing all the models developed from this project.
Exploitation Route While the main contributions of this project are primarily theoretical and methodological, our key findings have clear fundamental importance and profound implications for both academic and non-academic users in predominantly, but not limited to, the areas of statistical and economic analyses.

Academic users from a broad range of disciplines, such as statistics, economics, finance, biology, engineering, and so on, can potentially benefit significantly from the novel concept of stochastic modelling using Reducible Diffusions. More specifically, on one hand theoretical researchers from these disciplines can use our contributions to the theory of stochastic and econometric analyses as the foundation for further exploration of this useful framework with enhanced breadth and depth. On the other hand, empirical researchers from the same disciplines can directly use the new statistical models developed from this project, either as alternative or complementary tools, to improve the flexibility and efficiency in modelling random phenomena of their interests.

Non-academic users, such as central banks, financial sectors, private business, biological, and engineering companies, etc., can similarly use the models developed from this project as additional tools to improve their understanding of, for example, economic dynamics, financial markets behaviour, asset valuation methods, investment and risk management strategies, and so on.
Sectors Financial Services, and Management Consultancy
 
Description This research project mainly has impact on economic and financial aspects of the society in terms of flexible and efficient modelling of economic and financial dynamics such as interest rate, consumption, and financial market volatility. To maximize the potential impact, we took as many measures promised in our pathways to impact statement as we possibly could during and after the life this project. These include creating a dedicated webpage providing access to the progress of this project, circulating and promoting the concept and methodology of this project via university networks, industrial and business related meetings, and so on. One year since the end of the project, our research has indeed attracted the attention and interest of several non-academic organizations. These include a Chinese consultation company specialised in the modelling energy consumption dynamics in China's rural areas, a Shanghai-based fund management company promised to use advanced modelling and trading techniques for investing in the Chinese equity and futures markets. They are generally interested in our innovative methodology for modelling energy consumption dynamics and volatility dynamics of Chinese stock and futures markets, respectively, for risk control purposes. What is particularly encouraging is that we have been contacted by the Federal Reserve Board at Washington DC regarding the feasibility and suitability of applying our new methodology for extracting information from options on natural gas futures. As we are completing this summary, we are continuing our conversations with all three organizations in an effort to assist them to realize the maximum possible practical relevance and potential impact of our methodology to their investment strategy, risk management, and even policy-makings. Nevertheless, it is worth mentioning in this summary that it has been no more than 12 months since the end of this project. In research impact terms, this is a relatively short period of time, considering the fact that the complete set of research outcome from this project have yet to be fully published mainly due to the usual long but rigorous journal review processes. Therefore, the impact of academic research usually takes significantly longer than a year to fully realize its potential. However, as investigators of this project, we are fully committed to our impact pathways to maximize the reward of this project in terms of impact to the society. In 2018, a workshop has been organized by Shanghai Pinxi Investment Management Co., Ltd. which is a private hedge fund company. In this workshop, the principal investigator gave a course on semi and nonparametric modelling of continuous time models for financial derivative pricing. Part of the outcome from research associated with this grant has been considered adopted in the training of financial practitioners in this company.
First Year Of Impact 2018
Sector Financial Services, and Management Consultancy
Impact Types Economic,Policy & public services
 
Description Influence to financial practitioners
Geographic Reach Asia 
Policy Influence Type Influenced training of practitioners or researchers
 
Description BA/Leverhulme Small Research Grant
Amount £9,040 (GBP)
Funding ID SG131649 
Organisation The British Academy 
Sector Academic/University
Country United Kingdom
Start 04/2014 
End 09/2015
 
Title A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures 
Description Transformed diffusions (TDs) have become increasingly popular in financial modelling for their model flexibility and tractability. While existing TD models are predominately one-factor models, empirical evidence often prefers models with multiple factors. We propose a novel distribution-driven nonlinear multi-factor TD model with latent components. Our model is a transformation of a underlying multivariate Ornstein Uhlenbeck (MVOU) process, where the transformation function is endogenously specified by a flexible parametric stationary distribution of the observed variable. Computationally efficient exact likelihood inference can be implemented for our model using a modified Kalman Filter algorithm and the transformed affine structure also allows us to price derivatives in semi-closed form. We compare the proposed multi-factor model with existing TD models for modelling VIX and pricing VIX futures. Our results show that the proposed model outperforms all existing TD models both in the sample and out of the sample consistently across all categories and scenarios of our comparison. 
Type Of Material Data analysis technique 
Year Produced 2019 
Provided To Others? Yes  
Impact A new approach for modelling financial variable dynamics and the pricing of derivatives written on such financial variables. The model is flexible and easy to implement. 
 
