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Handbook of Asset and Liability Management: From models to optimal return strategies by Alexandre Adam

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22

Delta Equivalent Computation

Mauvais ouvrier ne trouve jamais bon outil.

22.1 PRINCIPLES

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”.

22.1.1 Delta equivalent computation in trading activities

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:

  • stock price of company X: 5;
  • strike call:5;
  • 1-day exercise.

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:

  • State 1: the company stock price is 6 (probability 50%).
  • State 2: the company stock price is 4 (probability 50%).

The value of the call in the trading book is the expected pay-off of this call, i.e. 5 since:

  • in state 1, the pay-off is 10 (probability 50%);
  • in state 2, the pay-off is 0 (probability 50%).

How will the trader hedge this position?

Before hedging, the trader profit and loss (P&L) will be the following:

  • State 1:5−10 = −5 (probability ...

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