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When implementing a Black-Scholes delta-neutral portfolio using Python to perform delta hedging, I am not sure whether I implemented it correctly or not.

Unlike coding binomial trees for European call option, we can compare Black-Scholes analytical pricing formula with the price given by binomial tree model. If they have small difference, it means that we have coded the tree correctly. Otherwise, it is not correct.

Is there any way we can use to check my delta hedging is implemented correctly?

The portfolio I am considering here is to hedge a short position of a European call option. So, the portfolio consists of longing delta shares of stock and shorting a call option.

Based on my limited knowledge, the only and naive way to check my delta hedging is on track is that through Black-Scholes European price, we know that the portfolio is upper bounded by strike price of the option.

However, other than this, I do not know what else to check.

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One way to check your hedging strategy would be to calculate its PNL distribution (histogram) of ( hedging strategy + option) . Mean PNL should be around 0, and shape should look like gaussian.

Also you can check https://www.pricederivatives.com/en/simple-example-simulation-of-delta-hedging-with-python/

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  • $\begingroup$ Does this apply to any portfolio, that is, PNL of any portfolio must follow a normal distribution centered at 0? $\endgroup$ – Idonknow Jun 7 at 3:29
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    $\begingroup$ any well hedged portfolio including hedges should have PNL centered around 0 with some small std dev (if not, it would not be a hedge). shape should "look like gaussian" but in general it's not gaussian (exact distribution depends on the pricing model, underlying model, transaction cost model ) $\endgroup$ – alexprice Jun 7 at 11:32
  • $\begingroup$ Do you have any reference to support your statement? $\endgroup$ – Idonknow Jun 7 at 11:33

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