​Options trading is a complex and dynamic field that requires a deep understanding of market volatility. Accurate modeling of volatility plays a crucial role in pricing options and managing risk effectively. Among the various volatility models available, this blog post aims to explore and compare five prominent models: Yang-Zhang, Rogers-Satchell, Parkinson, Hodge-Stompkins, and Garmann-Klass. By examining their unique features, strengths, and limitations, traders can make informed decisions about which model suits their trading strategies and risk management goals.

Yang-Zhang Model:
The Yang-Zhang model is widely used in options trading due to its simplicity and ability to capture both implied and historical volatility. It employs a hybrid approach that combines the advantages of the GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model and the realized volatility approach. This model has gained popularity for its effectiveness in capturing the volatility clustering phenomenon observed in financial markets.

Rogers-Satchell Model:
The Rogers-Satchell model is a stochastic volatility model that focuses on estimating the volatility of underlying assets. It assumes that volatility follows a mean-reverting process, which allows for better pricing accuracy in options. This model is particularly useful in situations where the volatility of the underlying asset exhibits persistent trends.

Parkinson Model:
The Parkinson model is a popular historical volatility estimator that considers the range of high and low prices over a specified period. It is based on the assumption that the highest and lowest prices observed within a given time frame provide a reasonable estimate of volatility. The Parkinson model is commonly used in options trading, especially for assets that experience high levels of intraday price fluctuations.

Hodge-Stompkins Model:
The Hodge-Stompkins model is a specialized volatility model designed for options on futures contracts. It takes into account the unique characteristics of futures contracts, such as expiration dates and continuous trading. This model incorporates information from both historical and implied volatility to provide traders with a comprehensive view of market expectations.

Garmann-Klass Model:
The Garmann-Klass model is a popular choice for options traders who rely on historical volatility to forecast future price movements. It uses the high, low, and closing prices of the underlying asset to estimate volatility accurately. This model has the advantage of simplicity and ease of implementation, making it suitable for traders who prefer straightforward volatility estimators.

Comparison of Models:
To assess the differences between these volatility models, several factors should be considered:

a. Mathematical Complexity:
Some models, such as the Yang-Zhang model, involve more intricate mathematical calculations, requiring a higher level of computational resources. In contrast, models like the Garmann-Klass model are simpler and more computationally efficient.

b. Sensitivity to Market Conditions:
Each model has its own sensitivity to different market conditions. For example, the Rogers-Satchell model performs well in trending markets, while the Hodge-Stompkins model caters specifically to futures contracts.

c. Volatility Smoothing:
Models may differ in the degree of volatility smoothing they apply to historical or realized volatility data. Some models, like the Parkinson model, place greater emphasis on recent price movements, while others, such as the Garmann-Klass model, take a more balanced approach.

d. Input Data Requirements:
Different models have varying requirements in terms of input data. Some may require more extensive historical data, while others may rely on implied volatility estimates derived from option prices.

Conclusion:
Choosing the right volatility model for options trading is crucial for accurate pricing and risk management. Each of the models discussed - Yang-Zhang, Rogers-Satchell, Parkinson, Hodge-Stompkins, and Garmann-Klass - has its own strengths and limitations

While many individuals are uncertain, regardless of his or her age, about the return on investment for education, one can fully comprehend the cost/benefit analysis about which degree is of utmost importance in regards to income potential. Likewise, some interesting findings for lower-ranked universities showed that individuals should strive towards technology, science, and mathematics as the pay differentiation between other universities was closely related. The website emolument shows that individuals regardless of age could make a mathematical determination of his or her returns associated with what school he or she can afford to attend, what type of job he or she wants, and lastly comparing schools amongst degrees for income potentials. In short, one must realize that the career goals and aspirations should align with the degree and not just base it on income. However, one needs to run the numbers to see if school is worth it for a given major or a given school. Please visit ​www.emolument.com/salary-reports/universities to learn more about salaries per job, university, or location.

​For years the condo market in New York was untouchable. Prices per square foot where at worst two times the price and at best 60% more. In addition to that, one not only had to pay maintenance, but also property tax. For those of you who are unfamiliar with the New York market condos, NYC condos allow the owner full fee simple property ownership whereas the majority of properties which are built fall under a co-op ownership.

