by **desperate dan** » Wed Aug 29, 2007 12:40 pm

my second interview

or

the praise of mark joshi's books

(no, I don't know him personally and I also do not receive any payments from him ;)

open position: a junior front office quant position, major investment bank

first topic: pricing forward / plain vanilla equity option. ~45min

Give definition of forward / option? What is the fundamental concept when you price a forward contract (non-arbitrage)? What are the natural boundaries of an option price? What different methods exist to price an option and what are the basic mathematical ideas behind these methods (replication, trees, pde, martingales…)? Give a sketch how you would implement one of these methods in c++. Do that again without including math.h this time, how do you approximate exp(), ln(), how big is the error (Taylor Series)?

To make it short: Read Joshi “The concepts and practice of mathematical finance” chapters 1-7 and “C++ design patterns and derivatives pricing” and do the exercises, brush up your first year calculus when it is a little bit rusty (as it is in my case) and you will do a perfect job!

Next question: brain teaser ~10min

Imagine a chocolate bar (yes, it was a Swiss bank…) consisting of n pieces. How many times do you have to split (? sorry for my English) the chocolate bar until you end up with single pieces? Does the result depend on the shape of the chocolate bar? Proof it (induction).

Additional question: How is it if it’s allowed to lay the already split parts on top of another (sorry for my English) before you split again?

Ha, ha, very funny. At that point I surrendered. I mean I would be able to solve this problem on a rainy Sunday afternoon with a good glass of red wine. But during an interview: impossible, at least for me…

Next question: maths ~20min

Stochastic process, random walk, Brownian motion, Martingales, Markov process: different names for the same thing? Why not? Give definitions and examples...

You choose randomly a number out of the set of R. What is the probability that it is a rational number? What is a measure space? What is a probability space?

Again, Joshi “The concepts and practice of mathematical finance”, chapter 5, 6 and appendix are very useful but I was happy that I read Oeksendal and Rogers/Williams and my maths scripts from university as well

Next question: pricing interest rate product, open discussion ~20min

What is the difference between pricing equity product and interest rate product? Are interest rates changing every second like a stock price or once per day or per year? Is there ONE rate, what different kind of interest do you know? How do you handle the changing shape of the interest rate curve? How does the curve look like today in the US and the Euro zone? Is there a drift in interest rates model, what about volatility? In which models volatility is constant, in which not?

Read Joshi (especially chapter 13) and FT (in this case for actual interest rates, shape of the interest curve)

My preparations for the interview:

- I read the books of Mark Joshi (“read” means: read, understand, memorize, do the exercises)

- I brushed up measure and probability theory and basic calculus

- I tried to follow more or less the market news with FT and NZZ (Ja ich spreche Deutsch, sogar "Puuredütsch" ;)

That time I was more lucky and today I got an invitation for a further interview for this position.

Many thanks!