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Use the value-maximising flat trigger in Bjerksund-Stensland - #2963
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lballabio merged 3 commits intoNov 2, 2026
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The published trigger is a heuristic that falls below the strike as T approaches T* = (2 sigma/|b|)^2 for negative carry, and the price then collapses to the European one. Every flat trigger gives a lower bound for the American price, so when the value still increases above the published trigger, search for the best one. The trigger drops out of the first-order greeks at the optimum; gamma gets a -V_SI^2/V_II term.
The very-high-volatility put in testBjerksundStenslandValues was priced at its European value; QdFp and CRR give 99.2035. Two Margrabe values from Haug move towards the QdFp values of the equivalent call.
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coverage: 79.468% (+0.01%) from 79.456% — himanshug9119:fix/bjs-maximise-trigger into lballabio:master |
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Fixes #2903, implementing option (a1) as discussed there.
Every flat trigger gives a lower bound for the American price; the published trigger is only a heuristic for the best one, and for negative carry it drops below the strike as T approaches T* = (2σ/|b|)², so the price collapses to the European value. The engine now checks whether the value still increases just above max(I, S); if so, it finds the best trigger by golden-section search on log(I) up to B∞ (about 88% of options stop at the check and keep today's price).
Greeks: at the optimum the value is stationary in I, so the trigger-derivative terms in rho, dividend rho and vega drop out. The optimal trigger moves with the spot, so gamma gets a −V_SI²/V_II term (finite differences in I). The existing finite-difference greek test covers 406 options that go through the search; without the gamma term, 90 of its gamma checks fail.
Tests:
testBjerksundStenslandNegativeCarryTriggerwith the cases from BjerksundStensland returns the European value (~97% too low) when the trigger falls below the strike (negative carry, long maturity) #2903 across T*: errors against QdFp were 1%–97% on master, now at most 1.4e-3, and the price no longer decreases with maturity;testBjerksundStenslandValueswas pinned at 95.12289, which is its European value; it's now 99.20350 (QdFp 99.203499, CRR 4001 steps 99.20338);On 10k random options (S/K 0.8–1.2, r, q 0–10%, vol 10–50%, T 30d–3y), 9.9% change (at most 0.68%); every changed price moves towards QdFp, and none goes above it. The full test suite passes.
AI assistance was used for the implementation and analysis; I reviewed every line.