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aileen20180623 · 2024年02月19日

您好

NO.PZ2023020101000025

问题如下:

Arnie Burr is CEO and chief investment officer of Princeton Capital, a registered investment advisory firm. He is working with Tom Jeffinsin, head trader, and Jim Madisox, a new analyst. They meet to discuss option valuation methodologies in the context of the firm’s use of derivatives to manage client portfolios.

Burr begins the discussion by stating that the Black–Scholes–Merton (BSM) model is a relatively straightforward tool for valuing options despite its rigorous computational components. Burr writes the BSM model on the firm’s whiteboard, presented as Exhibit 1.

Exhibit 1: BSM Model for Options on Non-Dividend Paying Stocks

Burr wants to assess Madisox’s comprehension of the components of the BSM. Madisox states that a call option can be viewed as a leveraged position in the underlying stock. To replicate a call option, the appropriate strategy is to purchase N(d1) shares and simultaneously borrow an amount erTXN(–d2).

Madisox’s statement about the BSM model is least likely correct with respect to:

选项:

A.

purchasing N(d1) shares.

B.

the leveraged position in a stock.

C.

borrowing an amount e–rTXN(–d2).

解释:

With respect to a call option, Madisox is incorrect with respect to his comment to simultaneously borrow an amount e–rTXN(–d2). To create a leveraged position in a stock, the correct components are to purchase N(d1) shares by borrowing an amount e–rTXN(d2). The term e–rTXN(–d2) represents the amount lent when purchasing a put option.

您好,我对lend和borrow这个背后的点有些迷糊,可否请老师指点一下知识点,和讲解一下。谢谢

1 个答案

pzqa35 · 2024年02月19日

嗨,努力学习的PZer你好:


这道题是考察的是我们如何去复制一个call option的头寸,那么根据公式我们可以看到call option是可以由long stock + short bond来进行组合,也就是long N(d1)份的股票,short Xe-rf*TN(d2)金额的债券。那么这道题错误的地方是将N(d2)写成了N(-d2),所以C选项是错误的。

我们short bond,相当于是发行债券,是在期初收到了钱,同时需要支付利息,所以是borrow money。Long bond,就是投资债券,期初要花钱购买债券,同时会收到债务人支付的利息,所以就是lend money。这段内容老师在基础班Interpret the Components of The BSM这节课中有详细的讲解,同学可以2倍速到6分钟左右开始听一下课程来加深理解一下。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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