week 5 opties & implied vol

Question 1

How do you recognise whether an option is deep in the money with delta?

Answer 1

It approaches 1or -1

Question 2

How do you hedge gamma?

Answer 2

-negative of portfolio gamma / the options gamma

Question 3

How do you hedge delta?

and gamma (not considering vega)

Answer 3

Question 4

How to hedge delta, gamma and vega?

Answer 4

1. matrix: Greeks go in rows, and calls in columns
2. portfolio greeks go in table
3. Mmult(mininverse(matrix,vector)
   Dont forget control shift enter
4. what delta position do we need? (org delta + delta option 1 + delta option 2
5. opposite delta

table: Greeks go in rows, and calls in columns

Question 5

What are the steps in risk neutral options simulation?

Answer 5

Question 6

What is delta? What happens to delta very deep out of the money? and deep in the money?

Answer 6

Delta is change in option value relative to change in stock price

Call options have positive delta values (usually between 0 and 1), indicating their price moves in the same direction as the underlying asset.
Put options have negative delta values (usually between 0 and -1), indicating their price moves inversely to the underlying asset.

• Call option: delta increases with the stock price
• If the option is very deep out-of-the-money = line is flat (=close to 0) = unlikely to be exercised at maturity = increase in stock price very little effect on the call as the call price remains very low = Delta is close to zero when the call is very deep out-of-the-money
• When the call is deep in-the-money = very likely to be exercised at maturity (right side) = if the underlying stock price increases by 1 dollar, the payoff of the call at maturity will also go up by 1 dollar => resulting, the value of the call almost increases by 1 dollar = delta of the option is close to 1

Question 7

What can you expect from the greeks in the covered call?

Answer 7

Long call: long delta
Short call: reduced delta, reduced vega
total: downside of covered call is the reduced ability to get gains from stock price (delta)
Vega: hoping for low vol, so negative vega

Question 8

What can you expect from the greeks in a straddle?

Answer 8

investors would like volatility -> a high vega
At the money -> delta are slightly higher than 0.5, thats why not 0.5

Question 9

Why does delta look like duration in bonds?
what are the same issue?

Answer 9

Bc its the price sensitivity effect in a key effect (duration = interest, delta price of underlying)

Issues:
Linear approximation (made up by gamma)

Question 10

What happens to delta very deep out of the money? and deep in the money?

Answer 10

In the money: if stock goes up a dollar, we will definetely get that dollar, if down, definetely not gonna get. Starts behaving like the stock bc we will for sure exercise
Out of the money ; if its so far gone, if stock goes up a dollar, doesnt make difference . we will for sure not exercise, close to zero

Question 11

What happends to delta when its far from maturity?

Answer 11

Question 12

Why is the delta of a long put negative?

Answer 12

If price of a stock goes up, value of put goes down