Options / Volatility Question

Does anyone here have a simple explanation for both implied volatility and realized volatility? I can't seem to be able to find it explained in laymans terms anywhere.

Is skew just the difference between the two?

 
Best Response

Implied volatility is what the market is pricing (their guess) the volatility of that option or in simple terms what the market expects the movement (speed) of the underlying to be.

Realized volatility is what the underlying ACTUALLY moves.

Now the market usually prices IV over RV for the possibility for it to increase speed, if the IV of the options are under priced to the RV if you can hedge the underlying to can make profitable hedges.

For example If you were to buy the Dec 13 Oil 102 straddle @ 970 the implied volatility (speed) is 21 Vol

You would need to the future to move daily around $1.35 to break even on your theta (or money you pay to own the options).

So in this example the straddle is $9.70 or IV is 21 vol or $1.35 in daily movement. BUT it could realize more for that for example Egypt takes off and the future moves $2 or around 31 vol, now the market might price the IV vol at 34 vol to include the recent moves in the underlying and a risk premium to the realized.

Hopefully you can now see how the IV and RV relationship exists and changes with supply demand.

Also skew or also called wings are a reference to out of the money options so using the example above Oil is trading $100, you might talk about Dec skew which might be the 70 puts or 135 calls for example.

 

There will be only one realized volatility for a given underlying.... that should be clear enough.

Given all other black scholes inputs are easily observed, the remaining variable is implied volatility. This is the value being used in the model to generate the current price of an option. If you live in a perfect black scholes world and delta hedge continuously you will make money if IV is less than RV over the life of the option and vice versa (for a long option position). You will break even if they are equal, and lose if Implied is more than Realized.

You will notice that options at different strikes on the same underlying have different implied volatilities even though there can only be one realized volatility. That is the skew. There can be both fundamental and technical reasons for volatility skew.

 

Best way to understand is to learn what gamma and dynamic delta hedging is. Frans de Weets Intro to Options is a great short and simple read that explains it very simplistically.

The general idea is that by delta hedging an option you make money if the stock moves up or down between hedges (to understand this think of a portfolio of 1 call option at 50 delta and short 0.5 shares against it, what is your payoff if the stock moves in either direction?). But you pay for this convexity by paying time decay every day o nthe option, so you need the stock to move enough each day to make this decay back. This is the implied vol in essence. It is the price of the option but not in dollars and cents, but in terms of how much you need the stock to move to break even on your decay bill. Realized volatility is ismply how miuch the stock has been moving historically.

 
Jimbo:

There will be only one realized volatility for a given underlying.... that should be clear enough.

I would caveat this with your hedging strategy can impact your "realised vol." 2 different strategies could yield entirely different results.

Jack: They’re all former investment bankers who were laid off from that economic crisis that Nancy Pelosi caused. They have zero real world skills, but God they work hard. -30 Rock
 
Revsly:
Jimbo:

There will be only one realized volatility for a given underlying.... that should be clear enough.

I would caveat this with your hedging strategy can impact your "realised vol." 2 different strategies could yield entirely different results.

Care to explain? Because I don´t follow. I understand that the strategy will impact PnL for obvious reason, but realized vol is realized vol, as in stdev of ln returns of the underlying right? And the returns of the underlying are unique, regardless of how you trade the position.

 
Maximus Decimus Meridius:
Revsly:
Jimbo:

There will be only one realized volatility for a given underlying.... that should be clear enough.

I would caveat this with your hedging strategy can impact your "realised vol." 2 different strategies could yield entirely different results.

Care to explain? Because I don´t follow. I understand that the strategy will impact PnL for obvious reason, but realized vol is realized vol, as in stdev of ln returns of the underlying right? And the returns of the underlying are unique, regardless of how you trade the position.

Returns ain't unique, innit? You can calculate daily returns, weekly returns, etc etc... I think that's the point here. Returns can be calculated over different horizons, just like one could delta hedge with different frequency.

Still, I do believe "realized vol" as a term is rather unambiguous and shouldn't be affected by the delta hedging choices.

 
Martinghoul:
Maximus Decimus Meridius:
Revsly:
Jimbo:

There will be only one realized volatility for a given underlying.... that should be clear enough.

I would caveat this with your hedging strategy can impact your "realised vol." 2 different strategies could yield entirely different results.

Care to explain? Because I don´t follow. I understand that the strategy will impact PnL for obvious reason, but realized vol is realized vol, as in stdev of ln returns of the underlying right? And the returns of the underlying are unique, regardless of how you trade the position.

Returns ain't unique, innit? You can calculate daily returns, weekly returns, etc etc... I think that's the point here. Returns can be calculated over different horizons, just like one could delta hedge with different frequency.

Still, I do believe "realized vol" as a term is rather unambiguous and shouldn't be affected by the delta hedging choices.

That's basically what I am getting at. Depending on the frequency/timing of re-hedging, you can certainly come up with very different realised vols given the same data.

I kind of disagree, that realised vol is unambiguous... once you agree on a rehedging strategy, agreed, but there are any number of strategies. Off the top of my head I could think of several underlyings which would probably look like low realised vol on daily strategies, and several vols higher on higher frequency/tight range rehedging (and I'm talking from a 6 vol base so a few vols is pretty massive).

Ain't door knockers innit.

Jack: They’re all former investment bankers who were laid off from that economic crisis that Nancy Pelosi caused. They have zero real world skills, but God they work hard. -30 Rock
 

Realized vol is completely contextual but it is a known variable as it's historical. If two traders look at the RV over the same time period and frequency they should get the same answer. This assumption is based on them having the same tic data.

Optimal hedging based on variations of RV is a totally different discussion and I don't think helps simplify the difference between IV and RV for a beginner.

 
wilder:

Realized vol is completely contextual but it is a known variable as it's historical. If two traders look at the RV over the same time period and frequency they should get the same answer. This assumption is based on them having the same tic data.

Optimal hedging based on variations of RV is a totally different discussion and I don't think helps simplify the difference between IV and RV for a beginner.

What Revsly is getting at is that even with the same exact data two traders can get two different realized volatilities, because RV depends how you define it. Using daily returns is the most mainstream, but that def doesnt mean its what a trader should def be using. As Revsly said, RV is defined by the hedging strategy you use so it is not a single known variable, it is a caculation and hence depends how its calculated. There is no hard and fast rule for how to do that.

 

Yes correct, movement is known and then it's how you define it. I tried and failed to imply they had the exact same definition/ parameters. Also I think you mean your inputs to calculation define your RV not your hedging strategy. Your RV might not be defined by the hedging strategy but your hedging strategy could be defined by your RV or vice versa for example.

 

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