## Problem Given a matrix of exchange rates between `n` currencies, detect whether an arbitrage opportunity exists — i.e., a cycle of exchanges starting and ending at the same currency that results in a profit. ```python def has_arbitrage(rates: list[list[float]]) -> bool: pass def find_arbitrage_cycle(rates: list[list[float]]) -> list[int] | None: # Return the sequence of currency indices forming the cycle, or None pass ``` ## Example ``` rates = [ # USD EUR GBP [1.0, 0.9, 0.75], # from USD [1.12, 1.0, 0.83], # from EUR [1.35, 1.22, 1.0 ], # from GBP ] # USD -> EUR -> GBP -> USD: # 1.0 * 0.9 * 0.83 * 1.35 = 1.008 > 1.0 -> arbitrage! has_arbitrage(rates) -> True find_arbitrage_cycle(rates) -> [0, 1, 2, 0] # USD->EUR->GBP->USD ``` ## Follow-ups 1. What graph algorithm detects this? Why does taking log of rates convert this to shortest-path? 2. What is the time complexity of your approach for `n` currencies? 3. In practice, bid/ask spreads and transaction fees eat into arbitrage. How do you model them? 4. How would you handle rates that change in real time?

InterviewDB Question · USA

Arbitrage System: Detect Arbitrage Opportunities in a Currency Exchange Graph

Onsite

Question Details

Problem Given a matrix of exchange rates between n currencies, detect whether an arbitrage opportunity exists — i.e., a cycle of exchanges starting and ending at the same currency that results in a profit. Example Follow-ups What graph algorithm detects this? Why does taking log of rates convert this to shortest-path? What is the time complexity of your approach for n currencies? In practice, bid/ask spreads and transaction fees eat into arbitrage. How do you model them? How would you handle rat…

Full Details

🔒

Unlock all Jane Street questions

Full insider details, leaked discussions, and candidate experiences.

Get full access — $100 a year, unlimited access

About This Question

This is a reported interview question from a jane street interview during the onsite round.

It covers the following topics: Coding, Graph, Onsite, Matrix .

Topics

Coding Graph Onsite Matrix

Arbitrage System: Detect Arbitrage Opportunities in a Currency Exchange Graph

Question Details

Full Details

About This Question

Topics

More Jane Street Interview Questions