Implied volatility surface and its impact on Greeks

One of the assumptions of the Black-Scholes model is that the volatility is constant for all strikes and maturities. The reality is that the implied volatility surface is not flat:
This has a significant implication on Greeks. For example, the true theta of an OTM put option is lower than estimated by the Black Scholes model. The reason is that over time the implied volatility of the out of the money put option is going up - the smile is getting bigger.
For example the SPY 2012 Dec 60 Put has an IV of 33.7%, while the 2011 Dec 60 Put has an IV of 35.4%. So over 1 year the IV goes up by 1.7%. The Black-Scholes model says that the theta is 0.0038. If we adjust for the increase in IV over time the theta drops to 0.0028 - a 30% reduction in theta.
On the other hand the IV of an ATM option is going down over time (at least based on the current IV surface), so the theta is underestimated.
To make things even more complicated, the IV surface is not static, it is changing all the time.

Market Review 3/5/10

Market jumped on better than expected job numbers. VIX and VIX futures fell. Even the long term VIX futures fell as the risk of a double dip recession diminished somewhat.

If you are a net option seller risk management is extremely important in days like this.

Market Review 3/4/10

Another relatively quiet day in the market. VIX is down to 18.7, the April VIX futures continued to fall.
Wall Street Journal had an article today about VIX being low.
There are a few reasons for the VIX to be this low:
-the realized volatility for the S&P over the past month is 11.6%. For the past 3 months it is 14.8%.
-the Greek credit crisis is easing. The CDS on Greece dropped below 300 bps yesterday (from the high of 420 bps)
-relatively positive economic news from US
-the market is up sharply from February lows
On the other side, the biggest argument against a low VIX is the high yield OAS. Early January when the VIX was below 20, the high yield OAS was around 5.9%. Yesterday the OAS was 6.4%. So the OAS has to come down or the VIX has to go up.
Tomorrow's job report could be a turning point.

Market Review 3/3/10

Even though the equity market was flat today, the VIX futures continued to fall. The Mar VIX futures fell to 19.6 while the Apr VIX futures fell to 22.55.
There was a significant VIX put option spread trade this morning. 45,000 Mar 20 put options were sold for $1.33 and 45,000 Apr 20 put options were bought for $0.83. This is a similar trade I mentioned last Friday, being neutral-long Mar VIX and short Apr VIX. So far this trade was profitable this week as the spread between the two narrowed.
Over the past year, at the VIX option expiration the median spread between the near month and next month futures was around 200 bps. The current spread is 295 bps, down from 310 last Friday.
Due to better economic news and ease of the Greek debt crisis the long term VIX fell this week. The high yield OAS fell as well but not as much as the VIX, so the drop in VIX could be overdone in the short term.
If you are short short-term volatility (short Mar VIX calls) it is probably a good time to lock-in your gains.

Market Review 3/2/2010

The S&P 500 was up 0.23% today and the VIX went down to 19.06%.

The spread between the April VIX futures and March VIX futures continued to narrow. See my earlier post.

Over the past month the volume of VIX options reached 5 million:

Yesterday the VIX put option volume reached 166,000. The put/call ratio for VIX options was around 1, which is significantly higher the the long term average of 0.52.

Interestingly the VIX option put/call ratio lags the VIX by about a month:

Market Review 3/1/10

The S&P was up 1% today, VIX was down to 19.26, VIX futures came down as well. The April VIX futures went from 23.5 to 23. On Friday I argued the the VIX futures term struture is too steep. Today the April VIX fell more than the Mar VIX lowering the spread between the two.

There was some notable volume in the Mar 20 and Apr 20 VIX put options. Benzinga reported a large (25,000) March 20 straddle trade as well.

Interestingly the implied volatility in the Mar VIX put options increased over the past few days while the Apr put and call options implied volatility was relatively stable.
For example, the Mar 22.5 put options IV increased from 81% to 90%, while the April 22.5 puts IV stayed at 64%.

