8 Implied volatility and greeks

Question 1

Implied Volatility
* The implied volatility of an option is the volatility for which the … as it cannot be observed directly.

• One can either use … or implied volatilities
• Traders and brokers often quote implied volatilities instead of …
• Why do historical and implied volatilities differ? because:
• Historical volatility might differ from the current market expectation
• B/S-Model is not perfectly applicable

Answer 1

Black-Scholes price equals the market price

historical volatilities

option prices

Question 2

implied volatility most of the time is …
than the historical volatility

VIX measures …

Calculated in …

What is volatility premium?

Answer 2

larger

1-month IV

1-minute intervals

difference between implied and realized volatility

Question 3

Im plied Volatility Surface of the EuroStoxx50

Explain “volatility skew”:

Dependence on time to maturity does not follow a clear pattern.

sometimes volatility increases for very high strike (unstable)

Answer 3

IV tend to be lower for options with higher strikes

Question 4

The Delta is the change in the … for a small change in the price of the underlying. Graphically, it can be expressed as the slope of a line tangent to the BS pricing function at a point S

Answer 4

option price

See slide 12

Question 5

by combining a position of N stocks with N/Delta options, we can construct a riskless portfolio. This is what is called …

Ideally such a portfolio has to be adjusted
instantaneously, i.e. this is a …

However, in reality the outcome of a Delta hedge is influenced by the simultaneous change in other factors such as …

Answer 5

Delta Hedging

dynamic hedging approach

volatility or maturity