Known Limitations

This page documents current limitations so users can make informed decisions about where and how to use TensorQuantLib.

Dimensionality

  • Designed for d ≤ 5 assets. Beyond 5 dimensions, TT ranks can grow rapidly for non-smooth payoffs and grid construction time becomes the bottleneck.

  • For 6+ assets, consider sparse-grid or quasi-Monte-Carlo approaches.

Assets

Grid Points

Full MB

TT Compression

Status

2–3

30/axis

< 1 MB

1–13×

✅ Excellent

4

20/axis

~1 MB

4×

✅ Good

5

15/axis

~6 MB

42×

⚠️ Usable

6+

10/axis

grows

varies

❌ Untested

Performance

  • Single-threaded: All computations run on a single CPU thread. No multi-threading, GPU, or distributed compute.

  • No JIT compilation: Unlike PyTorch/JAX, operations execute eagerly in Python.

  • TT evaluation overhead: For grids < 10,000 entries, direct NumPy indexing can be faster than TT-core contraction.

Autograd Engine

  • First-order only: Supports first-order derivatives (Delta, Vega). Gamma is computed via finite differences.

  • No in-place ops: += is not tracked. Use a = a + b instead.

  • Real-valued only: No complex number support.

  • 16 ops: Missing sin, cos, tanh, abs, where, concatenate.

Financial Models

What IS Implemented:

  • Black-Scholes: closed-form pricing and all analytical Greeks

  • American options: Longstaff-Schwartz LSM with polynomial regression

  • Asian options: Monte Carlo with variance reduction techniques

  • Exotic options: Barrier (8 types), Digital, Lookback, Cliquet, Rainbow

  • Heston stochastic volatility: semi-analytic CF (fast) + QE Monte Carlo

Important Note: Tensor-Train speedup (100-1000x) does NOT apply to Monte Carlo methods (American, Asian, Exotic). TT acceleration works only for smooth analytic surfaces (BS, Heston CF).

Model Limitations:

  • Constant parameters: No term structure or stochastic volatility (except Heston).

  • Basket approximation: from_basket_analytic uses a weighted BS approximation. For accurate basket prices, use from_basket_mc.

TT Compression

  • Smooth payoffs: TT-SVD achieves high compression on smooth surfaces. Discontinuous payoffs show higher ranks.

  • Uniform grid: No adaptive refinement near the strike.

  • Frobenius norm: The eps tolerance controls relative error in Frobenius norm, not pointwise error.

Roadmap

Completed ✅ (v0.3.0):

✅ Reverse-mode autodiff (23+ differentiable ops) ✅ American option support (Longstaff-Schwartz LSM) ✅ Stochastic volatility (Heston semi-analytic CF + QE) ✅ Exotic options (all types via MC + variance reduction) ✅ Second-order Greeks (Gamma, Vanna, Volga via autodiff) ✅ 698 test cases, 98% code coverage

Potential improvements (contributions welcome):

  1. GPU acceleration via CuPy/JAX backends

  2. Adaptive grid refinement near the strike

  3. Higher-dimensional support (d > 5) via cross-approximation

  4. Streaming/online TT updates for live pricing

  5. Stochastic correlation models