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 in a backwards-looking risk measurement. Such an approach is only appropriate if the past can be used as a proxy for the (near) future. However, given the dynamics behavior of financial markets, the information contained in past market data is deteriorating rapidly with the horizon and backwards-looking risk estimates are not always a good representation for the true risk levels. Moreover, the discrepancy between reality and model is large when a market is in distress, resulting in a bad risk estimate when it is needed the most.

Therefore, we investigate how option data on the components of a portfolio can be employed to determine the Value-at-Risk of the investment portfolio. Such an estimate is called an implied estimate.  Option prices are containing the aggregate view of the market on future price levels. Therefore, an implied portfolio Value-at-Risk is automatically forward-looking. Moreover, we investigate model-free approaches for determining the VaR. 

Students: Xuan Lin, Yifan Sun, Zixuan Wang
Supervisor: Daniël Linders
Graduate Supervisor: Elizaveta Sizova

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 extent to which stocks will move together in the future. However, intraday movements of stock prices are behaving differently from longer-term (daily, weekly or monthly) movements. Our aim in this project is to use high-frequency data of stocks to investigate how stock prices move together during a trading day. The intra-day co-movement may change rapidly, giving rise to changes in diversification when composing a portfolio.

The project is based on the order book data of the Chinese stock market. An order book is a list of orders for a certain security placed by the public, which contains detailed information about the order time, direction, depth, amount, etc. The observation interval is extended from 1 day to 3s. High-frequency raw data is associated with not only massive information but also massive noise, calling for different approaches to extract information about volatilities and co-movements. The size of the dataset to be used is up to 100G, which makes efficient code necessary.

Students: Neer Bhardwaj, Changyue Hu, Runshi Li, Yirui Luo
Supervisor: Daniël Linders
Graduate Supervisor: Yong Xie

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 sharing schemes exist that allow for such a risk transfer, but which are more efficient/cheaper than an insurance contract.

In this project we will compare classical insurance with Peer-to-Peer (P2P)-insurance. P2P insurance is a form of decentralized network, where the policyholders are assumed to make payments directly to each other. Such an approach is fundamentally different from classical insurance, where payments are made by and to a central unit (the insurance company)

Students: Shuyi Jiang, Churui Li, Jing Wu
Supervisor: Daniël Linders
Graduate Supervisor: Samal Abdikerimova

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 works, [1] and [2], and explore potential extensions in actuarial contexts.

References:
[1] Buehler, H., Gonon, L., Teichmann, J., and Wood, B. (2019). Deep hedging, Quantitative Finance 19, 1271-1291.
[2] Buehler, H., Gonon, L., Teichmann, J., and Wood, B., Mohan, B., and Kochems, J. (2019). Deep hedging: hedging derivatives under generic market frictions using reinforcement learning, available at SSRN: https://ssrn.com/abstract=3355706.

Students: Yuxuan Li
Supervisor: Alfred Chong and Haoen Cui

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 capital, aggregate capital, allocated capital, and diversification benefit, which is consistent with the current market practice of allocating diversified capitals. However, for parsimonious reasoning, [1] only studies a two-level corporate hierarchy model. This project aims to extend the results in [1] to the Solvency II standard, which involves a multi-level corporate hierarchy model; see, for example, [2].

References:
[1] Chong, W. F., Feng, R., and Jin, L. (2019). Holistic principle for risk aggregation and capital allocation. [The manuscript is available upon request.]
[2] Filipovic, D. (2009). Multi-level risk aggregation, ASTIN Bulletin: The Journal of the International Actuarial Association 39(2), 565-575.

Students: Ruiqi Liu, Yilin Zhu
Supervisor: Alfred Chong

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 model for cyber losses, and hence determine the aggregate cyber loss.

Students: Nargiz Alekberova, Evelyn Lai Jia Yi, Hanqing Wang
Supervisor: Alfred Chong, Daniël Linders
Graduate Supervisor: Linfeng Zhang

This project is a continuation of the IRisk Lab project, European-type basket option pricing: independence and comonotonicity approximations with modern machine learning approaches, in Fall 2019. Feedforward neural network (FNN) has been employed in the previous project to revisit the basket option pricing proposed in [1]. This project aims to further improve and investigate modern machine learning approaches on the basket option pricing, such as comparison of FNN with Gaussian process regression (GPR) and their error convergences.

References:
[1] Hanbali, H. and Linders, D. (2019). American-type basket option pricing: a simple two-dimensional partial differential equation, Quantitative Finance 19, 1689-1704.

Students: Jonathan Lu, Kara Wong
Supervisor: Alfred Chong, Daniël Linders