ns

NO.PZ2016082404000030

问题如下：

A bank has sold USD 300,000 of call options on 100,000 equities. The equities trade at 50, the option strike price is 49, the maturity is in three months, volatility is 20%, and the interest rate is 5%. How does the bank delta-hedge?

选项：

Buy 65,000 shares

Buy 100,000 shares

Buy 21,000 shares

Sell 100,000 shares

解释：

ANSWER: A

This is an at-the-money option with a delta of about 0.5. Since the bank sold calls, it needs to delta-hedge by buying the shares. With a delta of 0.5, it would need to buy approximately 50,000 shares. Answer A is the closest. Note that most other information is superfluous.

这里用BSM算出deltac=0.647，然后ns×Δs+nc×Δc=0，Δs=1，nc=-1000，Δc=0.647，算出需要买大约65000股票是常规做法吧？如果没有告诉计算BSM的相关数据是不是大概率就是at the money的情况用Δ约等于0.5来判断

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李坏_品职助教 · 2025年06月06日

嗨，爱思考的PZer你好：

对，这个题目的条件不足（没有正态分布表，算不出N(d1)或者N(d2)的），只能从题目说的股票价格现在接近于行权价格，那么delta近似约等于0.5. 用这个方法来做题。

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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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