Here is a short list of the most common 'big-concept' questions that I was asked throughout my years as a quant (whether coming from people on the trading floor, in control functions, or from newcomers to the team), in no particular order: What is the risk-neutral measure? What is arbitrage-free pricing? What is a change … Continue reading What is the risk-neutral measure?
No one in the mathematical world believes that Fermat actually had a valid proof of his famous Last Theorem (click here for the Wikipedia article). But I'd be interested to see what his non-proof looked like. Looking at why something is broken is often a good way to get insight into a new research direction. Think … Continue reading What was Fermat’s Non Proof?
One of my favourite abstract painters is Richard Diebenkorn. Click here to see an Art Blog which has a post on his most famous Ocean Park Series. Click here for a link to a blog showing one of the Dibenkorn's canvases in an NY apartment. In these sorts of works it is fascinating how you can see … Continue reading Experimentation in Art & non-deterministic grammars
Every quant knows the expression that defines a forward FX rate on date t with maturity T: where B_f is the foreign discount factor and B_d is the domestic discount factor. But what is the best way to explain this intuitively? Here is my suggestion. Let's pick an example pair, say EUR and CHF, and see … Continue reading Intuition for the forward FX equation
For anyone interested, here are a few links to academic articles I wrote during my PhD on probability theory. I would say that one of the most pleasing parts of the work I completed for my thesis was that we managed to find the right mathematical way to describe a complex problem, which essentially made … Continue reading PhD Mathematics
Ito's product and quotient rules are a corollary of the Ito lemma, and are one of the most important parts of the stochastic-calculus toolkit. When I first started working as a quant I managed to find an alternative form for the rules which sits well in a Black-Scholes type of world and corresponds more closely … Continue reading Ito’s product and quotient rules as described by a trader
It's trivial when you think about it: good mathematical notation is one way of making a problem easier to solve. In my introduction to advanced probability theory I put emphasis on how probability theory has developed a clever and natural way to describe the processes we deal with. If you think about it some more, … Continue reading The power of notation in problem solving