This co-op ownership type allows the building to regulate who can purchase based on their own private guidelines , they require board approvals interviews , reserves after closing, and typically only allow owner occupants meaning a purchaser must be willing to move in an with there as their primary residence. For this reason, condos which had none of these restrictions have easier guidelines and should be the first choice for any real estate investors. Historically speaking, about 50% of the existing inventory in Manhattan coop properties. These co-op properties could not be rented, therefore the only rentals available were all condos . This drove up the price of rent and attracted investors/speculators, which further drove up the price of  properties regardless of the condition.
 
Due to covid-19, we're now seeing a mass exodus of both renters purchasers in primary residences in what was historically one of if not the best rental market in the country. Overnight investor appetite to purchase properties has disappeared as well as the potential returns that they could reap from these rentals month over month. The causation of this occurrence could be due to the fact individuals continually pushed up prices because in NYC there is nowhere else to build because it's an one is landlocked you can only build up. Building up is only being reserved for high rise luxury buildings. In a city where everyone is reliant on public transportation and their jobs all being close by, one can demand a steeper price for a lower quality of winning and this model has worked for decades up until today.

Now due to the cyclical nature of real estate development, the approval process is time consuming, so finding a suitable piece of land anywhere from seven to ten years. What we're seeing now is that from 2010 to 2020 there's been an extreme boom of new high rise luxury buildings being built, which has left half of the city unrenovated pops. The vast majority of these luxury new developments were being built as condos, which could also command a higher purchase price. Therefore boosting the profits for the developer. 
 
Currently, the rental market has had a slowed inventory for sales, as well as rentals. The inventories have gone through the roof, and now more than ever we're starting to see a large shift of properties for sale go from not just the co-ops, which historically were making up 90% of the inventory of the city, but now we're starting to see uneven higher proportion of condos which are being put up for sale as well.

This can be driven in the large part because renters have been fleeing the city. If one were an investor purchasing these condos on the assumption that all of the debt would always be serviced through rent, this may now be in jeopardy. 
 
That's a very rough baseline because the cost per square foot for a New York City apartment is roughly $1000 per square foot, and for a condo historically you could expect to pay $1500 to $2000 per square foot. We're now seeing anywhere from first around 40% a 60/40 split between co-ops and condos which historically would never occur typically it would be 90/10.
 
Basic economics shows us that increased supply with reduced demand drop prices. That's exactly the force that we're seeing here with the condo average price coming in roughly at 1150 per square foot and co-ops coming in still at the $1000 to $1100 per square foot range. However, the smaller unrenovated properties are priced below $1000, hitting into the eight and $900 per square foot range. Now if one were to trace this back, we would see that this is starting to come in around the 2010-2011 year based on historical price alone.
 
Investors were flocking to these condo properties ten years ago because they knew that they were the only ones which would allow rentals, and that drove the price to double over the past decade. Similarly, New York City real estate has doubled as a whole. What we're seeing today is essentially a reset back to that time over that exact pricing scenario.
 
If we look back in that the 2010 interest rates were roughly 5 and 1/8% for a 30 year fixed rate purchase. Today, one purchase maybe a half a point at 2 1/2% for a 30 year fixed. Ten years ago, the financing was 30% higher to obtain the same purchase price, so that leaves one with a good assumption to purchase real estate in NYC today,
 
Historically one needed to put 20% down because that's how New York is with co-ops. With condos there are fewer restrictions in that you can put down less than 20% and still be allowed to purchase. Therefore if your bank will let you put down 5%, by all means put down a 5% payment and make the purchase.

Today one would need to offer a steep discount  at a 50%  discount, meaning if your mortgage is $2,000 on a $400,000 apartment, and you rent it for $1000 a month you'll be losing $12,000 per year. For many of you, that may be unacceptable, but you should also keep in mind that these losses are all tax deductible. Tax write offs are one of the amazing benefits of real estate. Take into account that this apartment which you just purchased you only had to put for example 10% down. This means that if it costs a total out of pocket of $78,000 for all of the expenses, due to all of the losses.

