Today I’ll cover a bit about volatility and the different topics relating to it. If there’s one topic, you want me to dive into, let me know and I can then make a full post on it.
- What’s volatility?
Volatility is a measure of price variation over time. The higher the volatility the more likely the price will vary (either up or down). Volatility can be measured historically by computing the standard deviation of the prices. Or it can be measured implied, that is to say by solving for the volatility of a quoted option.
2. Smile
When the volatility is solely time bound, we’re calling it the at-the-money volatility (or ATM vol if you prefer shortcuts). But often you’ll consider that volatility is not a constant for different strikes and it will change as you step away from the at the money point. Usually volatility increases as you move away from the central point effectively giving you a smile shaped curve. The driver behind this is that options further from the ATM point have effectively a higher price than if they were using the ATM vol point.
3. Interpolating and shaping the smile
When working with smile curves, you need to decide for an interpolation method. You can choose between parametric and geometric. Geometric interpolations take into account the pillars that you have provided to interpolate in between. Parametric requires for some parameters to be provided (correlation between spot and vol, shape of RR, etc..). SABR is getting used more and more for IRD products and traders start also to monitor the sensitivity of their positions to the SABR parameters.
4. Dynamic smile
It means that the smile is not a constant when spot rate is changing. So in terms of total vol, it is like defining a convexity to the volatility (smile being your first level). Murex can produce such effects when calibrating Tremor.
5. Short date model
Very popular in FX world, the idea is that you can attribute certain weights to specific days: Fridays are less volatile than the rest of the week, Weekends have a very low weight, Mondays are a bit higher, etc but also to specific events (Fed announcement, Big numbers publication, etc…) The short date model has really an impact on the shorter dates (the shorter the bigger), so while it goes up to 1 year, it is effectively really important up to 3 months.
6. Cut-off spreads
This one is more a workaround than a real need on the market. One should consider that an option with a Sydney 5pm cut has less time to mature than an option NYC 5pm. So the idea is that the NYC option should have a higher price. Ideally, one would increase the time value of that option (and t would then be able to cater for fractions of days). As this is not currently possible in the system, the volatility is effectively increased to mimic the increased price for later cuts.
That’s all that comes to mind right now but I’m sure I’ve forgotten a lot about it. Volatility is a rich topic and I just wanted to give her a flavor of the different functions which are attached to it.
Comments, requests below!