Why Black–Scholes Delta May Be Used in Local Volatility Hedging

Summary

This short exchange asks why a trader might hedge using Black–Scholes delta when pricing or modeling with a local volatility framework. The accepted response gives two practical reasons: Black–Scholes delta is straightforward to calculate from closed-form formulas, and using Black–Scholes for pricing can make it natural to calculate delta and other Greeks within that same model.

The answer is limited and does not compare hedge performance, quantify model risk, or explain when local volatility delta would be preferable. Its rationale is most applicable when Black–Scholes is the pricing framework; the post does not establish that this is appropriate for every local volatility valuation or hedge objective. It offers a compact convention-based explanation, not a general derivation or empirical study.

Key ideas

• Black–Scholes delta is convenient because it can be computed from closed-form formulas.
• Using one model for pricing and Greeks provides consistency within that framework.
• The answer gives no evidence comparing hedge outcomes under Black–Scholes and local volatility deltas.
• The stated rationale does not establish which delta is best for every hedging objective.

Tags

# Using BS Delta to hedge in a LV Model


# Using BS Delta to hedge in a LV Model












Why do some people use a Black Scholes Delta instead of the delta given by the Local Volatility model?

## Answer by Hui (score 1, accepted)

https://quant.stackexchange.com/a/39770

Here are the reasons:

1.Easy to calculate. You can easily calculate with closed-form formulas

2.If you the pricing model is BS, you should use the same model to calculate delta and other greeks. There are formulas for all of the greeks from BS model

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.