While stocks have rebounded quite nicely, NYC real estate has been down about 30%. This means that when real estate in NYC recovers the $78,000 total cost of ownership can allow for one to obtain about $150,000 in asset appreciation. That seems like a pretty good return on investment. Do you really think that restaurants will never rebound? Do you really think that you'll never go back to work in an office again? Don't you think that someone won't want to grab an amazing apartment for rent for only $1000 a month while you take the loss month over month?
 
This window of opportunity might not come back in quite some time, so if you have the risk appetite definitely go purchase some condos in NYC.

As always, we begin these posts to read the legal disclosure for any posts in regards to investments on our insights page. With interest rates for loans being close to 2.5% for a 30 year mortgage, one may be wondering where is the best place to invest right now? If you read how to minimize portfolio volatility,  one can see Investment Science made a good call on bonds when the market tanked. According to Investment Lab, the best place for investments right now is commercial real estate, especially in NYC, and converting that into residential property. As Baron Rothchild once said, 'Buy when there's blood in the streets.' Investment Science feels that NYC will recover, but our firm does not know the exact year, and people always will need a place to live. Buy low sell high!

We preface this post in that our firm is not licensed to provide financial advice to individuals, and this is just for your education.

What is a very interesting portfolio that Investment Science created was in the March 2020 coranvirus crash, when everybody was panicking, there was this portfolio we designed with our data-warehouse. We looked at the volatility of asset classes from each and every panic, and came up with the following for somebody who was 62. In summary we have bonds that pay in different dates in different currencies which diversifies risk.

1) GOLD CRASHED 60% IN 2009 AND 30% IN 2020, so it's not really the best for market panics.
2) Depending on your lifestyle, and how long you live one might need ~3 million to retire. You may need to count on social security. Likewise, look into renting out a house potentially. Otherwise one may want to sell the house and downsize it or buy more real estate to rent
         A. There could be a ton of deals in the next 2 years from this virus
      B. Rule of 72 dictates take the number 72/ divide by the interest rate, thats the number of years to double your money
      1) 38% of your retirement should be in stocks (Similar to Warren Buffet's advice in his books)
      2) 62% should be in bonds (Similar to Warren Buffet's advice in his books)
      3) We created this portfolio based off of knowing somebody in that age group hates risk, but giving them some upside international exposure on the bonds too on unrelated companies

Currency Exposure (Bonds all pay on different days which helps the currencies!!):
     A. Swiss franc 2%
     B.Norway Krona  2%
     C. South African Rand - 1%
     D. British Pound - 4%
     E. Euro - 4%
      F. USD - 87%

Buy: 62% Bonds especially because we are in a recession for 1-2 years (What's great is one has some exposure to different currencies too, and some very high return bonds, mostly investment grade bonds, the currency exposure may be able to amplify the returns from gold and oil from the currencies)

