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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!

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  • $\begingroup$ Note movement, no mouvement and you should write volatility no volatily $\endgroup$ – user16651 Sep 24 '16 at 16:19
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    $\begingroup$ "Short" not "shot" $\endgroup$ – Dom Sep 24 '16 at 17:31
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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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  • $\begingroup$ Haha .. Yes you will surely get it ! $\endgroup$ – Jelloul Ayoub Sep 24 '16 at 15:49
  • $\begingroup$ @Jelloul Ayoub I think Alex C's answer is useful. Why haha ? $\endgroup$ – user16651 Sep 24 '16 at 16:22
  • $\begingroup$ My "Haha" was about his way to answer my fourth question .. it was not an offense .. and thank you @Alex C for your precious time.. $\endgroup$ – Jelloul Ayoub Sep 24 '16 at 16:24
  • $\begingroup$ Indeed, you should ask one question $\endgroup$ – user16651 Sep 24 '16 at 16:25
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    $\begingroup$ I agree that question 4 needs to be clarified: what kind of Asian option + hedge in terms of what, spot moves, implied volatility moves, both? Probably that the interviewer is asking for the $\sigma_{\text{asian}} \approxeq 1/\sqrt{3} \sigma_{\text{eur}}$ approximation? As for question 3, I would argue that if you add (implied) volatility as parameter which affects the option price and which moves with the spot price (i.e. not a constant), delta becomes $ \Delta = \frac{\partial V}{\partial S} + \frac{\partial V}{\partial \sigma}\frac{\partial \sigma}{\partial S}$ $\endgroup$ – Quantuple Sep 26 '16 at 9:27

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