# Use cases for calibrated IV surfaces

What are common applications of a calibrated options IV surface when trading vanilla options only? Thank you!

## 3 Answers

Here are a few use cases.

1. If you have only a small number of quotes, then you can use a model to imply option prices where you don't have a market.

2. You want to create a smooth interpolation for other purposes, like calculating the local vol surface using Dupire's formula.

3. Converting the vol surface into a smaller number of points - i.e. your model parameters - then you can calibrate them each day and look at the time series. This is often a far easier way to look at a time series of vol surfaces - what you're doing is decreasing the dimensionality of the data for the purposes of understanding/visualisation.

4. They can also be a way of understanding your risk and attributing PnL.

a. For understanding your risk, you can fit a model, and then look at the change in value of your portfolio as you bump model params.

b. For attributing PnL, you can do the same as above, except instead of bumping for the understanding of moves, you move the params one by one (or one at a time, depending on how you want to think about the cross greeks) to get you from the params at the beginning of the period to those at the end, looking at the incremental PnL change as you move them.

Now, all of the above come with the very important caveat that you are projecting the world onto your model. There are a several impacts of this - for example:

• Inbetween points of market data, you are interpolating. Depending on the assumptions of your model, this will force various dynamics. A simple example is using a cubic spline where you have constraints on your derivatives (i.e. keeping the first derivative continuous, etc.)
• Outside of your calibration points you're extrapolating - this is where your model assumptions are really important, especially in cases where the price of the derivative you're looking to value strongly depend on the wings (i.e. var/vol swaps in equities, CMS in rates)
• everywhere, the assumptions of the second derivative have strong impacts on the calculated local vol using Dupire's formula.
• Thank you for the insightful answer. Is there any use case where it is used for static arbitrage? I guess that static arbitrage is directly detected using bid/ask book rather than IV parametrization. Since it is the presence of arbitrageurs that justifies that the surface should be arbitrage free, this confuses me in what we define as arbitrage in terms of the volatility surface (not considering that we buy at ask and sell at bid for e.g. butterfly arbitrage). I will open another question. – raptor22 Sep 25 '19 at 9:24
• Excellent! Much appreciated. Thank you all for your insights. – annon Sep 25 '19 at 14:05

A common use case is in FX, where the market convention is to quote a grid of maturities and deltas (typically 1W, 2W, 1M, 2M, 3M, ...) and (10, 25, 50, 75, 90) delta but the options that you hold in your portfolio will have strikes and maturity dates that don’t line up with this grid. If you want to price these options you need a calibrated volatility surface to interpolate them.

To calculate theoretical option prices using a smoothed IV surface. Because the market observed option prices can deviate from theoretical prices especially for far ITM and OTM options. This creates arbitrage scenarios.