ATM 期权怎么 delta 对冲

平值附近 call 的 delta 约为 0.5。

因此：

• 若你 short 1 张 ATM call，为 delta 中性应 买入约 0.5 股。
• 若你 long 1 张 ATM call，应 卖空约 0.5 股。

$$\boxed{\text{ATM：对冲股数约为 }\pm 0.5\text{（方向相反）}}$$

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英文解析

If you sold the option, you should hold about one- half a share to hedge. If you bought the option, you should short about one- half a share to hedge. If you are at- the- money, there is about a fifty- fifty chance the option finishes in- the- money; and with this expectation, you need about one- half a share to hedge.

Table 8.3: Pricing Methods Summary: Plain Vanilla Options

<table><tr><td>No divi-dends</td><td colspan="2">European-Style</td><td colspan="2">American-Style</td></tr><tr><td></td><td>Put</td><td>Call</td><td>Put</td><td>Call</td></tr><tr><td></td><td>Black-Scholes put formula</td><td>Black-Scholes call formula</td><td>No exact formula (use approximation formula, tree or fi-nite differences)</td><td>Black-Scholes call formula fearlly ex- ercise is never opti-mal)</td></tr><tr><td>Lump sum dividend D</td><td>Use S* = S - PV (D) in Black-Scholes</td><td>Use s* - S - PV (D) in Black-Scholes</td><td>No exact formula (use approximation formula, tree or fi-nite differences)</td><td>Roll-Geske-Whaley formula, or Black's pseudo formula</td></tr><tr><td>Continuous dividends at rate ρ</td><td>Use S* = Se-μT - t ) in Black-Scholes (Merton's formula)</td><td>Use S* = Se-ρ(γ-t) in Black-Scholes (Merton's formula)</td><td>No exact formula (use approximation formula, tree or fi-nite differences)</td><td>Adjust Roll-Geske-Whaley formula</td></tr><tr><td>s = (USP/NX)</td><td>Use ρ = rFX in Merton's for-mala (Garman-Kohlhagen/Grabbe formula)</td><td>Use ρ = rFX in Merton's for-mula (Garman-Kohlhagen/Grabbe formula)</td><td>Use ρ = rFX in the above</td><td>Use ρ = rFX in the above</td></tr><tr><td>All cases: Numerical</td><td>Monte Carlo, lattic</td><td>or finite differences</td><td>Lattice or fir</td><td>differences</td></tr></table>

Note: Pricing methods for European- or American- style plain vanilla puts or calls where the underlying pays no dividends, pays a lump sum dividend, pays continuous dividends, or is a foreign currency.

Table 8.4: Pricing Methods Summary: Exotic Options

<table><tr><td colspan="2">European-Style</td><td colspan="2">American-Style</td></tr><tr><td>Path-Independent</td><td>Path-Dependent</td><td>Path-kndependent</td><td>Path-Dependent</td></tr><tr><td>Lattice, Monte Carlo, or finite difference</td><td>Monte Carlo, finite difference, lattice (diff-cult)</td><td>Lattice or finite differ-ences</td><td>Lattice (difficult) or fi-nite differences</td></tr></table>

Note: Summary of pricing methods for exotic options that are European- or American- style, path- independent of path- dependent.