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On 27 September, Paul Gruntjes (1981) will be awarded his doctorate at the UvA. His doctoral research at the Korteweg-de Vries Institute for Mathematics (KdVI) involved developing new methods for quickly and accurately calculating the price of a financial option.

### What did you do?

‘I developed new mathematical models which can be used to determine the value of a financial option at a given moment. A financial option is the right to buy or sell something – such as a share, for example – at a previously agreed price. The question is always, what is the value of that right; or, what does the option cost? If it’s an option on just one share, that’s relatively easy to determine. I looked at what’s known as basket options. These are options on baskets which may contain 125 different products. Determining the price of that is not quite so easy.’

### Why is that more difficult?

‘The various products in the basket all influence each other. Calculating a high dimensional option, meaning a big basket, is therefore more difficult than for a basket with just one product. And you can’t just ‘add up’ all the different products. So the larger the basket, the more difficult it is to determine the price. There are models for high dimensional basket options, but they usually use a fixed correlation. That makes the outcome static. With the models I’ve developed, the correlation is variable over time, so they better reflect actual circumstances. For instance, if there’s a crash in the financial markets, everything drops and the correlation goes to +1. Existing models don’t pick that up, but the models I've developed do. It took me around a year to develop the first model. I then made another version of it, and two other models.

### Is the model being used yet?

‘Not yet, but I’d love to apply it in my own work. I’m a derivatives portfolio manager at Syntrus Achmea, which is the asset management operation within the Achmea Group. I came up with the idea of developing new models years ago because I could see that professionals, including myself, were coming up against the same problems. That’s why I embarked on this doctoral research six years ago. The only reason I’m not working with the model yet, is simply because I don’t have the time to implement it here.’

### Now that you’re working fulltime at Achmea again, do you miss doing research?

‘Absolutely, and I'd love to carry on doing it. I still have so many ideas that follow on from my doctoral subject that I would like to investigate. Ideally I would love to spend one day a week doing research at the UvA and continue working at Achmea the rest of the week. That mix of theory and practice suits me well. At the same time, what I loved about pursuing a doctorate was being able to do in-depth research. I’ve found that others find it hard to understand what I’m doing. But they’re always interested in knowing whether I have any investment advice to share.’

Author: Carin Röst