Optiver - Graduate quantitative eesearcher

Can you solve this puzzle?

An ant leaves its anthill in order to forage for food. It moves with the speed of 10cm per second, but it doesn’t know where to go, therefore every second it moves randomly 10cm directly north, south, east or west with equal probability.

1. If the food is located on east-west lines 20cm to the north and 20cm to the south, as well as on north-south lines 20cm to the east and 20cm to the west from the anthill, how long will it take the ant to reach it on average?
2. What is the average time the ant will reach food if it is located only on a diagonal line passing through (10cm, 0cm) and (0cm, 10cm) points?
3. Can you write a program that comes up with an estimate of average time to find food for any closed boundary around the anthill? What would be the answer if food is located outside an area defined by ( (x – 2.5cm) / 30cm )2 + ( (y – 2.5cm) / 40cm )2 < 1 in coordinate system where the anthill is located at (x = 0cm, y = 0cm)?

Was that easy to solve? 

If you enjoy mathematical challenges and writing computer programs, you could be instrumental in the success of Optiver's dynamic trading floor as our next Quantitative Researcher. With your statistics knowledge and top-tier analytical abilities, you’ll create the insights, reports and proposals that drive impactful new trading strategies. Get ready to collaborate with world-class Traders and Software Engineers from more than 50 countries to improve financial markets across the globe. This is your chance to demonstrate how valuable research and data are to the future of electronic trading.

WHO WE ARE:

Optiver is a tech-driven trading firm and leading global market maker. As one of the oldest market making institutions, we are a trusted partner of 50+ exchanges across the globe. Our mission is to constantly improve the market by injecting liquidity, providing accurate pricing, increasing transparency and acting as a stabilising force no matter the market conditions. With a focus on continuous improvement, we participate in the safeguarding of healthy and efficient markets for everyone who participates.

Our Amsterdam office is where it all began. Over 35 years ago, Optiver’s business started with a single trader on the floor of Amsterdam’s European Stock Exchange. Since our 1986 founding, Optiver’s Amsterdam office has grown into one of the most dynamic and exciting trading floors in Europe. Our culture reflects the Dutch capital city’s progressive, innovative and inclusive nature. With its unique spirit, Amsterdam is the ideal hub for our teams to trade a wide range of products from listed derivatives to cash equities, ETFs, bonds and foreign exchange.

WHAT YOU'LL DO:

Our research teams – experts with MSc and PhDs in a variety of STEM subjects – utilise a scientific approach to research and design our world-class trading algorithms. This means applying and developing state-of-the-art stochastic models to price options and predict market volatility, as well as utilising Monte Carlo methods to determine how to perform differentiation on discrete realisations of stochastic processes. It also means developing statistical arbitrage strategies by working with petabytes of low latency, high-frequency market data sets, an extensive high-powered computing back-testing framework and much more. Optiver Researchers believe in academic discourse, and therefore invite their teammates and Traders to challenge each hypothesis. Can it be mathematically improved? Does it pose potential risk? Does it exploit a market behavioural pattern? Can it sustain its output goals? Constant testing, analysis, refinement and innovation ensure our quantitative models remain at the cutting-edge of constantly evolving capital markets.