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EmilyZhou · 2025年05月07日

老师请解释一下这道题

NO.PZ2025040202000021

问题如下:

An arbitrageur dynamically manages a portfolio of options on a single stock. Using the Black–Scholes–Merton model, when the dividend yield on the stock increases, the arbitrageur should:

选项:

A.A.lower the number of stocks to buy for calls and lower the number of stocks to short sell for puts. B.B.lower the number of stocks to buy for calls and raise the number of stocks to short sell for puts. C.C.lower the number of stocks to short sell for puts and raise the number of stocks to buy for calls.

解释:

A Incorrect because with dividend paying stocks, the arbitrageur is able to receive the benefits of dividend payments when long the stock and has to pay dividends when short the stock. Thus, the burden of carrying the stock is diminished for a long position. The key insight is that dividends influence the dynamically managed portfolio by lowering the number of shares to buy for calls and also lowering, not raising, the number of shares to short sell for puts.

B Correct because with dividend paying stocks, the arbitrageur is able to receive the benefits of dividend payments when long the stock and has to pay dividends when short the stock. Thus, the burden of carrying the stock is diminished for a long position. The key insight is that dividends influence the dynamically managed portfolio by lowering the number of shares to buy for calls and raising the number of shares to short sell for puts.

C Incorrect because with dividend paying stocks, the arbitrageur is able to receive the benefits of dividend payments when long the stock and has to pay dividends when short the stock. Thus, the burden of carrying the stock is diminished for a long position. The key insight is that dividends influence the dynamically managed portfolio by lowering (not: raising) the number of shares to buy for calls and lowering, not raising, the number of shares to short sell for puts.

老师请解释一下这道题

1 个答案

pzqa35 · 2025年05月08日

嗨,从没放弃的小努力你好:


这道题考察的是dynamic hedge的知识点。

由于股利增加,标的资产的价格会下降,所以看涨期权的价值会下跌,看跌期权的价值会上升。因此看涨期权的delta会变小,而看跌期权的delta绝对值会变大。

所以我们hedge的时候看涨期权对应的股票数量要下降,而看跌期权对应的股票数量应该上升。因此B选项正确。

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努力的时光都是限量版,加油!

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