Title A Semiparametric Model for Tranformed Diffusions 
Description Our new semiparametric approach for modelling nonlinear univariate diffusions assumes that the observed processes are nonparametric transformations of underlying parametric diffusions (UPDs). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We show that this new class of diffusions can generate rich and complex nonlinear dynamics while at the same time admit closed-form transition densities. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations from discrete samples. vn-consistent semiparametric likelihood-based estimators of the UPD parameters as well as kernel-based drift and diffusion estimators are constructed, which are shown to be normally distributed in large samples. Our simulation study shows that the finite sample performance of our estimators performs closely to the fully parametric ML estimator. 
Type Of Material Data handling & control 
Provided To Others? No  
Impact This research has potential significant impacts on a wide range of non-academic sectors both in the UK and worldwide. Potential beneficiaries of this research include people from economic and financial sectors, management and business sectors, governmental sectors (including central banks, health sectors, public services sector), as well as various international organizations. 
 
Title Distribution-based transformed diffusion models for VIX and VIX futures 
Description Parametric transformed diffusion models where the transformation function is identified from the parametric marginal distribution of the data. Under the standard change of measures, derivative princes can be evaluated based on the closed form transition density functions. 
Type Of Material Data analysis technique 
Provided To Others? No  
Impact Potential impact on practical modelling of VIX derivatives particularly futures contracts. 
 
Title Modelling Stochastic Processes using Reducible Diffusions 
Description Models based on Reducible Diffusions (RDs) assume that the true data generating process is a monotone transformation of some analytically tractable underlying parametric continuous-time diffusions (UPDs). By construction, RDs are more flexible than conventional parametric models due to the variety of specifications we can possibly impose on the transformation function. In the meantime, they maintain sufficient tractability inherited from the more tractable UPDs. In a series of papers based on the findings from the ESRC funded project (ES/J00622X/1), we developed novel parametric and semiparametric methods for modelling univariate as well as multivariate RDs. Empirical evidence suggests that our new models are flexible enough to capture vital empirical features of economic variables such as the short-term interest rates while at the same time statistically efficient likelihood-based inference can be conveniently implemented for our models. 
Type Of Material Data analysis technique 
Provided To Others? No  
Impact Not yet available 
 
Title Parametric Reducible Diffusions with Time-Varying Transformations 
Description Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical point of views. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintain sufficient tractability of the resulting models. In the meantime, our modelling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to UK and US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly. 
Type Of Material Data handling & control 
Provided To Others? No  
Impact This research has potential significant impacts on real world financial modelers intending to capture time-variation in the stochastic financial variables such as interest rates, exchange rates, financial market volatility. The proposed model provides a flexible parametric structure which enables the researcher to model the complex dynamics more flexibly while at the same time the parametric structure allows the user to make inference from data very conveniently. The improved ability to model the reality more adequately and efficiently could improve investment decisions and manage financial risks more effectively. 
 
Description A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures 
Organisation University of Lille
Country France 
Sector Academic/University 
PI Contribution I am the leading contributor to this collaboration. I created the main research idea and played the main role in developing the theory and conducting the empirical exercises.
Collaborator Contribution Prof. Fredj Jawadi from University of Lille and Dr. Yuyi Li from the University of Liverpool contributed to this project by providing useful insight in the empirical application.
Impact The project led to the publication of article "A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures" in the journal "Econometric Reviews"
Start Year 2015
 
Description A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures 
Organisation University of Liverpool
Country United Kingdom 
Sector Academic/University 
PI Contribution I am the leading contributor to this collaboration. I created the main research idea and played the main role in developing the theory and conducting the empirical exercises.
Collaborator Contribution Prof. Fredj Jawadi from University of Lille and Dr. Yuyi Li from the University of Liverpool contributed to this project by providing useful insight in the empirical application.
Impact The project led to the publication of article "A Multi-Factor Transformed Diffusion Model with Applications to VIX and VIX Futures" in the journal "Econometric Reviews"
Start Year 2015
 
