To secure an offer at Akuna Capital, you must demonstrate mastery across three core pillars: algorithmic coding, mathematical foundations, and statistical modeling.
Algorithmic Coding & Data Structures
This area evaluates your capability to translate complex logic into highly optimized code. In high-frequency trading, poorly optimized algorithms can cost millions of dollars in milliseconds, so your code must be optimal from the start.
Be ready to go over:
- Time and Space Complexity – You must instinctively analyze and optimize your code to achieve the best possible asymptotic bounds.
- Custom Data Structure Design – Expect to combine multiple underlying data structures (like combining a doubly linked list and a hash map) to achieve O(1) operations.
- String and Array Manipulation – Master two-pointer techniques, sliding windows, and in-place mutations to handle streaming data efficiently.
Advanced concepts to master include low-level memory management in C++, bitwise operations, and designing thread-safe data structures.
Example scenarios:
- "Given a stream of real-time market trades, design an algorithm to maintain the median trade size in sub-linear time."
- "Optimize a string parser to extract specific financial metrics without allocating new memory buffers."
Probability & Mathematical Foundations
This is often the most challenging stage of the Akuna Capital pipeline. The firm evaluates your intuitive grasp of randomness, risk, and mathematical structures.
Be ready to go over:
- Conditional Probability & Bayes' Theorem – You must be able to calculate and update probabilities rapidly as new information arrives.
- Expected Value & Variance – Master properties of expectation, covariance, and correlation, especially in multi-variable settings.
- Continuous Distributions – Be comfortable with normal, exponential, and uniform distributions, including their probability density functions and moment generating functions.
Advanced concepts include Markov chains, stochastic processes, and properties of random walks.
Example scenarios:
- "Explain how you would calculate the probability that a random walk on a 1D grid reaches +10 before reaching -5, starting from 0."
- "Derive the expectation of the maximum of three independent, uniformly distributed random variables on the interval [0, 1]."
Statistical Modeling & Machine Learning
This area tests your ability to build models that actually generalize to unseen market data. The focus is on robust validation, understanding model limitations, and feature engineering.
Be ready to go over:
- Regression and Classification – Deeply understand linear regression, logistic regression, and tree-based models, including how to regularize them (L1/L2).
- Time-Series Validation – Explain how to prevent data leakage and lookahead bias when validating models on historical financial data.
- Evaluation Metrics – Know exactly when to use metrics like mean absolute error, root mean squared error, log-loss, or AUC-ROC based on the business objective.
Advanced concepts include Monte Carlo simulations, signal-to-noise ratio optimization, and dealing with regime shifts in financial markets.
Example scenarios:
- "Walk me through how you would design a Monte Carlo simulation to price an exotic prediction market contract with path-dependent payouts."
- "If your linear regression model shows a high R-squared on training data but performs poorly out-of-sample, how would you systematically diagnose the issue?"
