Option Greeks and Delta Hedging: Gamma, Rho, and Rebalancing
Summary
The response addresses several interview-style questions about option risk. For a delta-hedged short call, it identifies negative gamma: large moves in either direction are harmful, while smaller moves can help, with volatility changes offering a related way to view the exposure. It also notes that a long put has negative rho and suggests offsetting that sensitivity with positive-rho positions, including a long call or certain interest-rate swap exposure.
For a short call hedged with stock, the answer says a falling share price reduces the required long-stock hedge, so some shares must be sold. It cautions that the effect of rising volatility on delta depends on the option’s current moneyness, so the direction of the hedge adjustment cannot be determined from the prompt alone. The fourth question, on replicating Asian options with European calls, is not answered. These are concise interview responses; exact Greek signs and hedge quantities depend on contract conventions, rates, dividends, and model assumptions.
Key ideas
- A delta-hedged short call has negative gamma and is exposed to large underlying moves.
- A long put’s negative rho can be offset with positive-rho positions.
- When the stock falls, a short call’s long-stock delta hedge generally needs to be reduced.
- A volatility increase does not determine the direction of a call’s delta change without its moneyness.
- The response leaves the Asian-option hedging question unanswered.
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Full text
# I have an interview for an assistant trader, need your help with some questions # I have an interview for an assistant trader, need your help with some questions Hello all hope you're doing fine! Would you please help me answering these questions? 1) We're short a call option and we delta hedge. We know that there will be a move in the underlying asset price. Which move is good for us? 2) We're long a put option, how can we Rhô hedge? 3) We're short a call option and we delta hedge.. The stock price decreases and volatility rises.. What should we do? 4) How can we hedge Asian options using European calls? Thank you all! ## Answer by Alex C (score 3) https://quant.stackexchange.com/a/30280 On Question 1, you have zero delta (since you delta hedge) and negative gamma. So the cases where you lose money are (1) large upward movement of the underlying, (2) large downward movement of the underlying. The cases where you make money are small upward or downward movements. Another way to look at it is that you lose money in case of an increase in vol, make it with a decrease in vol. On Question 2, if you are long a put you have negative rho. You can hedge this with some positive rho, from a short put or a long call (or an interest rate swap where you received fixed and pay floating). On Question 3, we are short a call and therefore we are long stock as a delta hedge. Let's consider two cases separately: (a) The stock price falls, so the delta of the option position is reduced in absolute value (it is negative and moves towards zero), we have to sell some of our hedging stock to match this decrease. (b) The volatility rises, what do you think happens to the delta? I think it moves towards -0.5, but without knowing if it is above or below this now, I don't think we can predict the direction of change, up or down. If I answer Question 4, do I get the job?
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