Description Nonparametrically Transformed Recurrent Diffusions 
Organisation Harbin Institute of Technology
Department Harbin Institute of Technology Shenzhen Graduate School
Country China 
Sector Academic/University 
PI Contribution I contributed to this collaboration by providing the original novel research idea as well as the knowledge and experience that has been accumulated from research prior to the start of the collaboration. I will also contribute to all aspects of this project as we progress.
Collaborator Contribution My collaborator, Prof. Jihyun Kim from Toulouse School of Economics and Prof. Bin Wang from Harbin Institute of Technology will mainly contribute to the development the large sample theory for statistical inference of the model we intend to develop.
Impact The collaboration is still on-going and in its preliminary stage. This collaboration is multi-disciplinary connecting areas of economics, finance, and statistics.
Start Year 2015
 
Description Nonparametrically Transformed Recurrent Diffusions 
Organisation University of Toulouse
Department Toulouse School of Economics
Country France 
Sector Academic/University 
PI Contribution I contributed to this collaboration by providing the original novel research idea as well as the knowledge and experience that has been accumulated from research prior to the start of the collaboration. I will also contribute to all aspects of this project as we progress.
Collaborator Contribution My collaborator, Prof. Jihyun Kim from Toulouse School of Economics and Prof. Bin Wang from Harbin Institute of Technology will mainly contribute to the development the large sample theory for statistical inference of the model we intend to develop.
Impact The collaboration is still on-going and in its preliminary stage. This collaboration is multi-disciplinary connecting areas of economics, finance, and statistics.
Start Year 2015
 
Description Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates 
Organisation Keele University
Country United Kingdom 
Sector Academic/University 
PI Contribution I am the leader of this project and the main contributor. I provided the original research idea and developed the main theory for the proposed new modelling method.
Collaborator Contribution Prof Fredj Jawadi from University of Lille contributed to the project by providing useful insight to the empirical application. Dr. Jie Cheng from Keele University contributed to the empirical exercises.
Impact The project has led to the publication of the article "Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates" in the journal "Economic Modelling".
Start Year 2015
 
Description Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates 
Organisation University of Lille
Country France 
Sector Academic/University 
PI Contribution I am the leader of this project and the main contributor. I provided the original research idea and developed the main theory for the proposed new modelling method.
Collaborator Contribution Prof Fredj Jawadi from University of Lille contributed to the project by providing useful insight to the empirical application. Dr. Jie Cheng from Keele University contributed to the empirical exercises.
Impact The project has led to the publication of the article "Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates" in the journal "Economic Modelling".
Start Year 2015
 
Description Specification Analysis in Regime-Switching Continuous-Time Diffusion Models for Market Volatility 
Organisation Keele University
Country United Kingdom 
Sector Academic/University 
PI Contribution The project has been completed and the outcome of this collaboration is the publication of the article "Specification Analysis in Regime-Switching Continuous-Time Diffusion Models for Market Volatility" in the journal "Studies in Nonlinear Dynamics and Econometrics".
Collaborator Contribution My partner was mainly responsible for the data collection, simulation, and empirical analysis.
Impact The project has been completed and the outcome of this collaboration is the publication of the article "Specification Analysis in Regime-Switching Continuous-Time Diffusion Models for Market Volatility" in the journal "Studies in Nonlinear Dynamics and Econometrics".
Start Year 2015
 
Description Transformed Diffusion and Copula: Identification and Estimation 
Organisation University College London
Country United Kingdom 
Sector Academic/University 
PI Contribution I am the leader of this collaboration I contribute to the development of theory and I am also responsible for empirical exercises.
Collaborator Contribution Prof. Dennis Kristensen from University College London contribute to the development of theory.
Impact The collaboration has led to a submission to the Journal of Econometrics which is a top journal in the field of econometrics. This paper received the revise and resubmit response and it is being revised at the moment.
Start Year 2015
 
