If you apply for quant analyst/quant developer job at investment bank/ hedge fund your quantitative finance interview will generally consist of 4 parts:
- Programming (C++,python,data structures)
- General probability/calculus questions
- Stochastic calculus
- Derivatives pricing questions for asset class (equity derivatives,interest rate derivatives,credit derivatives)
usually 2 types of questions are asked:
– data structures questions (ex. how to construct queue using only 2 stacks,how to sort array)
– specific programming questions , usually it will be C++ or Python.
best ways to prepare for programming part interview is to write small programs and debug them to see the order of execution and variable’s content. this could be very useful (copy paste programs from tutorials to your IDE and debug them)
C++ questions usually would focus on your understanding of virtual functions mechanism,shared pointers and inheritance. so the best way to prepare is to write several minimal programs using derived and base class, and then debug the code to see what constuctor, destructor or member functions get executed.
also get familiar to const , mutable , auto keywords. typical question would be to implement shared pointer from scratch – look here for interview-style implementation
Python questions would usually include pythonic ways to do simple summations on dictionaries , yield keyword and closures. again, best way to prepare is to write minimal programs of different ways to sort array, traverse tree and debug them.
data structures questions would need from you understanding of common data structures (stack, queue, tree) and basic algorithms to work with them. one of the best resourses on this topic is coursera princeton course on algorithms and data structures
questions on data structures usually would involve deriving most optimal method in terms of speed , get familiar with O(N) notation and speed of common algorithms (quicksort, bubble sort, merging of arrays)
get to know well Bayes theorem and solve few dozens of exercises involving it.Calculus questions usually are about calculating integrals and solving simple differential equations.
a lot of questions would involve calculating conditional expectation, so prepare by solving few dozens exercises on discrete and continuous version of conditional expectation.
these questions would need you to demonstrate good knowledge of Ito lemma and martingale theory,remember by heart single and 2-dimensional Ito formula, and then derive differentials for common processes like W^2 , W^3 ln(S_t) exp(S_t) where S_t is black-scholes diffusion.
on questions involving same brownian motion at different times , remember that these points are jointly gaussian and use conditional expectation and variance results
Derivatives pricing questions
even if you interview for interest rate quant positions chances are you would still need to know well equity derivatives , as most questions are easier formulated using stock prices.
you would need to be confident deriving Black scholes equation using PDE and Expectation / Change of measure method. tipical questions would include calculating prices of Call,binanry options in black sholes and binomial tree model.get familiar with Local Volatility and Stochastic volatility heston model, some questions would involve qualitative price differences of , say , barrier options using both models (main thing to remember here is that in local volatility case forward skew is flatter than in stochastic volatility case), get familair with lookback option hedging argument by Gatheral (google “gatheral lookback”).
For Interest rate derivatives Girsanov theorem would invariably come in the interviews so learn how to derive Libor in arrears and CMS convexity adjustment using change of measure. Bermudan swaption pricing in one factor or libor market models can come up, so learn how to qualitativley estimate its price based on mean reversion/correlation.
for credit positions its useful to know how to derive NPV of floating and fixed leg of CDS, and poisson process characteristics.implementation of Credit Valuation Adjustment is discussed here :
Review your quant finance courses to understand basic concepts very well.debug line by line common implementations of algorithms, and practice on your phone using our app: Quant Finance Test. if you can solve all of these questions in under 5 minutes you are good to go.