Monte Carlo GBM Risk Simulation

We simulate M paths over T steps:

S ← S .* exp((μ − ½σ²)Δt + σ√Δt · Z),    Z ~ N(0, 1)
payoff = max(S − K, 0)
price  = mean(payoff) · exp(−μ T Δt)

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Results

Monte Carlo Perf Sweep

250k = 250,000 paths, 1M = 1,000,000 paths, etc.

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Core implementation in RunMat (MATLAB-syntax)

rng(0);
M = 10_000_000; T = 256;
S0 = single(100); mu = single(0.05); sigma = single(0.20);
dt = single(1.0/252.0); K = single(100.0);

S = ones(M, 1, 'single') * S0;
sqrt_dt = sqrt(dt);
drift = (mu - 0.5 * sigma^2) * dt;
scale = sigma * sqrt_dt;

for t = 1:T
  Z = randn(M, 1, 'single');
  S = S .* exp(drift + scale .* Z);
end

payoff = max(S - K, 0);
price  = mean(payoff) * exp(-mu * T * dt);
fprintf('RESULT_ok PRICE=%.6f\n', double(price));

Full sources:

• RunMat / Octave: runmat_rng.m
• Python (NumPy): python_numpy_rng.py
• Python (PyTorch): python_torch_rng.py
• Julia: julia.jl

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Why RunMat is fast (accelerate + fusion)

RunMat fuses elementwise stages and keeps tensors resident on device between steps, while random number generation and updates execute in large, coalesced kernels—a strong fit for GPUs. For the big picture on fusion and residency, see the Introduction to RunMat on the GPU document.

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Reproduce the benchmarks

See the benchmarks directory in the RunMat repo on GitHub for the full source code and instructions to reproduce the benchmarks: runmat-org/runmat/benchmarks.