qStorm turns a forecast of an asset's return distribution into option prices, with no option quotes. Draw a forecast, or pick one the model really made, and see the prices it implies. preliminary
01 The forecast
Over t days the return is your one-day shape widened by √t. Summing independent days pulls a shape toward a bell curve, so by default its departure from one shrinks like 1/√t.
02 What qStorm prices
Smiles
Lines: the exact finite-difference solve of the pricing equation. Dots: the trained network, which prices in microseconds. Dashed: Black–Scholes, which uses one vol for every strike.
03 Price one option
Per $100 of forward, undiscounted. The network is trained from 0.05 to 30 trading days and out to ±10 forecast sds.
What you are looking at
A forecast says how likely each return is: Qt = σ√t · yt(z) with z standard normal, where yt is the forecast's quantile curve. If tomorrow's return really has that law, the stock follows dS = μS dt + ϱS dW with ϱ = ∂Q/∂W, a local volatility read straight off the forecast. Delta hedging removes the drift and leaves the pricing equation Vt + ½S²ϱ²VSS + rSVS − rV = 0. For a bell curve ϱ is constant and this is Black–Scholes. Otherwise the skew and fat tails of the forecast become the smile.
qStorm solves that equation two ways. A network trained on the equation itself (a physics-informed solver) prices any strike and maturity in microseconds. A finite-difference solve is the exact reference. Both run here in your browser: the surface is the exact solve, and the dots on the smiles are the network. The real forecasts are qCast's walk-forward forecasts for 22 US stocks and ETFs, one per month from August 2022 to August 2023.
Preliminary. These results are work in progress and subject to change. qStorm is looking for more option data.
嵐 予測から、価格へ。