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明明要加油 · 2023年09月30日

如正文所说，关于折现率离散还是连续？

  1. CFA II
  2. Derivative

NO.PZ2019010402000007

问题如下：

A manager sold an equity forward contract one month ago. The maturity of forward contract is three months. A dividend of $1 will be paid in one month before contract expiration. The annually compounded risk-free rate is 3%. The current spot price of underlying is $56, and the initial forward price is $60. The value of the manager’s position is:

选项：

A.

-4.7026

B.

4.7026

C.

4.8512

解释：

B is correct.

考点：equity forward contract求value

解析：

画图（long方）：

valuelong=(56−1(1+3%)1/12)−60(1+3%)2/12=−4.7026value_{long}=(56-\frac1{{(1+3\%)}^{1/12}})-\frac{60}{{(1+3\%)}^{2/12}}=-4.7026

因为这一题的头寸是short方，所以value=4.7026

这道题已知，给了连续复利的无风险利率The annually compounded risk-free rate is 3%. 

折现的时候为啥用离散的方式折现呢？为啥不用e的Rfc来折现呢？虽然对结果影响不大，我想请老师给我解释一下。

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1 个答案

李坏_品职助教 · 2023年10月01日

嗨，从没放弃的小努力你好：


这个属于CFA的习惯，对于债券定价或远期合约定价，习惯上还是用离散复利比较多。对于期限很短的情况下，二者没有什么差别。

如果是计算期权价格那还是优先考虑连续复利。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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