Teaching a small LLM to call a Black–Scholes pricer

exact tool-call success, unit-normalized prompts

94.8%

routing accuracy, tool vs. no tool

97.5%

false-positive tool calls after selective SFT

85% → 5%

The question

The target is a structured call such as bs(S=100, K=110, T=0.5, r=0.05, sigma=0.2, type="call"). Getting the format right is the easy part. The hard parts are converting "5%", "six months", or "90 days" into the right arguments, and not reaching for the tool when the question has nothing to do with option pricing.

Approach

• Two synthetic data layers. Layer 1 teaches format and argument extraction with standard units. Layer 2 mixes rates, volatilities, and maturities across decimals, percent signs, percent words, years, months, and days, a full 3×3×3 grid of 27 unit combinations.
• Leakage control. Train, validation, and test are split at the level of the underlying scenario, so the same option never appears in two splits under different wording.
• Dense, interpretable reward. A restricted AST parser grades format, parseability, function name, required arguments, safe values, numeric correctness, and option type separately.
• Training. LoRA supervised fine-tuning, then GRPO, with a DPO ablation and a comparison against the 360M model.
• Over-tooling. A separate benchmark of prompts that should not trigger the tool, and a mixed selective SFT set to fix it. Paired bootstrap intervals guard against over-reading small differences.

Results

What I learned

• Supervised fine-tuning does most of the work of teaching an interface; reinforcement learning on top of a nearly saturated checkpoint did not improve it here.
• A model that has just learned a tool wants to use it everywhere. Over-tooling was the most practical failure, and targeted SFT fixed it better than mixed GRPO.
• Some remaining errors are about capacity: the 360M model closes most of the gap.