1) 2% of retirement  Pepsi Bonds ->  https://markets.businessinsider.com/bonds/1_250-pepsico-bond-ch0008941319 - 8% Yield (Pays in swiss franc) - Good historically swiss franc is worth more than the USD and it gives  you some currency diversification and the CHF shoots up whenever the market crashes here
2) 2% of retirement Albertson's Inc -> https://markets.businessinsider.com/bonds/6_625-albertsons-bond-2028-us01310qdb86 7.46% Yield (Pays in USD)
3) 2% of retirement  ADT https://markets.businessinsider.com/bonds/adt_corpdl-notes_201212-42-bond-2042-us00101jag13  8.03% Yield (Pays in USD)           
4) 2% of retirement American Express https://markets.businessinsider.com/bonds/dl-med-term_notes_201520-bond-2020-us0258m0dt32  7.56% Yield (Pays in USD)
5)  2% of retirement Genl Dynamics  https://markets.businessinsider.com/bonds/general_dynamics_corpdl-flr_notes_201820-bond-2020-us369550bb33  9.67% Yield (Pays in USD)
6) 2% of retirement Verizon https://markets.businessinsider.com/bonds/6_730-verizon-north-bond-2028-us362337ak38 8.04 % Yield (Pays in USD)
7) 2% of retirement Toyota https://markets.businessinsider.com/bonds/toyota_motor_credit_corpdl-flr_med-term_nts_201920-bond-2020-us89236tgp49 5.11 % Yield   (Pays in USD)
8)2% of Retirement United Health Group https://markets.businessinsider.com/bonds/unitedhealth_group_incdl-flr_notes_201720-bond-2020-us91324pdb58  5.92 % Yield   (Pays in USD)
9) 2% of Retirement Viacom https://markets.businessinsider.com/bonds/4_850-viacomcbs-bond-2034-us92553paz53  5.83 % Yield   (Pays in USD)
10) 2% of Retirement Catepillar - https://markets.businessinsider.com/bonds/caterpillar_finservices_corpdl-notes_201718-20-bond-2020-us14912hts93  8.32% Yield  (Pays in USD)
11) 2% Mortgage backed security AAA rated - https://markets.businessinsider.com/bonds/5_400-abn-amro-bank-bond-2026-xs0592463136   5.4 % Yield   (Pays in NOK) - this is awesome because oil should spike back up in  December, which means the currency conversion should rise in December and            payments are 1x per year
12) 1%  South African Bonds (Gives you exposure to gold) - https://markets.businessinsider.com/bonds/south_africa-_republic_of-bond-2040-zag000125980 - 10.21% Yield (Pays in ZAR [South African]-  - this is awesome                             because                  the ZAR currency should go up longer term due to gold, likewise it has              a potential to double as ZAR is at a historical low
13) 2% - USA treasury bills very safe - https://markets.businessinsider.com/bonds/united_states_of_americadl-flr_notes_201820-bond-2020-us912828y537 - 6.4% Yield (Pays in USD) 
14) 2% Burmingham, Alabama debt - https://markets.businessinsider.com/bonds/3_500-birmingham-city-of-bond-gb0000993211 - 11.14% Yield (Pays in British Pound) - Pound likely to go up to 40% value in next few years.
15) 2% China government debt - https://markets.businessinsider.com/bonds/china-_peoples_republic_of-Bond-2022-hk0000116407 - 8.69% Yield (Pays in Chinese currency) - This currency likely to increase by about 20% long term
16)  2% Clavas Securities PLC Debt - https://markets.businessinsider.com/bonds/clavis-securities-bond-2032-xs0302269096 - 6.9% Yield (Pays in Euro) - This currency will likely increase 30-50% long term
17) 2% Hypo Vorarlberg Bank AG Debt - https://markets.businessinsider.com/bonds/hypo_vorarlberg_bank-Bond-2020-at0000a10gb9 - 8.79% Yield (Pays in Euro) - This currency will likely increase 30-50% long term
18) 2% Bank of nova scotia - https://markets.businessinsider.com/bonds/bank_of_nova_scotia-_thedl-notes_201520-bond-2020-us064159gw01 5.44% Yield (Pays in USD) 
19) 2% Canadian Railyway -  https://markets.businessinsider.com/bonds/4_000-canadian-pacific-bond-ca136447ax71 - 9.59% Yield (Pays in GBP)
20) 2% New metro global - https://markets.businessinsider.com/bonds/dl-notes_201818-22-bond-2022-xs1839368831 - 8% Yield (Pays in USD)
21) 2% NordLB (German Bank) -  https://markets.businessinsider.com/bonds/norddeutsche_landesbank_-gz-nachrdl-ihss1748_v1424-bond-2024-xs1055787680   6.48% Yield (Pays in USD)
22)2% French Investment Bank - https://markets.businessinsider.com/bonds/soci%c3%a9t%c3%a9_g%c3%a9n%c3%a9rale_sadl-flr_nts_201621-und_regs-bond-usf43628c734 -    6.57% Yield (Pays in USD) 
23) 1% - https://markets.businessinsider.com/bonds/pyxus_international_inc-bond-2021-us018772as22 - 79.67% Yield (Pays in USD( - Junk Bond, they will need to pay you even if they go bankrupt, but I don't see any bad news)
24) 2% -https://markets.businessinsider.com/bonds/raiffeisen_bank_intldl-flr_med-term_nts_1520_90-bond-2020-at000b013628 - 10.37% Yield (Pays in USD)
25) 2% Interdevelopment Bank - https://markets.businessinsider.com/bonds/inter-american_dev_bankdl-flr_med-term_nts_201520-Bond-2020-us45818wbh88   - 5.45% Yield (Pays in USD)
26) 2% - African Development Bank - https://markets.businessinsider.com/bonds/african_development_bankdl-flr_med-t_notes_201620-Bond-2020-us00828ebs72 - 5.25% Yield (Pays in USD)
27) 2% - https://markets.businessinsider.com/bonds/swedbank_hypotek_abdl-mortg_cov_mtn_201520-bond-2020-xs1231116481 - 19% Yield  (Pays in USD)
28) 2% - https://markets.businessinsider.com/bonds/skandinaviska_enskilda_bankendl-med-term_nts_201520_144a-Bond-2020-us83051gad07 - 14.13% Yield   (Pays in USD)
29) 2%  barclays Investment Bank - https://markets.businessinsider.com/bonds/0_077-barclays-bank-Bond-2021-xs0126504421 - 13.11% Yield  (Pays in USD)
30)2% Swedbank - https://markets.businessinsider.com/bonds/swedbank_hypotek_abdl-mortg_cov_mtn_201520-bond-2020-xs1231116481 - 19.77% Yield (Pays in USD)
31) 2% - https://markets.businessinsider.com/bonds/golden_wheel_tianhldgs_coltddl-notes_201821-bond-2021-xs1751017218 - 14.39%  (Pays in USD)
32) 2% - https://markets.businessinsider.com/bonds/china_evergrande_groupdl-notes_201919-22-bond-2022-xs1982036961 - 13.02%  (Pays in USD)

