MonteCUDA
Monte Carlo options pricer built on custom CUDA kernels. Runs on NVIDIA A10G via Modal, with 1611x speedup over CPU at 10M paths.
A10G · Modal
option type
100
100
1.0 yr
3.0%
20.0%
method
$—
convergence — price ± 95% CI
stream
waiting for A10G...
European Call · S=100 K=100 T=1 r=3% σ=20% N=1M paths
standard error at 1M paths
run comparison to see results
results
| method | price | SE | time ms | VR |
|---|
SE comparison (log scale)
European Call · S=100 K=100 T=1 r=3% σ=20% · CRN bump-and-revalue · 5M paths
all 5 greeks vs black-scholes
| greek | GPU (CRN) | BS analytic | error | |
|---|---|---|---|---|
| Δ delta | — | — | — | |
| Γ gamma | — | — | — | |
| ν vega | — | — | — | |
| Θ theta | — | — | — | |
| ρ rho | — | — | — |
delta SE — 3 methods (8 trials · N=500K)
run computation to see results
naive bump — independent paths each leg: noisy
CRN bump — same Philox seed: noise cancels
pathwise — single pass, differentiates GBM step: lowest variance
CRN bump — same Philox seed: noise cancels
pathwise — single pass, differentiates GBM step: lowest variance
heston parameters
0.04 (σ=20%)
2.0
0.04 (σ=20%)
0.30
-0.70
ρ < 0 → equity skew (OTM puts expensive)
ρ > 0 → commodity skew (OTM calls expensive)
ρ > 0 → commodity skew (OTM calls expensive)
implied volatility smile
prices by strike — GPU MC vs Heston CF
| strike | GPU MC | Heston CF | impl. vol | flat BS vol |
|---|
basket parameters
100
100
100
20.0%
25.0%
Prices across ρ ∈ [−0.9, 0.9] in one shot.
Arithmetic ≥ geometric — Jensen's inequality.
Arithmetic ≥ geometric — Jensen's inequality.
basket price vs correlation ρ
arithmetic vs geometric — Jensen's inequality
| ρ | arithmetic (GPU MC) | geometric (CF) | diff | Jensen |
|---|