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3 votes
Accepted

Ideas behind early exercise of American Option

What is the 20$ used in the below formula? The premium (option price) or the difference between the asset and strike price obtained by option exercise and immediate selling of the underlying? The ...
KaiSqDist's user avatar
  • 1,474
2 votes

Option: link between Vega and Gamma

This is simple. If you are far away from maturity, your option price will more sensitive to volatility on your underlying, effective change on your underlying price won't have any significative impact....
JohnGalt's user avatar
2 votes

Option: link between Vega and Gamma

$Vega*(Vol1-Vol2)=C(t,S(t),vol1)-C(t,S(t),vol2)$ (1=2) where vol1 and vol2 are close enough for 1 and 2 to be the same. Now we delta hedge both calls at implied volatility. We ignore that change in ...
Arshdeep's user avatar
  • 2,451
2 votes

Complicated barrier options

Based on my understanding of what you wrote, I would propose the following solutions: The down-in-call barrier doesn't expire when $S_t < B$, it just activates and changes into the long call short ...
KaiSqDist's user avatar
  • 1,474
1 vote

Arbitrage between implied and realised spot-vol beta

To clarify terms , implied beta means the spot-vol correlation that is implied by the price of risk reversals. Realized beta means spot-vol correlation measured from recent market behavio. I don’t ...
dm63's user avatar
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1 vote
Accepted

Option: link between Vega and Gamma

When you hedge an option's delta at implied volatility, the resulting PnL over timestep, dt, is: $$ PnL = (\Delta_i * dS + \frac{\Gamma_i dS^2}{2} + \Theta * dt) - \Delta_i * dS $$ Leaving: $$ \frac{\...
Newquant's user avatar
  • 804
1 vote

Option: link between Vega and Gamma

I have another answer. We know by the link, the call valued at the incorrect vol (beta) loses gamma PnL. We know the call valued rightly loses no PnL (all strategies are fair in the risk neutral world)...
Arshdeep's user avatar
  • 2,451
1 vote

Why would you take a Loan when trying to Illustrate a Riskless Hedge?

I don't really have much to add to the other comments, but I just want to emphasize the general principle of opportunity cost and the intuition behind it. You should only invest in something if you ...
LongTimeLurker's user avatar
1 vote
Accepted

Why would you take a Loan when trying to Illustrate a Riskless Hedge?

More generally, in finance almost all replication arguments always assume that you have no cash to begin with (usually also there are simplifications such as assuming that there is no credit risk and ...
user68819's user avatar
  • 540
1 vote
Accepted

time value of option proportional to sqrt(time)

Vol scales with the square root of time (i.e. variance is linear in time), therefore the value of an option diminishes with it too.
user68819's user avatar
  • 540
1 vote

Purpose of Vega Hedging

No, changes in implied volatility do not affect the PnL at maturity because at maturity his option positions collapse to the terminal payoff [s-k]+, and his futures positions will settle. Vega is only ...
Newquant's user avatar
  • 804

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