“Passing monotonicity and bounds tests validates the full pricing model.”
Not quite.These checks reject impossible behavior but do not establish overall correctness.
Architecture & Systems
Sanity Checks: Monotonicity and Bounds
Simple economic constraints such as monotonicity, sign, and arbitrage bounds catch deep bugs with minimal effort.
Mental model
Simple economic invariants can expose deep implementation errors early.
Monotonicity checks verify, for example, that call prices decrease with strike and increase with underlying price.
Bounds checks ensure prices stay within known ranges, such as calls lying between max(S − K·DF, 0) and S.
Explore the mechanism
Which economic direction, sign, or bound must hold even before a precise benchmark is available?
Sanity checks: monotonicity and bounds
Simple economic constraints catch deep bugs with minimal effort.
S
100
K
100
r
0.020
vol
0.25
T
1.00
Inject a bug
At (S,K)
10.8706
No-arbitrage bounds
[1.9801 , 100.0000]
Checks
PASS
These checks are cheap. They should run on grids, not only on a single trade.
Strike sweep (S fixed): monotonicity + boundsOK
- Monotonicity in strike catches sign mistakes and payoff logic errors.
- Bounds catch discounting bugs and pathological negative prices quickly.
Spot sweep (K fixed): monotonicityOK
Interpretation
- Sanity checks are fast enough to run on grids in CI.
- They are not “proof”. They are early warning systems.
- If a bug toggle breaks these, it would break production in subtler ways too.
UNDERSTAND
What to notice
Sign checks confirm that probabilities stay between 0 and 1 and that quantities like discount factors remain positive.
Sweeping across grids of parameters with these checks often reveals structural errors long before production.
Where it appears
- testing option and bond pricers
- screening malformed market data
- catching unit and sign errors
Where the intuition breaks
What this view leaves out
- Necessary conditions are not sufficient: a model can satisfy simple bounds and still be numerically or economically wrong.
Common mistakes
Where this concept sits
Follow the strongest prerequisites, applications, extensions, and contrasts.
Connections for Sanity Checks: Monotonicity and Bounds
Sanity Checks: Monotonicity and BoundsYOU ARE HERE
Used byValidation Toolbox for PricersMonotonicity and bound tests are core low-cost checks in a pricer validation toolbox.
ValidatesArbitrage and No-ArbitrageMonotonicity and bound checks test whether prices respect basic no-arbitrage restrictions.
Used by · Validation Toolbox for Pricers
Monotonicity and bound tests are core low-cost checks in a pricer validation toolbox.
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