The Vasicek model of interest rates education and training requires an understanding of mathematics and finance. The Vasicek short rate model and exponential Vasicek model are advanced financial models used to describe interest rate movements. The Vasicek model was the first to capture mean reversion, or the concept that the interest rate cannot rise indefinitely and states that the instantaneous interest rate follows the stochastic differential equation.

Oldrich Vasicek was a Czech mathematician who earned a masters degree in math and a doctorate in probability theory. He worked for Wells Fargo Bank in the late 1960s and 1970s and developed a short rate model that was named for him. The model was described in a paper in the Journal of Economics in 1977. It's used by financial experts, scholars and computer simulations to predict interest rates in various financial markets. To understand and use the Vasicek model:

1. Get an overview of the interest rate Vasicek model from online sources;

2. Choose online training to get a general understanding of financial models;

3. Become an expert at Vasicek and other models with advanced training in finance.

Action Steps
The best contacts and resources to help you get it done

Find Vasicek interest rate information online

Online overviews can help if you already understand financial modeling or just need a refresher on the Vasicek model. Resources include programming for computer simulations.

I recommend: Read an abstract on the Vasicek model from the Social Science Research Network. Find simulations that lay out the model from Lifelong-learners, Quant Code and Sitmo.

Get online training to learn about the Vasicek model and futures rates

Online training courses are self-paced and available right from your web browser. They are a good choice for finance experts and students who want to learn more about Vasicek and other financial modeling tools, as well as for those who need to utilize the model for their businesses.

I recommend: The Financial Management Training Center offers free courses accessible from the web. The Analyst Exchange offers comprehensive financial modeling training on several levels. The SAS Institute provides courses that teach students to use models to determine credit risks.

Get an advanced degree that covers the Vasicek model of interest rates

If the Vasicek model is fascinating and easy to understand, it may be time to consider obtaining an advanced degree in finance. Advanced degrees open up more opportunities for an exciting and lucrative career and many schools offer convenient online courses.

I recommend: Find online degree programs for advanced finance at Online Education. Earn a finance MBA from an established university that offers online options, like Drexel University.

Tips & Tactics

Helpful advice for making the most of this Guide

• •  If your business needs to use simulations of the Vasicek model interest rates, consider outsourcing. Determine whether the costs of training and software exceeds those of hiring an external consultant.

The Vasicek Model of Interest Rates is one of the simplest methods to value interest rate derivatives. Yet, the decision whether to insource or outsource Vasicek model valuation is one that takes forethought.

Perhaps you enjoy hands-on experience with software development and you want to flex your brain and reminisce about grad school. Conversely, perhaps you have moved forward enough in your life that you don't want to get down into the nitty-gritty of oldrich Vasicek and Vasicek bond prices. You may wish for someone else to take care of that. In either case, consider the following three items:

1. Investigate the Vasicek model to better understand your company's capabilities.

2. Understand that Vasicek model and futures rates require keeping abreast of industry changes and new philosophies.

3. Determine whether you have the time or talent to perform Vasicek calibration yourself.

Action Steps
The best contacts and resources to help you get it done

Research before deciding to insource or outsource the Vasicek model

Better than the generic Yahoo or Google search sites, topic-related online resources provide relevant information to keep abreast of new developments.

I recommend: Quant Code helps seekers with everything from exponential Vasicek to two-factor Vasicek. They also have white papers explaining the various aspects of Vasicek model interest rates. Check out sitmo for latest articles and the Quant Equation Archive.

Outsource the Vasicek model if it makes sense

Outsourcing saves your time and reduces stress. However, determine your budget limit for this business item prior to making any inquiries. This prevents cost creep and gives you a target range to shoot for.

I recommend: If you hunt for one of the leaders in software development, The Math Works provides your hearts desire. On the other hand, your budget may enjoy Quant Tools which utilizes public domain source codes to provide solutions at minimal cost. Often, these provide more flexible features as well.

Consider a do-it-yourself Vasicek model

If you are in a position to spend the time yourself, and wish to save outsourcing dollars altogether, you may want to take the DIY approach.

I recommend: A fun site to visit is Lifelong Learners. Their class variety (self-learning, intensive, and masters levels) facilitates a greater understanding at whatever level you want to take it to. Many people also enjoy Jan Roman's site - Analytical Finance. You can try out several models there for comparison.

Tips & Tactics

Helpful advice for making the most of this Guide

• •  Consider all additional costs (i.e., benefits, bonuses, taxes, etc...) as well as the savings (i.e., quick revisions, in-house convenience, and tax deductions) before making a decision to insource or outsource the interest rate Vasicek model.
• •  Bounce your final decision off someone else prior to making the commitment. Co-workers, forum friends, and others may spot gaps or spark questions you may need to ask before it is too late.

