Options Pricing Engine

Hard ● Live C++ Rust Java Python

The Problem

Price 500,000 European options contracts using the Black-Scholes model. For each contract, compute the theoretical price and the five key Greeks (delta, gamma, vega, theta, rho).

Handle numerical stability for extreme market conditions, optimize for speed, and ensure precision to 6 decimal places.

Evaluation Criteria

Correctness (70%)

All Greeks and prices must be computed correctly using the Black-Scholes model. Output tolerance: 0.0001 per value.

Performance (30%)

Wall-clock time on the 500K option dataset. Memory usage (peak RSS).

Input Format

First line: N = number of options to price.
Each row: S,K,T,r,sigma,type where type is C (call) or P (put).
S, K: underlying spot price and strike, both as floats.
T: time to expiry in years (e.g., 0.5573 for ~6 months).
r: risk-free rate (annualized, e.g., 0.025).
sigma: annualized volatility (e.g., 0.40).

Output Format & Sample

Sample input (first 8 lines, full file linked below):

10
145.91401976868258,118.19098374774204,0.5573083435545473,0.025624751670417594,0.4682356070820062,C
138.57387686735595,112.62080113909408,0.19645352732456897,0.026286262537351772,0.40100936452499014,C
157.40294193836053,170.07859918986685,0.8448444437137009,0.04144463323986976,0.23909535411533137,C
163.8211050694651,141.51911031297107,0.8510026523254701,0.02945099391701493,0.2076568810537944,P
65.33154147797731,62.19372766246351,0.7243689671644106,0.03407690057352798,0.23226043361100654,C
159.45976800407269,161.77053722751145,1.9465003703189474,0.036497406404584744,0.37602031563661353,P
136.6028217885143,147.78085782268082,0.1011905234747678,0.02595287929560828,0.2446939818010536,C
... (more)

Expected output for that sample (first 8 lines):

36.495247 0.793449 0.005596 31.088347 -15.091332 44.183451
27.783064 0.900546 0.007097 10.736097 -13.507498 19.057783
10.919573 0.466838 0.011493 57.518481 -10.731879 52.855270
2.912576 -0.160955 0.007783 36.913577 -3.641387 -24.917638
7.629057 0.681789 0.027625 19.837684 -4.438250 26.738818
27.876982 -0.355579 0.004453 82.872937 -4.917736 -164.630319
0.961265 0.174172 0.024170 11.167668 -14.095087 2.310290
24.721737 0.497928 0.004943 62.271897 -23.678292 49.097100
... (more)

↓ download full sample input | ↓ download expected output

Test your solution locally: ./your_solution < input.txt | diff - output.txt

Common Pitfalls

Per option, output: price, delta, gamma, vega, theta, rho. In that order, on one line, comma-separated, ~6 decimal places.
Vega and rho conventions vary. The reference uses per-1-vol-point and per-1-rate-point (so divide raw partials by 100 if you derived them from d(price)/d(sigma)).
Theta is per year, not per day. Multiply by -1/365 if you want a per-calendar-day number; the grader expects the raw per-year partial.
Use erf for the normal CDF. Don't roll your own approximation; precision on tail strikes matters for the accuracy check.
Tolerance is 0.0001. Make sure your erf implementation is double precision, not float.

Performance Tier Thresholds (applied by the grader)

Language	Gold	Silver	Bronze	Tier 4
C++	<400ms	<1500ms	<8000ms	else PASS
Rust	<400ms	<1500ms	<8000ms	else PASS
Java	<800ms	<3000ms	<15000ms	else PASS
Python	<4000ms	<12000ms	<50000ms	else PASS

Submission Rules

Single-file solutions only. All code must be in one file.
Your program must read from stdin and write to stdout.
Java class must be named Solution.
No network access, no filesystem access beyond stdin/stdout.
Time limit: 120 seconds. Memory limit: 2 GB.

Challenge Stats

Contracts: 500,000

Greeks per contract: 6

Gold Target: <400ms (C++/Rust)

Languages: 4

Starter Templates

↓ skeleton.cpp ↓ skeleton.rs ↓ Skeleton.java ↓ skeleton.py

Submit Your Solution

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