第8题的prepaid variable forward是一个collar和一个loan的组合（教材3.3.1）。
In a PVF, the dealer has downside risk and unlimited upside potential.
The variable part of a PVF is the number of shares you have to deliver at expiration, which will depend on the share price at expiration.
A PVF is essentially a combination of an equity collar and a loan.
Suppose that you own 100,000 shares of ABC Company stock selling at $50/share. You enter into a 5-year PVF with a lower strike of $47/share and an upper strike of $55/share; today the dealer gives you $44/share ($4.4 million) for you to do with as you wish.
At expiration in 5 years:
- If the share price is less than $47/share, you simply deliver all 100,000 shares.
- If the share price is between $47/share and $55/share, you deliver $47(100,000) = $4.7 million worth of shares. For example:
- If the share price is $48/share, you deliver $4.7 million / $48 = 97,917 shares.
- If the share price is $50/share, you deliver $4.7 million / $50 = 94,000 shares.
- If the share price is $55/share, you deliver $4.7 million / $55 = 85,455 shares.
- If the share price is above $55/share, you deliver $4.7 million plus the excess of the share price above $55/share. For example:
- If the share price is $60/share, you deliver $4.7 million plus ($60 − $55)(100,000), or $5.2 million; at $60/share, that’s 86,667 shares.
- If the share price is $65/share, you deliver $4.7 million plus ($65 − $55)(100,000), or $5.7 million; at $65/share, that’s 87,692 shares.
- If the share price is $100/share, you deliver $4.7 million plus ($100 − $55)(100,000), or $9.2 million; at $100/share, that’s 92,000 shares.
Note that you also have the option of settling in cash.
