Quant Interview Questions

This is a collection of quantitative problems/questions of the sort you may encounter in a quantitative finance job interview for a derivative pricing related position, e.g. Front Office or Model Validation Quant, Trader, Risk Management etc. You can also find these videos on our youtube channel.

Problem 1: ATM Option Price Approximation

Derive the well-known trader’s approximation for an AT-THE-MONEY Call or Put Option under the assumption of zero interest rates and no dividends for the stock process. $$\begin{align} \text{Option Price} \approx \frac{1}{\sqrt{2 \pi}} S \sigma \sqrt{T-t} \end{align}$$ where $S$ is the current stock price, $\sigma$ is the volatility, $T$ is the expiry time of the option and $t$ is the current time.
Solution
You may have seen the formula for an approximation of an at the money call or put option price before, but not seen the derivation. I will derive it for you in two ways! Hit the play button

Problem 2: How can you simulate Brownian Motion in Python?

Problem 3: What is a Brownian Bridge and how can you use it to simulate Brownian Motion? Can you derive the mean and variance of a Brownian Bridge?