# Is mathematical finance relevant in asset managament?

I was hoping to consult on the relevance on the relevance of mathematical finance in the asset management business. Traditionally, mathematical finance focuses more on topics related to stochastic process and model under certain assumptions, risk-neutrality for example.

AM seems to prefer another sets of skills concentrated on corporate finance, econometrics (time series, panel, cross section) and recently, machine learning.

So the question is, what do you think of the relevance of mathematical finance in asset management?

• "Traditional" mathematical finance knowledge - stochastic processes, PDEs, monte carlo, trees (often called $\mathbb{Q}$ topics) - is less often used in asset management. However, I would consider time series, econometrics, statistics, portfolio optimization to be mathematical finance knowledge also (often called $\mathbb{P}$ topics) which are very commonly used in asset management. – Chris Taylor Jan 19 '17 at 8:18
• I agree. It is a P vs Q distinction: quant.stackexchange.com/questions/25942/… – Kiwiakos Jan 19 '17 at 9:12

As a start: I am sure some asset managers don't know too much mathematical finance and do a good job. They exist. On the other hand as a mathematician I see mathematics (and classicial mathematical finance - math.fin.) still in various areas and sometimes it is not that easy to draw the line. Let's look at examples:

• If you think of stocks then mathematical finance is hardly needed in AM.
• If you look at bonds then a proper notion of yield curve, forward curve and so forth is useful. You can do a lot of math with floating coupon bonds. Even more with callable bonds and financials like to issue callable bonds. Even a yield-curve (OIS or similar) is much more complicated these days. Thus bonds and moneymarket still use math.finance.

• Concerning derivatives we have the exchange traded derivatives. You can trade stock-futures with only little knowledge of math.fin.. Plain vanilla options are still there. You can "live" without math.fin. there - but it helps if you want to do further analyses.

• Concerning OTC derivatives EMIR made it more complicated and expensive to trade them - thus the variety has decreased (though, we still use IR-swaps ;)). This is not bad in my mind as in the days back then people invented a lot of derivatives that nobody could handle. You needed a lot math.fin. but it often gave you a wrong feeling of control and security.
• newer derivatives: volatility itself is traded these days (exchange traded e.g. as VIX-futures and OTC as variance-swap) and you certainly need math.fin. in this area.

Summing up: For cash instruments you hardly need any mathematical finance. Bonds and moneymarket instruments are still best described using the notions of mathematical finance.

To understand derivatives (which is the core of the subject) you still need it. However, OTC derivatives are much more regulated today and therefore less often implemented.

There are multiple reasons as to why 'traditional' mathematical finance or $P$ topics are not as prevalent in the industry as $Q$ topics.

• A major reason for this is that the latter makes numerous simplifying assumptions, which oversimplify the models, and detach it from reality
• Also, most of the latter models do not have closed form solutions
• $Q$ topics generally leave us with models that require significant computing time - and hence it might be more rewarding to use less accurate but much faster statistical models

That said and done, the distinction between the two is a fine line, and more often than not, you'll find one drawing from the other. Also, some of the assumptions that we make, when drawing up $P$ models, are results from $Q$ topics

PS: 'P' Versus 'Q': Differences and Commonalities between the Two Areas of Quantitative Finance would be an interesting read!