做多跨式

做多 straddle = 买入同到期同执行价的 call + put。

执行价 $K=25$，成本 5，因此到期盈亏平衡点为

$$S_T=K\pm 5 \Rightarrow 20\ \text{和}\ 30.$$

所以你希望标的价格大幅波动，即

$$\boxed{S_T<20\ \text{或}\ S_T>30}\quad\text{（波动越大越好）。}$$

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英文解析

A give-away question!
A long straddle is a long call plus a long put with the same strike.

If you hold the straddle until maturity, then you need a price change of more than $5$ either way in the underlying to profit.

A smaller price change, however, can lead to profits if it happens before maturity.

For example, using Black-Scholes (ignoring that :contentReference[oaicite:0]{index=0} equity options are American-style), if
$\sigma = 0.357$,
$T - t = 0.5$,
$S = 25$,
and $r = 0.02$,

then a straddle struck at $25$ costs $5$.

If the price of the underlying suddenly jumps to $27$, then the straddle is suddenly worth $5.50$ and you have an immediate $10\%$ gain.
See Table 8.1 for details.

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Table 8.1: Straddle Prices when the Stock Price Jumps

	Stock Price = $25.00$	Stock Price = $27.00$
Price of the Call ($X=25$)	$2.625$	$3.875$
Price of the Put ($X=25$)	$2.376$	$1.626$
Price of the Straddle (sum)	$5.001$	$5.502$

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Note:
The option prices in the table are calculated using:

• volatility $\sigma = 0.357$ per annum
• time to maturity $T - t = 0.5$ years
• riskless rate $r = 0.02$ per annum

and the :contentReference[oaicite:1]{index=1}.

A long straddle is a long call plus a long put with the same strike.
A straddle struck at $25$ costs $5$ when stock price is $S = 25$,
but if the stock price jumps immediately to $27$, the straddle is worth $5.50$, giving an immediate $10\%$ gain (ignoring transactions costs).