Finite Differences
Approximate derivatives and solve pricing PDEs on a grid.
Build the mental model first.
Finite Differences becomes useful once its observable quote, state variables and governing convention are kept separate. Build the mental model before selecting the numerical method.
Approximate derivatives and solve pricing PDEs on a grid.
Now make it exact.
Notation and units
Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.
Every model has a price.
Educational conventions are stated explicitly and may simplify market quotation or settlement details.
Rates are continuously compounded unless the section says otherwise.
Inputs are deterministic in the base model.
“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
Why a quant cares.
Finite Differences appears in pricing, scenario analysis, risk aggregation or hedge design. Production use requires explicit units, calendars, interpolation and data lineage.
The hedge has opinions.
Start with the quote convention, then ask which Foundations risk survives the hedge. A number without its convention is merely well-dressed ambiguity.
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