Core mechanism
The output adjoint reaches every connected active input. Naming those inputs converts a raw gradient vector into a risk report such as timing risk, cross-risk or a model-parameter sensitivity.
Start Here — Price, Then Differentiate
Every Input You Record Becomes a Sensitivity
Theta was never coded into the vanilla option payoff. It falls out of the same Java adjoint sweep as delta and vega because maturity is a named input.
Market data
SimulationOptional
This exact source runs in TeaVM. Form changes update its Java literals and reset manual edits.
import com.nablatensor.engine.Nabla;
import com.nablatensor.quant.EquityMarket;
import com.nablatensor.quant.MonteCarlo;
import com.nablatensor.quant.Products;
public final class UnaskedGreek {
private UnaskedGreek() {}
public static void main(String[] args) {
EquityMarket market = EquityMarket.of()
.spot(100)
.strike(100)
.vol(20 / 100.0)
.rate(3 / 100.0)
.maturity(1)
.build();
long scenarios = 20000L;
long seed = 42L;
double oneDay = 1.0 / 365.0;
try (MonteCarlo<EquityMarket> pricer = MonteCarlo.of(Products.europeanCall())
.market(market)
.steps(1)
.fp64()
.greeks()
.on("cpu")
.build()) {
Nabla.TypedValuation<EquityMarket> value = pricer.run(scenarios, seed);
double theta = -value.greek(EquityMarket::maturity);
double thetaPerDay = theta / 365.0;
EquityMarket shorter = market.withMaturity(Math.max(1.0e-6, market.maturity() - oneDay));
double thetaBump = pricer.run(shorter, scenarios, seed)
.price() - value.price();
System.out.println("RESULT|" + value.price() + "|" + value.greek(EquityMarket::spot) + "|"
+ value.greek(EquityMarket::vol) + "|" + thetaPerDay + "|" + thetaBump);
System.out.println("INPUTS|" + scenarios + "|" + seed + "|" + pricer.nodes());
}
}
}
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Implementation guide
Named inputs make sensitivities available
A reverse sweep returns the derivative for every recorded input, including an economically useful factor that was not the original reporting target.
Practical workflow
Define a deliberate risk-factor schema at recording time, retain labels and units with the input vector, and surface only sensitivities that have a clear economic interpretation and validation route.
Scope and review point
An available derivative is not automatically a hedgeable Greek. Liquidity, calibration stability, factor definition and reporting materiality still matter.