Market Review 2/26/10

Market was slightly up today due to better economic news. The CDS on Greece went down today to 364 bps, proving my argument that the spread between the CDS on Greece and VIX has to come down. See my earlier post. I argued that either the VIX has to go up or the CDS on Greece has to come down.

As I mentioned before the VIX futures term structure is very steep, and it actually steepened today. The short term volatilties collapsed since February 8. The March VIX futures closed at 20.35, while the April futures closed at 23.45. The difference of 3.1 points is significantly higher than historical medians. Around 90% of the time the spread is smaller than 3.1 points.

So I argue that the spread between the two has to come down. Either the Mar VIX has to go up or the April VIX has to come down.

How could you take advantage of the difference? You could go long Mar VIX and short Apr VIX or sell some ITM Mar VIX puts and some ITM Apr VIX calls.

Any other ideas?

Euro implied volatility smile

Today the WSJ had an article about several hedge funds betting on weaker Euro. The demand for puts shifted the implied volatility smile to the left:

Compare this to 5/31/09 smile:

Late last year the papers were all over Gold. The implied volatility smile was skewed to the right due to demand for Gold calls. GLD reached 119 on Dec 2. Today the GLD smile has a negative skew as well.

VIX and CDS on Greece

Over the past month Greece was in the news almost every day. It clearly had an impact on the U.S. market. Here is a chart comparing the CDS on Greece to the VIX:

Recently the CDS went up but VIX stayed around 20. Some investors are buying European stocks because they look at VIX and they think the Greek crisis is going to go away. Others are buying volatility, betting that the Greek crisis is not over.

First Week

I'm really exited to see more than 1,000 visitors of my blog in the first week. What is more surprising is that fact that the visitors came from 38 countries. I would never guessed that someone from Paraguay, Malaysia or Latvia would be interested in VIX options.

I have to thank Bill Luby at Vixandmore again for his endorsement. I'm looking forward for his Expiring Monthly magazine which is the brainchild of five of the top options bloggers on the Internet: Adam Warner of the Daily Option Report, Bill Luby of VIX and More, Jared Woodard of Condor Options, Mark Wolfinger of Options for Rookies, Mark Sebastian of Option 911. I learned a lot from these guys over the years.

I find options on volatility a fascinating subject and I hope I will have the energy to write about interesting topics for long time.

Market Review 2/25/10

The S&P 500 sold off 1.5% this morning on Greek debt concerns and higher than expected jobless claims. The VIX spot jumped to 22.7% slightly higher than the March VIX futures.

On February 8 the costs of protecting against a government debt default by Greece was trading at 425 bps. At that point the VIX was 26.5, and the S&P 500 was around 1,050. Prospects that the EU would extend a financial lifeline to Greece sent Greek bonds to their biggest rally since the introduction of the euro.

While the VIX stayed around 20 over the past week the CDS on Greece went up from 350 bps to 400 bps today. As the market started to focus on this issue again, I wonder what would happen to the VIX and the S&P 500 if the CDS on Greece would reach new highs.

Maybe this is the reason the April VIX futures are still high, and actually rose today to 23.7. The spread between the VIX spot (20.1) and the April VIX futures is pretty wide at 3.6 points.

Market Update 2/24/10

The VIX term structure steepened as markets rebounded after Bernanke's speech.

Over the past 2 weeks VIX and VIX futures came down significantly. VIX call options lost value over this time period.
For example the 25 March VIX call options were trading at $3 on Feb 8. Today they closed at $0.6.
Here are the factors driving the price change:
-the March VIX futures went down from 26.2 to 21.7 today. This caused a loss of $2.3 in the price of the VIX call options
-options loose value over time, this option lost about $0.6 over this time period
-the option gained about $0.5 due to the increase in the implied volatility (from 73% to 88%). This is something unique to VIX options as I mentioned in my prior post, the IV goes up as they get closer to expiration. It is interesting how this reduces the cost of carry (theta) of these options.

If you add these up you get to the price difference of $2.4.

In case you were shorting this monster you are a happy guy.

Introduction to VIX options (Part 1)

First I want to mention that I’m honored to be included among Bill Luby’s (Vixandmore) favorite option blogs. Bill is one of the top option bloggers.

