# Option Replication Explained

**Achieve option like payoff without owning an option**

* Option replication via dynamic delta hedging using Black-Scholes model is a strategy used to replicate the payoff of an option by trading in the underlying asset.
* *Black-Scholes Model* is a mathematical formula used to calculate the theoretical price of an option. It takes into account factors such as the current underlying asset price, strike price, time to expiration, volatility, and interest rates.
* *Dynamic Delta Hedging* involves adjusting the position in the underlying asset to maintain delta neutral. As the underlying asset price changes, the delta of the option changes too. To hedge, traders continuously buy or sell the underlying asset to offset the delta exposure.
* *Option Replication* means creating a similar risk and return profile as the original option structure, in this case a Long Straddle. Instead of buying the option itself, dynamic delta hedging aims to replicate its performance. The Black-Scholes model provides the delta value for an option, which indicates the proportion of the underlying asset required to replicate the option's price movement. By dynamically adjusting the position in the underlying asset based on changes in delta, traders can replicate the option's performance.

<figure><img src="/files/fZJzUHOLctmHUFuAOHgo" alt="" width="563"><figcaption><p>Black-Scholes Formula<br>Source: Options, Futures, and Other Derivatives : Hull, John C.</p></figcaption></figure>

* To know more about Option pricing and Black-Scholes Formula: <https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model>

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