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The terms delta equivalent or delta hedging refers to the representation techniques of options in gaps and refers to the hedging techniques used by A/L managers.
The term “delta hedging” means “hedging with derivatives computation” or “first-rate hedging”.
These delta-hedging techniques refer to delta hedging practices used by front-office traders in trading books for products accounted as marked-to-market.
Let us show an example to explain how delta-hedging techniques operate in trading activities. We consider a trader selling 10 call options on a company X with these characteristics:
The counterparty who bought the call will receive tomorrow 10 times the maximum between 0 and (S–5) where S is the stock price of company X tomorrow.
We suppose that in one day, there are two possible evolutions for the company stock price:
The value of the call in the trading book is the expected pay-off of this call, i.e. 5 since:
How will the trader hedge this position?
Before hedging, the trader profit and loss (P&L) will be the following: