Financial Engineering: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=219
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 30 Jun 2016 12:16:04 GMTThu, 30 Jun 2016 12:16:04 GMTNew applications in the Financial Engineering categoryhttp://www.mapleprimes.com/images/mapleapps.gifFinancial Engineering: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=219
Local Volatility and Implied Volatility
http://www.maplesoft.com/applications/view.aspx?SID=4878&ref=Feed
This application explores two different methods of exploring financial data. The first example examines fitting an implied volatility surface based on data from S&P 500 call options. The second computes option prices and models the local volatility for simulated market data.<img src="/view.aspx?si=4878/volatility.png" alt="Local Volatility and Implied Volatility" align="left"/>This application explores two different methods of exploring financial data. The first example examines fitting an implied volatility surface based on data from S&P 500 call options. The second computes option prices and models the local volatility for simulated market data.4878Wed, 11 May 2016 04:00:00 ZMaplesoftMaplesoftPortfolio Optimization with the Omega Ratio
http://www.maplesoft.com/applications/view.aspx?SID=153994&ref=Feed
Traditional investment performance benchmarks, like the Sharpe Ratio, approximate the returns distribution with mean and standard deviation. This, however, assumes the distribution is normal. Many modern investments vehicles, like hedge funds, display fat tails, and skew and kurtosis in the returns distribution. Hence, they cannot be adequately benchmarked with traditional approaches.
<BR><BR>
One solution, proposed by Shadwick and Keating in 2002 is the Omega Ratio. This divides the returns distribution into two halves the area below a target return, and the above a target return. The Omega Ratio is simply the former divided by the latter. A higher value is better.
<BR><BR>
This application finds the asset weights that maximize the Omega Ratio of a portfolio of ten investments, given their simulated monthly returns and a target return.
<BR><BR>
This is a non-convex problem, and requires global optimizers for a rigorous solution. However, a transformation of the variables (only valid for Omega Ratios of over 1) converts the optimization into a linear program.
<BR><BR>
This application implements both approaches, the former using Maple's Global Optimization Toolbox, and the latter using Maple's linear programming features. For the data set provided in this application, both approaches give comparable results.<img src="/view.aspx?si=153994/omega_ratio.png" alt="Portfolio Optimization with the Omega Ratio" align="left"/>Traditional investment performance benchmarks, like the Sharpe Ratio, approximate the returns distribution with mean and standard deviation. This, however, assumes the distribution is normal. Many modern investments vehicles, like hedge funds, display fat tails, and skew and kurtosis in the returns distribution. Hence, they cannot be adequately benchmarked with traditional approaches.
<BR><BR>
One solution, proposed by Shadwick and Keating in 2002 is the Omega Ratio. This divides the returns distribution into two halves the area below a target return, and the above a target return. The Omega Ratio is simply the former divided by the latter. A higher value is better.
<BR><BR>
This application finds the asset weights that maximize the Omega Ratio of a portfolio of ten investments, given their simulated monthly returns and a target return.
<BR><BR>
This is a non-convex problem, and requires global optimizers for a rigorous solution. However, a transformation of the variables (only valid for Omega Ratios of over 1) converts the optimization into a linear program.
<BR><BR>
This application implements both approaches, the former using Maple's Global Optimization Toolbox, and the latter using Maple's linear programming features. For the data set provided in this application, both approaches give comparable results.153994Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanDrawdown of Historical Stock Prices
http://www.maplesoft.com/applications/view.aspx?SID=153992&ref=Feed
The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.
<BR><BR>
This application:
<UL>
<LI>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol,
<LI>defines a procedure that calculates the drawdown of the historical stock price,
<LI>and plots the drawdown against the adjusted close price of the asset.
</UL>
By changing the ticker and the dates, you can examine drawdown of any stock between your chosen dates.<img src="/view.aspx?si=153992/Drawdown.png" alt="Drawdown of Historical Stock Prices" align="left"/>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.
<BR><BR>
This application:
<UL>
<LI>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol,
<LI>defines a procedure that calculates the drawdown of the historical stock price,
<LI>and plots the drawdown against the adjusted close price of the asset.
</UL>
By changing the ticker and the dates, you can examine drawdown of any stock between your chosen dates.153992Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanDownloading Stock Prices and Plotting Returns Distributions
http://www.maplesoft.com/applications/view.aspx?SID=153991&ref=Feed
This application:
<UL>
<LI>downloads historical stock prices from Yahoo Finance,
<LI>calculates the returns,
<LI>plots the distribution of the returns in a histogram,
<LI>and overlays a normal distribution with the same mean and standard deviation as the historical data.
</UL><img src="/view.aspx?si=153991/Stock_Prices.png" alt="Downloading Stock Prices and Plotting Returns Distributions" align="left"/>This application:
<UL>
<LI>downloads historical stock prices from Yahoo Finance,
<LI>calculates the returns,
<LI>plots the distribution of the returns in a histogram,
<LI>and overlays a normal distribution with the same mean and standard deviation as the historical data.
</UL>153991Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanIs a Stock Overvalued or Undervalued?
http://www.maplesoft.com/applications/view.aspx?SID=153993&ref=Feed
This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.
<BR><BR>
Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.
<BR><BR>
The stock is undervalued if the fair value is greater than the current market price, and vice-versa.
<BR><BR>
This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols.<img src="/view.aspx?si=153993/stock_overvalued.png" alt="Is a Stock Overvalued or Undervalued?" align="left"/>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.
<BR><BR>
Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.
<BR><BR>
The stock is undervalued if the fair value is greater than the current market price, and vice-versa.
<BR><BR>
This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols.153993Wed, 02 Mar 2016 05:00:00 ZSamir KhanSamir KhanIs a Stock Overvalued or Undervalued?
http://www.maplesoft.com/applications/view.aspx?SID=153740&ref=Feed
<p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p><img src="/view.aspx?si=153740/stockovervalued.png" alt="Is a Stock Overvalued or Undervalued?" align="left"/><p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p>153740Tue, 20 Jan 2015 05:00:00 ZSamir KhanSamir KhanDrawdown of Historical Stock Prices
http://www.maplesoft.com/applications/view.aspx?SID=153624&ref=Feed
<p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p><img src="/view.aspx?si=153624/2def9a8f2111f9b47d0bee568aed6035.gif" alt="Drawdown of Historical Stock Prices" align="left"/><p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p>153624Mon, 07 Jul 2014 04:00:00 ZSamir KhanSamir KhanDownloading Stock Prices and Plotting Returns Distributions
http://www.maplesoft.com/applications/view.aspx?SID=153539&ref=Feed
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance,</li>
<li>calculates the returns,</li>
<li>plots the distribution of the returns in a histogram,</li>
<li>and overlays a normal distribution with the same mean and standard deviation as the historical data.</li>
<li>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL straight into a matrix using <span ><a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</li>
</ul><img src="/view.aspx?si=153539/stockreturns.png" alt="Downloading Stock Prices and Plotting Returns Distributions" align="left"/><p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance,</li>
<li>calculates the returns,</li>
<li>plots the distribution of the returns in a histogram,</li>
<li>and overlays a normal distribution with the same mean and standard deviation as the historical data.</li>
<li>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL straight into a matrix using <span ><a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</li>
</ul>153539Thu, 03 Apr 2014 04:00:00 ZSamir KhanSamir KhanThe Greeks
http://www.maplesoft.com/applications/view.aspx?SID=153533&ref=Feed
<p>In mathematical finance, The Greeks are measurements of risk that are used to represent the sensitivity of the price of a derivative to underlying variables, such as time-value decay and the implied volatility or price of the underlying asset.<br /><br /></p>
<p>This application calculates the Greeks for a European call or put option using the Black-Scholes model.</p><img src="/view.aspx?si=153533/TheGreeks.png" alt="The Greeks" align="left"/><p>In mathematical finance, The Greeks are measurements of risk that are used to represent the sensitivity of the price of a derivative to underlying variables, such as time-value decay and the implied volatility or price of the underlying asset.<br /><br /></p>
<p>This application calculates the Greeks for a European call or put option using the Black-Scholes model.</p>153533Mon, 24 Mar 2014 04:00:00 ZDaniel SkoogDaniel SkoogJump-diffusion stochastic processes with Maple
http://www.maplesoft.com/applications/view.aspx?SID=153516&ref=Feed
<p>The application presents and definition, creation and handling of jump-diffusion processes. In general, jump-diffusion is an extension to the theory of stochastic processes where the underlying parameters exhibit shocks and "jump" to their new values. Stochasticity with jumps is well recognised in several scientific branches including physics, chemistry, biology, but also economic and finance. The application looks at the example of the last-mentioned fields where the theory of jump-diffusions has been particularly actively researched and applied.</p><img src="/view.aspx?si=153516/Jump_image1.jpg" alt="Jump-diffusion stochastic processes with Maple" align="left"/><p>The application presents and definition, creation and handling of jump-diffusion processes. In general, jump-diffusion is an extension to the theory of stochastic processes where the underlying parameters exhibit shocks and "jump" to their new values. Stochasticity with jumps is well recognised in several scientific branches including physics, chemistry, biology, but also economic and finance. The application looks at the example of the last-mentioned fields where the theory of jump-diffusions has been particularly actively researched and applied.</p>153516Sat, 08 Mar 2014 05:00:00 ZIgor HlivkaIgor HlivkaCar Loan Calculator
http://www.maplesoft.com/applications/view.aspx?SID=145174&ref=Feed
<p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Car Loan Calculator" align="left"/><p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p>145174Wed, 27 Mar 2013 04:00:00 ZZinan WangZinan WangPricing European Call Options with FFTs
http://www.maplesoft.com/applications/view.aspx?SID=144589&ref=Feed
<p>This application compares the price of a European call option with FFTs (using the approach outlined by Carr & Madan in <em>Option Pricing Using the Fast Fourier Transform</em>) and the analytical approach. The application uses the efficient FFT function offered by Maple 17’s new <a href="/products/maple/new_features/signal_processing.aspx">Signal Processing tools</a>.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Pricing European Call Options with FFTs" align="left"/><p>This application compares the price of a European call option with FFTs (using the approach outlined by Carr & Madan in <em>Option Pricing Using the Fast Fourier Transform</em>) and the analytical approach. The application uses the efficient FFT function offered by Maple 17’s new <a href="/products/maple/new_features/signal_processing.aspx">Signal Processing tools</a>.</p>144589Wed, 13 Mar 2013 04:00:00 ZSamir KhanSamir KhanPortfolio Optimization with the Omega Ratio
http://www.maplesoft.com/applications/view.aspx?SID=140702&ref=Feed
<P>This application finds the asset weights that maximize the Omega Ratio of a portfolio of ten investments, given their simulated monthly returns and a target return. This is a non-convex problem, and requires global optimizers for a rigorous solution. However, a transformation of the variables (only valid for Omega Ratios of over 1) converts the optimization into a linear program.<P>This application implements both approaches, the former using Maple's <A HREF="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</A>, and the latter using Maple's <A HREF="/support/help/AddOns/view.aspx?path=Tour/opt1">linear programming</A> features. For the data set provided in this application, both approaches give comparable results.<img src="/view.aspx?si=140702/140702_thumb.jpg" alt="Portfolio Optimization with the Omega Ratio" align="left"/><P>This application finds the asset weights that maximize the Omega Ratio of a portfolio of ten investments, given their simulated monthly returns and a target return. This is a non-convex problem, and requires global optimizers for a rigorous solution. However, a transformation of the variables (only valid for Omega Ratios of over 1) converts the optimization into a linear program.<P>This application implements both approaches, the former using Maple's <A HREF="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</A>, and the latter using Maple's <A HREF="/support/help/AddOns/view.aspx?path=Tour/opt1">linear programming</A> features. For the data set provided in this application, both approaches give comparable results.140702Thu, 22 Nov 2012 05:00:00 ZSamir KhanSamir KhanGreat Expectations
http://www.maplesoft.com/applications/view.aspx?SID=127116&ref=Feed
<p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p><img src="/view.aspx?si=127116/expectation_thum.png" alt="Great Expectations" align="left"/><p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p>127116Thu, 27 Oct 2011 04:00:00 ZFinancial Modeling in Maple
http://www.maplesoft.com/applications/view.aspx?SID=103793&ref=Feed
