S&P 500オプション予測のLSTM系列モデリング

# S&P 500 Options: LSTM


# S&P 500 Options: LSTM

This notebook fits the declared LSTM member of the sequence population snapshotted by
`09_deep_learning`. Chronological windows, validation gaps, checkpoints, and prediction
eligibility are resolved through the shared sequence boundary.

Prerequisite: `09_deep_learning` must create the complete official sequence population.

**Why the population is declared in one notebook and filled by several.** The set of members is
a claim made once, before any of them is fitted, so that no family can be added or dropped after
its results are visible. This notebook fits one declared member into a population it did not
define and cannot extend; running it alone leaves the population incomplete rather than smaller.

## What this model is, and what it is being asked to do here

An LSTM reads a symbol's history one session at a time and carries a state forward, updating it
at each step through gates that decide how much of the new observation to admit and how much of
the existing state to keep. The gates are what separate it from a plain recurrent network: they
give the model a route by which information from many steps back can reach the output without
being multiplied away at every step, which is what makes a long lookback usable at all.

**What that buys on this data, and what it costs.** The cross-sectional families in this case
study see one row per symbol per decision time: whatever history matters has to have been
compressed into a feature first. This model is handed the window instead and left to decide what
in it matters, so a pattern nobody wrote a feature for is reachable. The cost is that it has far
more freedom to fit noise, and options data on a few hundred names is not abundant, so the
comparison against the cross-sectional families is the point of running it rather than a
formality.

**It is not expected to win, and that is worth saying before the numbers.** A sequence model
earns its keep where the ordering of observations carries information the features do not. If
it does not beat a gradient-boosted model on engineered features here, that is a result about
this data, not a failed run, and the chapter reports it either way.

```python
"""Fit the declared S&P 500 options LSTM request."""

import polars as pl

from case_studies.sp500_options.research_workflow import (
    ALL_LABELS,
    declared_dl_device,
    model_request_catalog,
    open_study,
    published_dl_device,
    resolve_model_requests,
    resolved_model_plan,
    run_official_model_subset,
    run_resolved_model_requests,
)
```

```python
EXECUTION_TIER = "canonical"
WORKSPACE: str = ""
PREVIEW_REDUCTIONS: dict = {}
DEVICE: str = ""

POPULATION_NAME: str = ""
```

### The device the population was fitted on

A network trained on a GPU and the same network trained on a CPU accumulate their sums in a
different order and reach different weights, so the device is part of what the fitted model is
and sits inside the training identity rather than beside it. The device this population was
fitted on is declared once, in `modeling.dl.device` in `config/setup.yaml`, and read from there
by all four deep-learning notebooks rather than retyped in each. On a machine with no NVIDIA
card the run stops here rather than quietly training something else: set `DEVICE="cpu"` and pass
a `POPULATION_NAME` to fit the same requests there, under a name of their own.

**Why a second name rather than a second run under the first.** The published population is a
claim about a specific set of fitted models. A CPU fit of the same request is a different set,
close but not identical, and letting it join the published name would make the population mean
"these requests, fitted somewhere" instead of "these models". The check above refuses that
combination outright rather than warning about it, because a warning in a long run is read once
and then not read.

**This is why the gradient-boosted families run on CPU and these run on GPU.** A reader without
a card can reproduce everything the book compares on trees; the sequence families are the part
that needs hardware, and they are separated so that the absence of a GPU costs a chapter's
comparison rather than the whole case study.

```python
CANONICAL_POPULATION_NAME = "sp500-options-sequence-validation-v1"

published_device = published_dl_device()
device = declared_dl_device(DEVICE)
population_name = POPULATION_NAME or CANONICAL_POPULATION_NAME
if device != published_device and population_name == CANONICAL_POPULATION_NAME:
    raise ValueError(
        f"this run fits on {device!r}, not the published {published_device!r}, so its "
        f"identities are not the ones {CANONICAL_POPULATION_NAME!r} holds; pass "
        f"POPULATION_NAME to give them a population of their own"
    )
print(f"training device: {device} (declared: {published_device})")
```

## Declared request

**What the settings decide.** `lookback: 60` is the window handed to the model: sixty sessions,
about a quarter, so a fitted state can span an earnings cycle without reaching back to a regime
the symbol has left. `hidden_size: 64` and `n_layers: 2` set how much the state can hold and how
many times it is re-read before the output; larger values fit more and generalize less, and on a
panel this size they are the first place overfitting shows. `dropout: 0.1` drops a tenth of the
connections on each training pass, which stops the network leaning on any single one.

