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Quantitative Finance · शब्दावली

Hedging band क्या है?

Definition 26.3 Derivatives and Volatility · अध्याय 26 — Options Market Making in Practice

A hedging band is a range around the target delta within which the hedge is left alone; when the delta leaves it, the hedge trades back to the band’s nearest edge, not to its centre, so that trades are only as large as the risk requires.

Hedging cost against the remaining risk for a short one-month straddle: time-based hedging at intervals from one to 26 checks (13 checks a day), and bands of increasing width. The band’s frontier lies below the clock’s. Data: the tutorial.
Figure 26.2. Hedging cost against the remaining risk for a short one-month straddle: time-based hedging at intervals from one to 26 checks (13 checks a day), and bands of increasing width. The band’s frontier lies below the clock’s. Data: the tutorial.

उदाहरण

Example 26.4 (Bands against the clock)

A short one-month at-the-money straddle on a share at 100 (20% volatility) is hedged over its life, checking 13 times a day, with a cost of 5 basis points of the traded notional. Hedging at every check costs 0.525 on average and leaves a P&L standard deviation of 0.321. Once a day costs 0.142 with a standard deviation of 0.855. A band with c=1c=1 costs 0.140, the same as daily hedging, with a standard deviation of 0.505, 41% less. With c=0.25c=0.25 it costs 0.313 with 0.313, and every-third-check hedging costs about the same (0.302) with 0.434 (Figure 26.2).

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