One of my goals with this blog is to explore the VIX options, which are one of the most complex instruments available for individual investors.

Volatility is certainly a fascinating subject. Imagine a formula for gauging human emotion – what could be more interesting than that?

Implied volatility of VIX options is the second derivative of the price of the S&P 500. Unless you like math, it gives you a headache just thinking about it.

Even CBOE admits “calculating exact theoretical values for VIX options can be very complex”.

Why is so complex?

First reason:
CBOE decided to base the price of VIX options not on the current level of the VIX, but on the anticipated level of the VIX at expiration. The price of any index option depends on the forward price of the index and the expected shape of the forward price distribution. Forward prices of option volatility exhibit a "term structure", meaning that the prices of options expiring on different dates may imply different volatility estimates.
VIX options investors look at the prices of the VIX futures to gain a better general idea of how the market is estimating the forward value of VIX.
As I mentioned before on average the VIX term structure is upward sloping, probably due to investor demand for volatility hedging.
Historically, VIX futures have tended to be less volatile, on average, than the VIX index itself. The volatility is lower for longer dated futures.
This means that as they get closer to expiration the VIX options implied volatility is increasing.
In option language this means that if you hold a VIX option you lose money due to theta but you make money due to higher implied volatility as you get closer to expiration.

To be continued….

Market Update 2/23/10

Stocks pulled back today, SPY lost 1.2%, HYG lost 0.7%.

VIX spot is up 1.4% points to 21.37%.

The VIX futures term structure flattened today:

Even with this up move the VIX is still lower than the average for the past month.

Market Update 2/22/10

Even though the market closed down today, the implied volatilities continued to go down.

In the past 2 weeks (since February 8) the VIX came down from 26.51% to 19.94% today. In the same time S&P 500 was up 5% while HYG (high yield) was up 2.7%.

The VIX Futures term structure went from flat on February 8 to upward sloping today. The longer term VIX futures came down as well. The August VIX futures went down from 26.25% to 24.2% over this time period.

Several bloggers talk about the VIX being oversold.

Since 1993 the VIX (starting between 25% and 30%) fell at least 5% points over 2 weeks 65 times. On average over these 2 week periods the VIX fell 6.1% points and the SPY was up 4.8%.

In the past 2 weeks VIX fell 6.6% and the SPY was 5%, which is consistent with historical data.

High yield OAS did not tighten as much over this period. My VIX fair value model (which is based on OAS) shows that the VIX might be slightly oversold relative to high yield.

VXX and the term structure of VIX

There are a lot of discussions about VXX and the usefulness of this ETN. The biggest criticism is coming from the fact that it loses value over time. As most people realized the VIX term structure is upward sloping under normal conditions.

If you look at the median VIX term structure since 1992, you can clearly see that over the long run the VIX futures are in contango:

Are there any uses for the VXX?

For example you can use VXX to delta hedge your short VIX call options position. If you short the first and second month VIX call options VXX can be a usefull tool to delta hedge your portfolio.

Let me know your thoughts.

VIX Fair Value Model

I created a model which comes up with the fair value of the near-tem+6 VIX value.

The CBOE website has the historical VIX term structure.

As I mentioned before there is a strong relationship between high yield OAS and VIX.

Here is the model vs. the actual near-term+6 VIX:

I'm using the high yield OAS as the only input for the model. The R-squared is an impressive 94%.

So, what is this model telling us today?

The fair value for the Dec VIX is about 24.95%. The actual as of 2/19/10 was 23.95%, so about 1% lower than the model tells us.

As you can see this is the Dec VIX fair value, the VIX spot and the near term is a lot more volatile.

I'm working on a model to come up with a fair value for the shorter term VIX as well.

Let me know you thoughts.

First Trade Idea

Here is my first trade idea:

On 2/18/10:
Short 4 April 20 Vix Put option for $70
Short 2 April 30 Vix Call option for $130
Long 2 March 50 Vix Call option fro $10 (will buy 2 April 50 Calls after the March expiration)
Expected Net Credit: $70*4+$130*2-$10*2*2=$500
Max loss $3,500 {2*(50-30)*100-500}

This looks like something between an iron condor and short strangle. The reason it is not an iron condor because I'm not hedging on the downside since VIX probably will not go below 10.

