I'm not an expert on VIX contracts etc, but I can tell you that some exchange traded derivatives compute daily settlement prices based on observed trade prices of the derivative itself. In other words, the determination of the 'fair' price of the asset is left to the market itself, rather than some other reference. After all, many commodities function that ...
You are an investment bank. You trade a multitude of vanilla and exotic options. You want to make sure the option prices you quote as a client are arbitrage-free with respect to liquid option prices quoted in the market $-$ and also consistent between the different trading desks within your bank.
Basically you want to avoid other market participants taking ...
The answer in Implied Vol vs. Calibrated Vol as suggested by noob2 is more complete.
But it may be slightly misleading in your last example.
I've been a vanilla option market maker for ten years, so I'll chime in on what I would mean by that.
If a market maker says he's calibrating his vols to the market it means exactly what you're saying: getting prices ...
“How would've the 50 dollar call earned an additional 1 dollar if IV dropped to merely 30? Did the author just assume that it would? Or can you calculate this?”
1 is it not a 50 dollar call, the 50 dollars is the strike price. This is a hypothetical stating the option premiums, to calculate the implied volatility is not needed. If you want to in ...
It's all about transposing prices into some space that changes more slowly, such that data you can garner from prices provided by someone else at some other point in time can be used to estimate value at some other point in time.
Its effectively an interpolation and extrapolation tool.
Say you have option prices at strikes of 10, 20, 30, 40, etc. And you ...
I am using FinPricing data service API for both swaption implied volatility surfaces and cap implied volatility surfaces. It supports both C# and Java. They use SABR model for calibration and generate so fine-granular data grids that users can use linear interpolation directly without arbitrage. Data are updated every day.
It is poorly worded. Replace "options markets" with "stock markets" and it becomes clear that they're just noting typical spot vol correlation. When stock markets trade up volatility tends to fall and when stock markets trade down volatility tends to rise. This has been the case, on average, historically. For more on why, see here: Why does implied ...
Assuming that $r$ and $r_f$ are the same, you should use continuous compounding:
and if the underlying is a dividend paying instrument, then
with $y$ the annualized continuous dividend yield.
Since you talk about a variance risk premium, a word about some of the details involved might be important. Technically, your variance premium is the difference between the expected volatility under the physical and risk-neutral measures. In general those quantities aren't equal.
For example, in a stochastic volatility model, market incompleteness implies ...
In a Full reval scenario, you would 1) identify your risk factors (ATM point? Skew? Surface? SABR?)
Say you want to simulate all surface points. Then, after you have applied your surface returns you need to first make sure that your new IV surface is free of arbitrage. That is an art in itself, though. Then you do the valuation as is usual.