Intrinsic Value Bounds for Black–Scholes and Black–76 Implied Volatility
Summary
The post questions whether the minimum option price checks used before implied volatility calculations are correct in the Black–Scholes and Black–76 models. It observes that the two implementations use the same expressions, even though Black–76 uses a futures price where Black–Scholes uses a spot price. The author proposes separate lower-bound expressions for calls and puts in each model, based on whether discounting applies to the underlying or to the strike.
The document presents the code fragments and the proposed corrections as a question, not as a resolved derivation. It gives no numerical examples, proof, or confirmation from a maintainer, so readers should treat the suggested edits as a hypothesis. Its useful lesson is that implied volatility routines must check model-specific no-arbitrage price bounds, with discounting consistent with the model’s underlying and payoff conventions.
Key ideas
- Implied volatility calculations need a minimum option price check before solving for volatility.
- Black–Scholes and Black–76 use different underlying price conventions, which affect intrinsic value bounds.
- The post proposes changing the call and put checks but does not establish that the proposed formulas are correct.
- Discounting in an option price bound must match the model’s treatment of spot, futures, and strike.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.