I will follow the performance of this trade and compare it to the CBOE S&P 500 VARB-X Strategy Benchmark.

No statement within the blog should be construed as a recommendation to buy or sell a security or to provide investment advice.

Market Update 2/19/10

The Fed's decision to hike the discount rate after the prior session's close stirred market participants to dump stocks but the market managed to recover by the end of the day.

The S&P 500 ended up 0.22%, while the VIX went down 61 bps and finished the week at 20.02.

It was interesting to see the parallel shift down in the VIX Futures term structure. The March, April and May futures all lost 45 bps:

The May 2010 VIX futures closed at 24.05 the lowest for the week, but still slightly higher than a month ago when they were traded at 23.8.

The VIX options implied volatility surface remained relatively unchanged from yesterday:

Today we saw higher volume for the April 25 and 37.5 call VIX options. 25,000+ and 50,000+ were traded respectively.

VIX and OAS

So VIX is an "uncertainty barometer" of the stock market.

Is there anything else comparable in the capital markets?

The OAS (Option Adjusted Spread) on corporate debt is viewed as a gauge of credit spreads and uncertainty about the future. The OAS measures the difference between interest rates for similar-maturity high yield corporate bonds and treasury bonds.

A higher OAS implies greater anticipated default risk and therefore a higher risk premium.

Here is the relationship between high yield bond OAS and VIX:

So there is a high correlation between high yield OAS and VIX, which helps us to come up with a fair value for VIX.

The volatility of the spot VIX is significantly higher that the volatility of the high yield OAS. The VIX futures volatility is closer to the OAS volatility.

More on this later.

Introduction to VIX, VIX Futures, and VIX options

VIX is the implied volatility of S&P 500 index options.
It is considered one of the best barometers of investor sentiment and market volatility.

The VIX is often called the fear index. When it is high investor sentiment is toward increased volatility and corresponding higher risk. A lower number indicates investors are less concerned about the market and anticipate low volatility.

Fear and greed are the two most powerful emotions stock investors must acknowledge as driving the market over the short-term.

History
• 1993 - The VIX Index is introduced in a paper by Professor Robert E. Whaley of Duke University.
• 2004 - On March 26, 2004, the first-ever trading in futures on the VIX Index began on the CBOE Futures Exchange (CFE).
• 2006 - VIX options were launched in February 2006

Vix Options
VIX options are the first exchange-traded options that give individual investors the ability to trade market volatility. Trading VIX options can be a useful tool for investors wanting to hedge their portfolios against sudden market declines, as well as to speculate on future moves in volatility.
For experienced traders VIX options can be used for volatility arbitrage.

The CBOE website has detailed information about the VIX index and VIX options.

I would also like to mention VXX and VXZ which are exchange traded notes designed to track the S&P 500 VIX Short-Term Futures Index and the S&P 500 VIX Mid-Term Futures Index respectively. These products offer individual investors a daily rolling long exposure to VIX futures contracts.

These are the building blocks of my trading ideas.

Welcome to Volatility Square

Volatility Square is a research and trading blog about VIX options.

Why VIX options?

- I'm passionate about complex derivative products

- VIX options won the Award For Most Innovative Index Derivative Product

- It is a relatively new market, so a standard pricing model has yet to be developed. Calculating exact theoretical values for VIX options can be very complex.

- Because of this complexity the return expectations of a volatility arbitrage strategy using VIX options is higher than the same strategy using other options.

What to expect?

- Market updates, review of academic research and trading ideas.

What is the main driver of the expected returns of my trading strategy?

- The difference between the implied and realized volatility of VIX Index is the driver of returns.

- I will use the CBOE S&P 500 VARB-X Strategy Benchmark to measure the performance of my strategy.

Who should follow?

- Option traders and investment professionals who have experience in trading options and they are interested in the VIX option market.

Enjoy