Kelly Position Sizing API

Endpoint

Computes Kelly criterion optimal position sizing for an option trade. Uses numerical integration over the full lognormal distribution of the underlying to maximize expected log-wealth growth - not the simplified gambling formula. Requires Growth plan or higher.

Parameters

How mu works

The key input is mu - your expected annual return for the underlying. This is what gives you an edge over the market price, which uses r:

• mu > r - you are more bullish than the market, so calls have positive edge
• mu < r - you are more bearish, so puts have positive edge
• mu = r - no edge, so Kelly recommends no position

For example, if SPY is priced with r = 4.5% but you expect mu = 12%, your calls have an edge and Kelly tells you how much to risk.

Request

curl -H "X-Api-Key: YOUR_API_KEY" \
  "https://lab.flashalpha.com/v1/pricing/kelly?spot=580&strike=580&dte=30&sigma=0.18&premium=12.69&mu=0.12&type=call"

import requests

resp = requests.get(
    "https://lab.flashalpha.com/v1/pricing/kelly",
    params={"spot": 580, "strike": 580, "dte": 30, "sigma": 0.18,
            "premium": 12.69, "mu": 0.12, "type": "call"},
    headers={"X-Api-Key": "YOUR_API_KEY"}
)
resp.raise_for_status()
k = resp.json()
print(k["recommendation"])

const qs = new URLSearchParams({ spot: 580, strike: 580, dte: 30, sigma: 0.18, premium: 12.69, mu: 0.12, type: "call" });
const resp = await fetch(`https://lab.flashalpha.com/v1/pricing/kelly?${qs}`, {
  headers: { "X-Api-Key": "YOUR_API_KEY" }
});
if (!resp.ok) throw new Error(`HTTP ${resp.status}`);
const k = await resp.json();
console.log(k.recommendation);

{
  "inputs": {
    "spot": 580,
    "strike": 580,
    "dte": 30,
    "sigma": 0.18,
    "premium": 12.69,
    "mu": 0.12,
    "type": "call",
    "risk_free_rate": 0.045,
    "dividend_yield": 0.013
  },
  "sizing": {
    "kelly_fraction": 0.076842,
    "half_kelly": 0.038421,
    "quarter_kelly": 0.01921,
    "kelly_pct": 7.68,
    "half_kelly_pct": 3.84
  },
  "analysis": {
    "expected_roi": 0.160546,
    "expected_roi_pct": 16.05,
    "expected_payoff": 14.7273,
    "probability_of_profit": 0.391739,
    "probability_of_profit_pct": 39.17,
    "probability_itm": 0.557494,
    "probability_itm_pct": 55.75,
    "max_loss": 12.69,
    "breakeven": 592.69,
    "expected_growth_rate": 0.005844
  },
  "recommendation": "Risk 3.8% of bankroll (half-Kelly). Probability of profit: 39.2%. Expected ROI: 16.1%.",
  "endpoint_version": "2026.09.30",
  "data_as_of": {
    "node": "fa5",
    "equity_feed": "2026-10-30T13:46:18.181Z",
    "equity_options_feed": "2026-10-30T13:46:18Z",
    "index_feed": "2026-10-30T13:46:17.119Z",
    "index_options_feed": "2026-10-30T13:46:16Z",
    "futures_feed": "2026-10-30T13:46:15.271Z",
    "futures_options_feed": "2026-10-30T13:46:14.335Z",
    "flow_feed": "2026-10-30T13:46:00Z",
    "oi_feed": "2026-10-29T20:00:00Z",
    "macro_feed": "2026-10-29T21:00:20Z"
  }
}

Response Fields

Fields of inputs

Negative expected value

If the option has negative expected value (your view does not justify the premium), Kelly returns zero:

{
  "sizing": { "kelly_fraction": 0, "half_kelly": 0, "quarter_kelly": 0 },
  "recommendation": "Negative expected value - Kelly recommends no position."
}

Notes

• All probabilities use the real-world measure (with mu), not the risk-neutral measure (with r).
• The Kelly fraction is bounded to [0, 1]: it never recommends shorting or leverage beyond 100%.
• Half-Kelly is strongly recommended in practice - full Kelly is mathematically optimal but very aggressive and assumes perfect parameter estimates.
• The integration uses 2,000 steps over ±6σ of the lognormal distribution.

Errors

Authentication (401) and rate-limit (429) errors use the common error format, see Error Responses.

What Is the Kelly Position Sizing Endpoint?

The Kelly criterion picks the fraction of your bankroll that maximizes long-run growth given your edge. Standard Kelly is built for fixed-odds bets; an option has an asymmetric, bounded-loss payoff, so this endpoint integrates the payoff over the full lognormal distribution of the underlying instead. You supply your own expected return mu; the gap between that view and the risk-free rate the market prices with is the edge Kelly sizes.

Common Use Cases

• Size directional option trades - turn a price target view into a bankroll fraction
• Filter trades by edge - skip contracts where Kelly returns zero
• Compare strikes - run several strikes and pick the best expected growth rate
• Add risk guardrails - cap automated orders at half or quarter Kelly

Related

Related reading

• Build a Kelly criterion options calculator - a worked sizing example

Complementary endpoints

• BSM Greeks Calculator - price the option before sizing it
• Implied Volatility Solver - get sigma from the market price
• Option Quote - live premiums to feed premium