The Vasicek model of interest rates originates to 1977 when Oldrich Vasicek introduced the model to the world. The Vasicek model is what economist call a "one factor" model in that its only driver is market risk. You can also use the model for the valuation of interest rate derivatives. One drawback is that the interest rate can appear negative and in reality that can't happen. To gain a proper knowledge base for the Vasicek model, you'll need to know some key terms.

Here are a few key terms to help you attain this knowledge base.

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Drift factor

Drift factor represents the part of the Vasicek model that represents the change of interest rates over a given time period. In the Vasicek equation the drift factor is 'a(b-rt).' In this part of the equation 'a' equals the velocity at which Interest rates return to the mean, 'b' is the long run mean of these rates and 't' equates to borrowing timeframe.

I recommend: Review the definition of drift factor and how it's incorporated in the Vasicek model at Absolute Astronomy. For an in-depth view of the drift factor that goes beyond the Vasicek model, examine the report from the Journal of Future Markets.

Term structure of interest rates

Determining the term structure of interest rates in the future is the primary objective of the Vasicek interest rate model. The model uses other financial variables to predict the plot point of interest rate on the yield curve. Changing these variables allows you to build a model for the term structure of Interest rates.

I recommend: Use the term structure of interest rates tutorial at Investopedia to determine the definition and uses for the term structure of interest rates.

Short rate model

The short rate model is for determining interest rate in which the entity in question can borrow money at short-term rates for an infinite period of time. In the Vasicek equation, the borrowing rate for the short rate model is 't.'

I recommend: For an expanded definition of a short rate model, examine the information available at Quant Notes.

Interest Rate Derivatives

An interest rate derivative is where the underlying gives the purchaser the right to pay or receive a nominal interest rate. The Vasicek model attempts to price these instruments correctly for sale in a free market.

I recommend: Register to evaluate the interest rate derivative pricing model tutorial from Jstor.

Negative probabilities

Negative probabilities are one of the criticisms of the Vasicek model. In the model, interest rates can appear negative and in reality, the interest rate can't drop below zero.

I recommend: Study the negative probabilities tutorial from DrChinese.

Mean reversion

Mean reversion is the tendency of the model to return to the average given a long enough period of time. In the Vasicek model, there is indeed a tendency towards mean reversion.

I recommend: Examine the mean reversion tutorial from the Risk Glossary.

The Vasicek Model as it pertains to interest rates is a tool that is utilized to predict interest rate movements from only one source of market risk. (This is known as a one factor predictor.) The model is often used to determine the valuation of various interest rate derivatives within the market.

Take the time to learn about the Vasicek Model and see how it might apply to your financially-based business. Here are some resourceful links to get you started on your journey. Think of this as "the Vasicek Model of interest rates for beginners."

1. Find the equation for the interest rate Vasicek Model so that you can learn how it is calculated.

2. Learn how the exponential Vasicek Model affects bond pricing and yield curves on a moment-to-moment basis while the bond market is open.

3. Learn about the finer point of the Vasicek Model like points of Vasicek distribution or calibration.

Action Steps
The best contacts and resources to help you get it done

Educate yourself about the interest rate Vasicek Model equation

Like any set of interest rates or calculations, there is a corresponding equation that produces the result. (It hasn't always been calculators.) Take the time to learn about the Vasicek interest rate equation so that you may understand the principal of how it is calculated and how it predicts the movement of interest rate derivative products.

I recommend: Go to the website for the Waikato Management School. They have the equations for how to determine several different interest rate models including the Vasicek Model of interest rates. Investopedia is another quality resource that details the Vasicek Model interest rates equation in depth.

Educate yourself on how a exponential Vasicek Model affects the price of bonds

The basic theory behind bond investing is that an investor purchases a bond for a price. After the bond reaches maturity, the investor is then paid back his initial investment, plus some additional money. The additional money is called the interest. The amount of interest the investor will be paid is based on the risk they took (how reputable the company was to be able to pay back the bond) as well as other market factors such as the current interest rates on other bond products. In this way, the Vasicek Model may be utilized to predict the yields as certain bonds might pay based on risk.

I recommend: Read the Journal of Applied Mathematics and Decision Sciences for a very informative tutorial on the relation of the Vasicek Model to bond pricing. The website Lifelong Learners also presents multiple equations for figuring out interest rate yields while employing various bond strategies.

Find out about the subtler points of the Vasicek Model such as points of distribution

Now that you understand the basic equations associated with the model, and have learned how it interacts with bond prices, you now want to study the finer points so that you can read the charts and graphs associated with the Vasicek models. Things to look out for are the Vasicek distribution, Vasicek calibration, two factor Vasicek and more.

I recommend: Go to the website for BIS II Information to learn more about Vasicek distribution. The website The Mathworks also has dozens of articles that discuss the Vasicek Model and all associated terms and equations. Simply use the search engine to locate the articles.