Can you solve this puzzle?
Calvin has to cross several signals when he walks from his home to school. Each of these signals operate independently. They alternate every 80 seconds between green light and red light. At each signal, there is a counter display that tells him how long it will be before the current signal light changes. Calvin has a magic wand which lets him turn a signal from red to green instantaneously. However, this wand comes with limited battery life, so he can use it only for a specified number of times.
- a. If the total number of signals is 2 and Calvin can use his magic wand only once, then what is the expected waiting time at the signals when Calvin optimally walks from his home to school?
- b. What if the number of signals is 3 and Calvin can use his magic wand only once?
- c. Can you write a script (in any programming language of your choice) that takes as inputs the number of signals and the number of times Calvin can use his magic wand, and outputs the expected waiting time?
Did you like this puzzle? Are you looking for bigger challenges? Do you want to use your analytical skills to solve real world problems and see the results right away? Do you enjoy writing computer programs? Then the Quantitative Researcher position might be a great opportunity for you!
What you’ll do
As a Quantitative Researcher you will work in a team with Traders and Researchers, right on the trading floor. You will spend your first weeks at Optiver in a structured training program to learn about options, market making and delta 1. You will then immediately start your first project, with the support of a Senior Researcher. We expect you to be versatile, flexible and very creative to think of new innovative solutions. In return we give you the freedom to pursue your ideas and implement them right into our production systems. Within a few months, you will play a key role in developing automated analysis programs and trading algorithms.
What you'll need
- Academic degree with very good grades (e.g. engineering, physics, math, econometrics, computer science);
- Programming experience in any language (C, C++, Python, Basic, JAVA, etc.);
- Ability to apply basic concepts of probability, calculus and linear algebra;
- Ability to carry a project on your own in a structured way within a short timeframe;
- Competitive attitude and eagerness to constantly improve yourself;
- Self-starting, ‘can do’ attitude;
- Ability to learn quickly;
- Excellent verbal and written English skills.
What you’ll get
- The chance to start your career working alongside best-in-class professionals from over 43 different countries.
- Our performance based bonus structure is unmatched anywhere in the industry. We combine our profits across desks, teams and offices into a global profit pool fostering a truly collaborative environment to work in.
Alongside this you will get great secondary benefits such as 25 paid vacation days, fully paid first-class commuting expenses, training opportunities, discounts on health insurance, breakfast and lunch facilities, sports and leisure activities, Friday afternoon drinks and even weekly in-house chair massages. Being highly international, we are accustomed to guiding expats through their relocation, offering competitive relocation packages and providing visa sponsorship where necessary.
Are you interested in starting your career on one of the most dynamic and exciting trading floors in Europe?
Apply directly via our website for the position of Quantitative Researcher. Please provide us with a CV, a solution to part (a) of the puzzle highlighting in bold your final answer in seconds and a letter of motivation in English. Applications without an answer to the puzzle and a letter of motivation will not be reviewed. If you have any questions feel free to contact the recruitment team on firstname.lastname@example.org or on +31 (0)20 708 70 00.