Options: Implied Volatility Smiles and Skews

Question 1

What are possible reasons of a volatility skew?

Answer 1

1. Non-lognormal distribution, especially on one side (extreme price falls more likely)
2. Demand/supply factors (e.g . crashophobia leading to greater demand for OTM put options)

More frequent for:
- equity options
- bond futures options

Question 2

What is the nature of a volatility skew?

Answer 2

Implied volatility is higher for OTM puts (the lower than the ATM the higher the volatility) and lower for OTM calls.

In other words implied volatility decreases as the ratio of the strike/underlying increases

Question 3

What is the nature of a volatility smile?

Answer 3

Implied volatility is lowest ATM (when Strike/underlying = 1). It increases towards both the maximum and the minimum, usually at a faster rate towards 0.

Question 4

What are possible reasons of a volatility smile?

Answer 4

1. Non-lognormal distribution (extreme price movements more likely)
2. Demand/supply factors (leading to great demand for OTM put options, but also for OTM calls, depending on currency exposure…)

More frequent for:
- Currency options
- Interest rate options such as caps/floors

Question 5

What does the volatility term structure look like?

Answer 5

Implied volatility can differ between short and long maturities, depending on market conditions, both increasing and decreasing term structures can be observed

Question 6

What is a volatility matrix/volatility surface?

Answer 6

A volatility matrix is a way to report implied volatility date for different strikes and maturities. When represented graphically it becomes a volatility surface. Data are presented in terms of moneyness (strike price/spot or future price of the underlying asset)

Question 7

What conclusion can be drawn from the Eurostoxx volatility surface?

Answer 7

The implied volatility has a skew which is steeper for short maturities and flatter on longer ones. However, due to the fact that the impact of a different volatility input on the option prie is a function of Vega, we should still be concerned with the skew for long term option as well. (Options with longer maturity have a far larger Vega)

Question 8

What are the two main implications for Vega and trading strategies from volatility skew/smiles?

Answer 8

1. Vega = 0 implies zero volatility exposure to a paraller/identical change of all implied volatilities while it implies to remain exposed to a differentiated change in the implied volatilities of individual positions.
2. One can create strategies that rely on flattening/steepening of the skew and parallel shifts.

Question 9

What is a long risk reveral strategy?

Answer 9

Long risk reversal is a strategy to capitalize on the flattening of the volatility skew and involves a long OTM call + short OTM put.

Question 10

What is a short risk reversal?

Answer 10

Short risk reversal is a strategy to capitalize on the steepening of the volatility skew and involves a short OTM call + long OTM put.

Question 11

How does one ensure that a risk reversal is profitable no matter the parallel shift of the implied volatility curve?

Answer 11

The risk reversal should be Vega neutral. This way any parallel change in volatilities would be neutralized and the profit would depend only on the reduction of the slope of the skew. (It should also be Delta neutral)