Why Accurate Option Pricing Does Not Guarantee an Effective Hedge

Summary

The document distinguishes estimating an option’s theoretical value from replicating its payoff through hedging. It considers a proposed approach that reads implied volatility from a surface by moneyness, assumes sticky delta, and applies the Black–Scholes formula. The answer’s main point is that even a precise model price does not ensure a trading gain or a successful hedge: a quoted theoretical difference is not locked in unless market prices move in a way that lets the trader realize it.

Hedging instead involves dynamic trades in the underlying, and practical constraints can make replication imperfect. The response gives discrete rebalancing, trades in fixed share units, and discontinuous underlying price moves as sources of hedging error. It does not evaluate the proposed volatility-surface assumption, specify how the surface should be updated, or quantify the error. Its central lesson is narrower: pricing error and hedging error are distinct, and a model valuation alone does not establish that a strategy can capture a mispricing.

Key ideas

• A model’s theoretical option value and the profitability of a trade based on it are separate questions.
• Dynamic hedging attempts to replicate an option payoff by trading the underlying.
• Discrete rebalancing can leave exposure between hedge adjustments.
• Fixed trading units and jumps in the underlying can cause replication losses.
• The response does not test the sticky-delta assumption or quantify hedging error.

Tags

# Hedging - calculating option prices using implied volatility surface


# Hedging - calculating option prices using implied volatility surface












To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding IV and then price can be calculated using BS formula.

I think this has to be an over simplification, but I'm not sure why. Can someone show me where this falls apart?

## Answer by onlyvix.blogspot.com (score 2)

https://quant.stackexchange.com/a/22165

You're confusing two different issues - your "pricing" can be accurate to a fraction of a penny, but it does not mean that your hedging (replicating) strategy is. Let's say that options is theoretically worth 0.1 and you sold it for 0.3. You still have not locked in any gain. Market may immediately wise up, and come in agreement with your valuation so you would be able to repurchase your option for 0.1, and lock in your gains, but that is very, very unlikely.

Otherwise you would be hedging, that is attempting to replicate option payoff, and mitigate the risk, by dynamically trading in the underlying. But your trading is discrete (let's say twice per day) and in discrete units ( 100 shares ), and underlying may move discontinuously (jump) . That means that your replicating strategy may result in a loss of more or less than 0.2 of theoretical difference you were hoping for. To summarize, your hedging error is not your pricing error.

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