Study On Models Of Term Structure Finance Essay - Free Essay Example

Sample details Pages: 4 Words: 1173 Downloads: 8 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? One of the earliest stochastic models of the term structure was developed by Vasicek (1977). His model is based on the evolution of an unspecified short-term interest rate. Although the model is developed in a fairly general framework, it is most frequently applied in a more specific form that is presented here. Don’t waste time! Our writers will create an original "Study On Models Of Term Structure Finance Essay" essay for you Create order The Vasicek model has many advantages, though it also has some shortcomings. The model assumes that the short rate follows the stochastic process dr = a(b-r)dt + sdz Here, dz = a standard process a = coefficient for the formula r = the current level of the interest rate. b= parameter for long run normal interest rate If the interest rate is above the long run mean (r b), then the coefficient a (0) makes the drift become negative so that the rate will be pulled down in the direction of r. Likewise, if the rate is less than the long run mean, r b, then the coefficient a makes the drift become positive so that the rate will be pulled up in the direction of r. The coefficient a is, thus, the speed of adjustment of the interest rate towards its long run normal level. This feature is particularly attractive because without it, interest rates could drift permanently upward the way stock prices do and this is simply not observed in practice. In our century the in terest rate has an important place in all transactions that include simply lending and borrowing. However, its importance has risen with developing and slight stationary economic conditions of the world. The desire to have foresight for the level of future interest rate has become crucial in the sense that to know the lending and borrowing rate and not to miss price the interest rate instruments. As a result, the modeling of interest rate has risen as a problem. As solution to this problem there have been many models proposed. Their common feature is that they all model a stochastic problem, i.e. they deal with uncertainty. The first model in 1973 was proposed by Merton. However, the pioneering one was suggested by Vasicek in 1977 and in the following years many there models that are much more analytically un tractable has come out. These stochastic models are mainly classified with respect to the number of factors which are assumed to have a stochastic evolution in the model. In this study we will use Vasicek short-rate model among some of the most fundamental one factor interest-rate models to predict the yield curve of tomorrow by using todays observed yield data It was introduced by Oldrich Vasicek in the year of 1977. It is a mathematical model that describes the interest rate growth. The Vasicek Model is a type of one-factor model that explains the movements of short time interest rate when it is only driven by the market risk. In Vasicek model wiener process shows the random market risk while the standard deviation shows the volatility of the interest rate. The Vasicek Model is also applied for the interest rate derivative assessment. The theory of Vasicek Model is very well adapted by the credit markets. However the interest rate may not be original future interest rate but the interest rate must be closer to the original rate. If we use correctly the Brownian motion and the volatility related to the market rate than it may give the righ t desired outcomes. However the major problem will occur when there will be a sudden change in market risk. Vasiceks revolutionary work is the earliest account of a bond pricing model that incorporates stochastic interest rate. The short rate dynamics is modeled as a distribution process with constant parameters. When the bond price is based on this assumption, it has the feature that on a given date, the ratio of expected excess return per unit of volatility (the market price of risk) is the same, regardless of bonds maturity. 2.6.1 Pricing Bonds with Vasicek Model Given the term structure of interest rates (fully described in this model by the spot rate) the pricing formula for bonds is straight forward. Bond prices are determined by summing the present value of the coupons and terminal value, discounting at the discount factors P(r, 0, T). Thus, the value of a bond paying coupon c at time 1, 2, . . . , M and having face value of 1 is given by the function: Bond Price[c, r, M]:= Sum [P[r, 0, t] * c, {t, 1, M}] + P[r, 0, M] It is often convenient to consider continuously paid out coupons, in which case the above formula becomes: Bond Price[c, r, M]:= Integrate [P[r, 0, t] * c, {t, 0, M}] + P[r, 0, M] A European option on a bond can also be priced analytically with the Vasicek term structure model. 2.6.2 Advantage and disadvantages of Vasicek model We know that nothing is perfect in the world. Every effective thing has negative effect with their positive elements. The advantages and disadvantage of Vasicek model are as follow: a) Advantages The method is based on reliable mathematical calculation which makes the future forecasted interest rate near to the future original interest rate. Its a short rate model which gives a future interest rate nearly to the same which will happen in future like future spot rate. It also helps in risk hedging. By using the Vasicek model we can forecast the future interest rate and if there is any uncertain risk in interest rate then we can hedge our amount which can be affected by the uncertain risk. The interest rate is calculated for the shorter time period under Vasicek model i.e. the volatility factors almost keep the same as it was taking at the time of interest rate derivation. b) Disadvantages shortcomings of the Vasicek model: Interest rate can become negative. It only happens when people like to hold the cash instead to invest it. Difficult to make the model fit the yield curve exactly. Like if there occur a change between the derived interest rate and the original interest rate then the yield curve of derived interest rate will vary from the original yield curve. And it affects the other estimations based on the model. Constant local volatility is not realistic, but it is easy to generalize with market rate but we know that the volatility changes as the time is passes on. So its not good to generalize the volatility. Numerous generalizations are possible. However the more generalization input will affect the output result. The estimation is always unreliable. If we take rates of two or three parameters as general rates then it may affect our future forecasting rate. It must be different from the original one. Even with the Vasicek model, we need to solv e non-linear equations to construct the tree. So its mean there is more than one variable and sometime its very difficult to calculate the more variables. Increase in variables make chances of error high. More complicated models typically imply that we need to solve even more complicated equations. Because to solve the more variable we need to solve more equations.