Description Uniform Convergence of Nonparametric Estimation for Recurrent Diffusion Processes 
Organisation Harbin Institute of Technology
Department Harbin Institute of Technology Shenzhen Graduate School
Country China 
Sector Academic/University 
PI Contribution I contribute to this collaboration by providing the original novel research idea as well as the knowledge and experience that has been accumulated from research prior to the start of the collaboration. I will also contribute to all aspects of this project as we progress.
Collaborator Contribution My collaborator, Prof. Jihyun Kim at Toulouse School of Economics and Prof. Bin Wang from Harbin Institute of Technology will mainly contribute to the development the large sample theory for statistical inference of the model we intend to develop.
Impact The collaboration is still on-going and we have developed the most important large sample theory for nonparametric estimation of recurrent diffusion processes. This collaboration is multi-disciplinary connecting areas of economics, finance, and statistics.
Start Year 2014
 
Description Uniform Convergence of Nonparametric Estimation for Recurrent Diffusion Processes 
Organisation University of Toulouse
Department Toulouse School of Economics
Country France 
Sector Academic/University 
PI Contribution I contribute to this collaboration by providing the original novel research idea as well as the knowledge and experience that has been accumulated from research prior to the start of the collaboration. I will also contribute to all aspects of this project as we progress.
Collaborator Contribution My collaborator, Prof. Jihyun Kim at Toulouse School of Economics and Prof. Bin Wang from Harbin Institute of Technology will mainly contribute to the development the large sample theory for statistical inference of the model we intend to develop.
Impact The collaboration is still on-going and we have developed the most important large sample theory for nonparametric estimation of recurrent diffusion processes. This collaboration is multi-disciplinary connecting areas of economics, finance, and statistics.
Start Year 2014
 
Title Matlab Codes for Reducible diffusions with time-varying transformations 
Description This set of matlab codes enable the users to implement the models developed and published in the journal article "Reducible diffusions with time-varying transformations with application to short-term interest rates" published in "Economic Modelling". 
Type Of Technology Software 
Year Produced 2016 
Impact This set of matlab codes enable the users to implement the models developed and published in the journal article "Reducible diffusions with time-varying transformations with application to short-term interest rates" published in "Economic Modelling". The publication of this paper and code has lead to an growing number of citations by researchers. 
 
Title Matlab codes for distribution based transformed diffusions for pricing VIX and VIX futures 
Description This set of matlab codes enable the users to implement the models developed and published in the journal article "An Empirical Comparison of Transformed Di¤usion Models for VIX and VIX Futures" published in "International Journal of Financial Markets, Institutions and Money". The publication of this paper and code has lead to an growing number of citations by researchers. 
Type Of Technology Software 
Year Produced 2017 
Impact This set of matlab codes enable the users to implement the models developed and published in the journal article "An Empirical Comparison of Transformed Di¤usion Models for VIX and VIX Futures" published in "International Journal of Financial Markets, Institutions and Money". The publication of this paper and code has lead to an growing number of citations by researchers. 
 
Title Matlab codes for regime-switching continuous-time diffusion models 
Description This set of matlab codes enable the users to implement the models developed and published in the journal article "Specification analysis in regime-switching continuous-time diffusion models for market volatility" published in "Studies in Nonlinear Dynamics and Econometrics". The publication of this paper and code has lead to an growing number of citations by researchers. 
Type Of Technology Software 
Year Produced 2017 
Impact This set of matlab codes enable the users to implement the models developed and published in the journal article "Specification analysis in regime-switching continuous-time diffusion models for market volatility" published in "Studies in Nonlinear Dynamics and Econometrics". The publication of this paper and code has lead to an growing number of citations by researchers. 
 
Title Matlab codes for two-factor transformed diffusion model for pricing VIX and VIX derivatives 
Description This set of matlab codes enable the users to implement the models developed and published in the journal article "A Multi-Factor Transformed Di¤usion Model with Applications to VIX and VIX Futures" published (forthcoming) in "Econometric Reviews". 
Type Of Technology Software 
Year Produced 2019 
Impact No notable has yet been observed as the article is still forthcoming. 
 
Description Workshop provided to financial modeller 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact A workshop was organized by Shanghai Pinxi Investment Management Co., Ltd. which is a private hedge fund company based in Shanghai, the financial centre of China. In this workshop, I have a course on semi and nonparametric modelling of continuous time models with applications to financial forecasting derivative pricing. The purpose of this workshop is to disseminate the most cutting edge development in semi and nonparametric modelling of continuous time models in finance to the professional practitioners at the forefront of financial market practice. The workshop also aims to gain the first hand feedback from the practitioners about the the financial modelling problems that they are most concerned about and the most needed research directions.
Year(s) Of Engagement Activity 2018