You are a market maker, and you just rebalance your inventory to make it delta and gamma neutral. Right after setting your inventory delta and gamma to zero, you are long 200 shares of the stock, short 400 calls (C1) on the stock with delta 0.40, and long 200 calls (C2) on the stock with delta 0.60. Which of the following statements is correct if your objective is to further make your inventory delta neutral?

Question

BlackTom AI · Accepted Answer

We start by restating the scenario and each answer option to ensure clarity.
Question setup: You are a market maker who has already rebalanced to delta and gamma neutral. Current positions: long 200 shares of the stock, short 400 calls (C1) with delta 0.40, and long 200 calls (C2) with delta 0.60.
Answer options:
- a. You will need to buy 160 shares of the stock.
- b. You will need to buy 266.67 calls C2.
- c. You will need to buy 400 calls C1.
- d. You will need to sell 160 shares of the stock.

Step-by-step analysis of each option:
Option a: Buy 160 shares. Since you already have a net delta exposure, adding +160 delta from 160 more shares would push your delta further positive, moving away from neutrality rather than toward it. This option would not help achieve delta neutrality; it would require an even larger opposite hedge later.

Option b: Buy 266.67 calls C2. Each C2 carries a delta of about +0.60. Purchasing 266.67 calls would add roughly 160 additional delta (266.67 × 0.60 ≈ 160). That would again increase your overall positive delta instead of reducing it to zero, making neutrality farther away. Moreover, the fractional number of options is practically awkward, signaling a mismatched hedge scale.

Option c: Buy 400 calls C1. Each C1 has a delta of about +0.40. Buying 400 calls would add about 160 delta (400 × 0.40 = 160). This would raise your net delta by 160, not reduce it, so you would not achieve neutrality and would still be left with a positive delta after this trade.

Option d: Sell 160 shares. Your current net delta is the sum of all positions’ deltas. With +200 from the stock, -160 from the 400 C1, and +120 from the 200 C2, the total delta equals +160. Offloading 160 shares reduces delta by 160, bringing the net delta to zero and achieving delta neutrality.

Putting it together, only the action in option d directly reduces the net delta by the exact amount needed to reach zero, whereas all other options either increase delta or mis-scale the hedge. The reasoning aligns with the goal of maintaining a delta-neutral portfolio by counterbalancing the existing positive delta with a corresponding negative delta hedge.

类似问题

When you established the hedged options trade, as in the assignment, what would have been your P&L the first day if these had been the call and stock prices (numbers slightly modified from the original, in part for ease of calculation):

You buy call options on a stock index, and wish to trade shares of the underlying stock index to establish a delta-neutral position. To maintain a delta neutral position, you will need to:

You purchase put options on a stock index, and wish to trade shares of the underlying stock index to establish a delta-neutral position. To maintain a delta neutral position, you will need to:

A call option on a stock has a delta of 0.4 and a trader has just sold 1000 calls. The trader decides to delta-hedge his call position by trading a put on the same underlying. What position should the trader take in the put to delta-hedge her call position if the put delta is -0.5?

A call option on a stock has a delta of 0.7 and a trader has just sold 1000 calls. The trader decides to delta-hedge his call position by trading a put on the same underlying. What position should the trader take in the put to delta-hedge her call position if the put delta is -0.5?

You are an option trader, and you just sold a European call option on a given underlying. You decide to delta hedge your position. Which of the following statements is correct?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单