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Dynamic Hedging in Practice In a typical arrangement at a financial institution,the responsibility for a portfolio of derivatives dependent on a particular underlying asset is

Dynamic Hedging in Practice In a typical arrangement at a financial institution,the responsibility for a portfolio of derivatives dependent on a particular underlying asset is assigned to one trader or to a group of traders working together. For example, one trader at Goldman Sachs might be assigned responsibility for all derivatives dependent on the value of the Australian dollar. A computer system calculates the value of the portfolio and Greek letters for the portfolio. Limits are defined for each Greek letter and special permission is required if a trader wants to exceed a limit at the end of a trading day. The delta limit is often expressed as the equivalent maximum position in the underlying asset. For example,the delta limit of Goldman Sachs on a stock might be specified as $10 million. If the stock price is $50, this means that the absolute value of delta as we have calculated it can be no more that 200,000.The vega limit is usually expressed as a maximum dollar exposure per 1% change in the volatility. As a matter of course, options traders make themselves delta neutralor close to delta neutralat the end of each day. Gamma and vega are monitored, but are not usually managed on a daily basis. Financial institutions often find that their business with clients involves writing options and that as a result they accumulate negative gamma and vega. They are then always looking out for opportunities to manage their gamma and vega risks by buying options at competitive prices. There is one aspect of an options portfolio that mitigates problems of managing gamma and vega somewhat. Options are often close to the money when they are first sold so that they have relatively high gammas and vegas. But after some time has elapsed, the underlying asset price has often changed enough for them to become deep-out-of-the-money or deep-in-the-money.Their gammas and vegas are then very small and of little consequence. The nightmare scenario for an options trader is where written options remain very close to the money as the maturity date is approached.

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