Stocks - 32% Of  money could be technically in safe haven assets that could provide a 2% return while we wait for the stock market to finish crashing + there are some deals trading less than NAV:

1)  1% - Buy EWEM (barely dropped and less than NAV) -  safe
2) 2% - Buy  RAVI (barely dropped and less than NAV) - 2% Yield safe
3)  2% - Buy  GSY  (barely dropped and less than NAV) - 2% Yield safe
4) 2% - Buy  CYB   (barely dropped and less than NAV) - 2% Yield safe
5) 2% - Buy  LDRI (barely dropped and less than NAV) - 2% Yield safe
6) 2% - Buy  MBSD  (barely dropped and less than NAV) - 3% Yield safe
7)  2% - Buy  SCHO  (barely dropped and less than NAV) - 2% Yield safe
8) 2% - Buy  AGZ (Government agency bond etf backed by federal government) -  2% Yield safe
9) 2% - Buy GNMA  (barely dropped and less than NAV) - 2% Yield safe
10) 2% Buy LGOV (barely dropped and less than NAV) - 3% Yield safe
11)  2% Buy PHDG  (Good ETF) - Safe
12) 2% Buy  CBON   (barely dropped and less than NAV) - 3% Yield safe

***Stocks 1-10 you hold onto until the market hits bottom, but sell when ready to buy other stocks*****

13) 1% - Buy BTAL (Good ETF) - Hold onto this long-term dont touch it
14) 1% - Buy FUT  (Good ETF)  - Hold onto this long-term dont touch it
15) 1% - Buy  EMTY   (Good ETF)  - Hold onto this long-term dont touch it
16) 1% - Buy CLIX  (Good ETF)  - Hold onto this long-term dont touch it
17) 1% Buy DLBR (Good ETF)  - Hold onto this long-term dont touch it
18) 1% Buy IVOL (Good ETF)  - Hold onto this long-term dont touch it
19) 1% Buy FUT  (Good ETF)  - Hold onto this long-term dont touch it
20) 1% Buy GLDI   (Good ETF)  - Hold onto this long-term dont touch it
~~~~~~~~~~~~~~~~~

Some interesting purchases, when the market bottoms would be:
1) Specifically  Home Depot and XOM 
2) Airlines will go back up too keep an eye out as well as hotels + cruise ships

As of August 2nd, the portfolio is up about 50%, and interestingly enough the federal reserve bought all of those bonds after the dip because flight to safety dictates in market panics everybody sells all assets (that's why basically almost everything crashes outside of some options and short positions) - so it's important to properly diversify and this was one of the few ways we thought you could, and it looks like it played out for the best! The bond etfs we selected we back-tested and saw they barely moved in other stock market panics.

Interest rates are technically going to eventually go negative because millennial's are not having children and the US GDP shrank by 30%+, so that means the fed will keep printing money and making the rates low, which means people who have stable jobs can take on debt because the money is almost free - just ensure that money is used for investments associated to your risk tolerance levels.

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