This project solves the European-type basket option pricing problem. Finding analytical solutions or stable numerical schemes for the corresponding high-dimensional PDE is still an open problem. Hanbali and Linders (2019) propose an approximation of the problem using the element of comonotonicity. Their theoretical results have been further strengthened by Ling (2019) using a modern machine […]
The Value-at-Risk (VaR) is one of the key risk measures to determine the risk levels of trading portfolios. The VaR gives information about the maximal future loss of the portfolio in a given time frame. However, determining a VaR for a given trading portfolio based on historical data of the stocks composing the portfolio results […]
Measuring the degree of co-movement between stock prices is of utmost importance when dealing with portfolio selection, risk measurement and multivariate derivative pricing/hedging. Daily stock price information is easily accessible for a large number of stocks and indices and allows to calibrate multivariate stock price models. Such a model can then be employed to investigate […]
The main objective of an insurance contract is to provide an adequate risk sharing scheme between insured and insurer. An insurance contract should allow the insured to make a risk bearable, which would be unbearable without an insurance contract (e.g. the risk of major damage to your house in case of fire). However, other risk […]
Under the complete market model assumption, risk neutral approach for pricing and hedging financial derivatives have been the standard solution for quite a while. With the rise of machine learning in the past decade, even in an incomplete market, efficient hedging of financial derivatives becomes feasible. This project aims to revisit the two recent groundbreaking […]
A novel holistic principle for risk aggregation and capital allocation has recently been proposed in [1], to remedy the issues of lack of consistency, negligence of cost of capital, and disentanglement of allocated capitals from standalone capitals in the state-of-the-art two steps procedure. Astonishingly, the proposed holistic principle provides a natural structural relationship among standalone […]
This project is a continuation of the IRisk Lab project, Cyber risk profile construction via individual cyber losses aggregation, in Fall 2019. Multivariate frequency model for cyber losses has been constructed, fitted, and tested, in the previous project. This project aims to further improve the multivariate frequency model, as well as construct the multivariate severity […]
Can we simply reboot 2020? Definitely not. But, if so, could we have prepared better for the COVID-19? Most media attention focused on intervention measures to “flatten the curve” such as social distancing, stay-at-home order, mandatory face masks, etc. Another equally important approach to combat an epidemic is through contingency planning and medical resources allocation. […]
Evaluating the performance of an active manager in institutional fixed income portfolios is often challenging due to the necessary customization of issuance-based benchmarks to meet specific investment objectives. These constraints can be related to risk limits including factors such as aggregate credit quality, issuer concentration, or asset type. Other constraints can be more liability-based such as duration, convexity, or minimum yield. Simply assessing a manager’s total returns relative to a broad-based index or peer group in isolation does not provide a complete representation of the quality of management. […]
The Terry Group is a Chicago-based actuarial consulting firm focusing on health care and pensions. The firm is made up of 25 individuals, and includes actuaries, researchers and clinicians. The project was designed for the I-Risk Lab to assist the Terry Group in building a forecasting model using the programming language R. The goal of the […]