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The International Business Machines Corporation - 2503 Words

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Live Music vs. Recorded Music Essay Example For Students

Live Music vs. Recorded Music Essay Live Music vs.. Recorded Music As Mark Morris addresses the people at the Midwest Arts Conference in 1998, he explains how deeply he feels about the importance of live performances as opposed to recorded performances. He feels that each time tickets are sold and a performance takes place it is a true miracle. In todays world live performances are separating farther away from society and recorded performances are taking control. This needs to change. Live performances and recorded performances are incomparable and will ultimately affect human beings in very different ways. Live performances provide a special opportunity for the performer and audience, whereas recorded performances will not. Live performances are spontaneous and a spur of the moment experience. This spontaneity creates a more natural performance since mistakes will be made, but the piece will ultimately be greater than the number of mistakes made. Recorded performances are an attempt at creating something perfect without any mistakes, but as humans, that is something we are not capable of doing. Furthermore, recorded performances are unrealistic and are an untrue performance. As a performer performs live, the audience will help create a positive atmosphere for the performance, however recorded performances do not rely on an audience. In live performances there is an exchange of energy that also does not occur in recorded performances. This energy can only occur between a live performer and an audience. Since it is difficult to fully understand the energy taking place while watching or listening to a recorded performance, the viewer/ listener will not have the same experience as an audience member that watched that act same performance live. In addition to the energy, the visual elements oaf live performance will impact the experience. Also the body language has a deep visual impact on the message and the experience of the performance. A performance is not about how the act was performed, but rather how the audience perceives it. Unfortunately, recorded performances are having a large affect on live performances. Currently, people are becoming so used to recorded performances, that performers will try to replicate their recordings during their live performances. In music, many artists have been caught lip-syncing to their own recording in public instead of actually singing. This is a much larger mistake than the small mistakes that might be made during a truthful live performance. Having recently been to several live performances, I can personally attest that viewing a performance live is more affective then watching it on a TV or listening to it on your pod. Each time I go Tao concert the music always sounds different. The singers voice is much more natural, as you hear the heavy breathing in the microphone and the interactions that the reformer has with the audience. This does not occur in recorded music. Although I enjoy listening to music, especially the same music that I Just heard live, the recorded music is impractical. Although there is a Joy to listening or watching a recorded performance at home while sitting in your own comfortable space, viewing a live performance provides an entirely different type of comfort. While sitting in a theater, a space specifically made for performances, one will experience a series of programs By emanated home will force the viewer to become a lazy viewer, because they can sample, skip round, and even turn it off. The experience is different at a live performance; you are not sampling, but rather you taste the entire performance. As Mark Morris explains the importance of live performances and his experience at church in Seattle, he discusses the utterly private experience and the music that we all shared in the air. These words are the essence of a live performance. One will not feel this connection when viewing or listening to a recorded performance. Live performances have always and will continue to blow the mind of their audience.