努同學(xué)
2026-01-20 08:45原版書上這句話看不懂，allows volatility sellers to sell variance swaps at a higher price than at-the-money options，這個跟atm option有什么關(guān)聯(lián)？A feature of variance swaps that makes them particularly interesting to investors is that their payoffs are convex in volatility, as seen Exhibit 4. This convexity occurs because being long a variance swap is equivalent to be long a basket of options and short the underlying asset (typically by selling a futures contract). A long position in a variance swap is thus long gamma and has a convex payoff. This characteristic allows volatility sellers to sell variance swaps at a higher price than at-the-money options because the swap’s convex payoff profile is attractive to investors who desire a long volatility position as a tail risk hedge.
所屬：CFA Level III > Derivatives and Risk Management 視頻位置 相關(guān)試題
來源： 視頻位置 相關(guān)試題
1個回答
Simon助教
2026-01-20 18:13
該回答已被題主采納
核心是賣方利用了方差互換的“凸性”這個高級功能來獲得更高的定價權(quán)。
因為方差互換的收益具有凸性，這使它成為一個非常有吸引力的產(chǎn)品。投資者（買方）為了獲得這種凸性，愿意支付比用一籃子平價期權(quán)“自己動手”復(fù)制一個類似頭寸更高的價格。因此，賣方就能以這個“更高的價格”賣出。
variance swap 的pay off具有正凸性，見截圖
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追問
正凸性我能理解，賣得好也理解了，但是為什么挑atm option 對比？跟它gamma最大有關(guān)系？
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追答
做多波動率，有一個策略是straddle，就是long ATM call + long ATM put，所以與ATM option比較。
gamma是在ATM時，且臨近到期日時，gamma最大。
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