`batch_size: 2048` is a throughput choice rather than a modelling one, but it is not neutral:
gradient noise falls as the batch grows, so a large batch trains more smoothly and explores
less. It is declared rather than tuned because tuning it would change what was fitted while
looking like an infrastructure decision.

**The configuration is read from a preset, not written here.** `lstm_h64` names a file under
`case_studies/config/`, so this notebook cannot quietly differ from the same architecture in
another chapter, and a reader comparing the two is comparing declarations rather than code.

**Every label is fitted, not just the primary one.** The request spans `ALL_LABELS`, because
selection downstream ranks across labels as well as across configurations, and a label with no
candidates cannot be chosen or ruled out.

```python
study = open_study(execution_tier=EXECUTION_TIER, workspace=WORKSPACE or None)
requests = model_request_catalog(
    "deep_learning",
    labels=ALL_LABELS,
    config_names=("lstm_h64",),
)
resolved = resolve_model_requests(
    study,
    requests,
    execution_tier=EXECUTION_TIER,
    overrides={"device": device},
    preview_reductions=PREVIEW_REDUCTIONS,
)
resolved_model_plan(resolved)
```

## Execute and validate

The shared sequence runner owns chronological window construction, fold fitting, fitted-state
reload, checkpoint publication, restart, and exact eligible-key validation.

**A checkpoint is part of a configuration, not a detail of how it was fitted.** Training runs for
100 epochs and publishes every fifth, so this one request becomes twenty scored candidates rather
than one. That is deliberate: a network's validation performance is not monotone in training
time, and the epoch at which it peaks is a property of the fit that a reader is entitled to see
rather than a number chosen after the fact. Each published checkpoint therefore carries its own
identity and competes on its own downstream, and picking the best epoch after seeing the results
is selection, which happens once, downstream, on backtests.

**Restart is a correctness property, not a convenience.** Fold fits are written as they finish
and reloaded rather than refitted, so a run interrupted after eight of ten folds resumes at the
ninth. What matters is not the time saved: it is that the alternative - starting over - invites
quietly reducing the job to make it fit, and a population assembled from a reduced re-run and a
full first attempt is not one population. Reloading a fitted state means the checkpoint that
reaches the registry is the one the schedule asked for, whatever happened to the process.

**Windows are built chronologically and never span a fold boundary.** A sequence handed to the
model has to end before the fold's validation window opens, or the state carries information
from the period being scored. The runner owns that construction for the same reason the fold
geometry is shared: it is the kind of rule that is easy to restate slightly differently in each
notebook and impossible to notice when someone does.

```python
if EXECUTION_TIER == "canonical":
    execution, population = run_official_model_subset(
        study,
        resolved,
        population=population_name,
    )
else:
    if not WORKSPACE or not PREVIEW_REDUCTIONS:
        raise ValueError("preview execution requires WORKSPACE and PREVIEW_REDUCTIONS")
    execution = run_resolved_model_requests(study, resolved)
    population = None
```

```python
catalog = execution.catalog_rows.select(
    "family",
    "label",
    "config_name",
    "checkpoint_kind",
    "checkpoint_value",
    "execution_tier",
    "complete",
    "training_hash",
    "prediction_hash",
).sort("checkpoint_value")
if catalog.filter(~pl.col("complete")).height:
    raise RuntimeError("LSTM execution returned a partial checkpoint")
catalog
```

The complete LSTM checkpoint population is ready for model analysis and backtesting. This
notebook does not compare it with another family or choose a checkpoint.

**What completeness means here and why it is checked before anything leaves.** Every requested
checkpoint produced predictions on exactly the rows its eligibility contract declared - not
more, and not fewer. A partial checkpoint is refused rather than published, because a downstream
comparison against a model scored on a subset of the panel is not a comparison, and the subset
is invisible by the time anyone reads the result.

**The eligible rows are fewer than the cross-sectional families see, and that is structural.**
A symbol cannot be scored until sixty sessions of it exist, so this family is eligible on
strictly fewer rows than a model reading one row at a time. `11_model_analysis` groups by
eligibility for exactly this reason: comparing an IC from this population against one from a
cross-sectional population mixes the models with the rows they were scored on.