The Finance package is new in Maple 15. It contains many tools for advanced financial modeling, as well as accessible tools for personal finance. On the personal finance side, there are tools that can be used for computing with mortgages or retirement packages. The financial modeling tools include a wide range of stochastic processes that can be used to model option prices, such as Brownian motion, Ito processes, an SVJJ process, and more. It also includes tools to compose complex processes out of these building blocks. You can also create, manipulate, and analyze many types of financial instruments, such as American, Bermudan, and European options and swaptions and several types of bonds; short rate models; term structures of interest rates; and cash flows. The instruments can then be priced using analytic methods, lattice methods or Monte Carlo simulation - all using one of many date arithmetic conventions. Finally, the processes occurring in the package can be visualized in several ways.<img src="/view.aspx?si=103793/thumb.jpg" alt="Financial Modeling in Maple" align="left"/>The Finance package is new in Maple 15. It contains many tools for advanced financial modeling, as well as accessible tools for personal finance. On the personal finance side, there are tools that can be used for computing with mortgages or retirement packages. The financial modeling tools include a wide range of stochastic processes that can be used to model option prices, such as Brownian motion, Ito processes, an SVJJ process, and more. It also includes tools to compose complex processes out of these building blocks. You can also create, manipulate, and analyze many types of financial instruments, such as American, Bermudan, and European options and swaptions and several types of bonds; short rate models; term structures of interest rates; and cash flows. The instruments can then be priced using analytic methods, lattice methods or Monte Carlo simulation - all using one of many date arithmetic conventions. Finally, the processes occurring in the package can be visualized in several ways.103793Wed, 06 Apr 2011 04:00:00 ZMaplesoftMaplesoftAn Interactive Stock Quote Importer
http://www.maplesoft.com/applications/view.aspx?SID=103805&ref=Feed
Financial engineers and quantitative analysts often exploit network services to retrieve stock quotes. A large number of services exist, including paid-for real-time feeds from Bloomberg and Reuters. Yahoo, however, provide a free service that is delayed by fifteen minutes.
The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application
provides text fields for specifying up to five ticker symbols,
allows the user to pick those quantities they want to import with check boxes,
summarises the data in a table,
assigns the values to variables for further processing and analysis.<img src="/view.aspx?si=103805/thumb.jpg" alt="An Interactive Stock Quote Importer" align="left"/>Financial engineers and quantitative analysts often exploit network services to retrieve stock quotes. A large number of services exist, including paid-for real-time feeds from Bloomberg and Reuters. Yahoo, however, provide a free service that is delayed by fifteen minutes.
The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application
provides text fields for specifying up to five ticker symbols,
allows the user to pick those quantities they want to import with check boxes,
summarises the data in a table,
assigns the values to variables for further processing and analysis.103805Wed, 06 Apr 2011 04:00:00 ZMaplesoftMaplesoftCopula function in multivariate dependency analysis
http://www.maplesoft.com/applications/view.aspx?SID=100528&ref=Feed
<p>Copula is a constructor function for multivariate distribution from univariate marginals. It is a method to link univariate samples, not necessarily from identical distributions, into joint multivariate distributions. In this way, copulas are more generic and flexible functions to study dependency arising from multivariate distributions.</p>
<p>Conceptually, copulas are based on transformation of the underlying marginal into new derived variable with uniform distribution. Consequently, any multivariate distribution can be expressed in the form of copula function. If each marginal is continuous then copula is unique. Sklar in 1959 was the first to point this out.</p>
<p>Copulas represent a broad set of functions and they generally differ by (i) number of dependency factors and (ii) construction complexity. The choose of copula depends on the nature of the multivariate study and fitting objectives to an underlying data.</p><img src="/view.aspx?si=100528/maple_icon.jpg" alt="Copula function in multivariate dependency analysis" align="left"/><p>Copula is a constructor function for multivariate distribution from univariate marginals. It is a method to link univariate samples, not necessarily from identical distributions, into joint multivariate distributions. In this way, copulas are more generic and flexible functions to study dependency arising from multivariate distributions.</p>
<p>Conceptually, copulas are based on transformation of the underlying marginal into new derived variable with uniform distribution. Consequently, any multivariate distribution can be expressed in the form of copula function. If each marginal is continuous then copula is unique. Sklar in 1959 was the first to point this out.</p>
<p>Copulas represent a broad set of functions and they generally differ by (i) number of dependency factors and (ii) construction complexity. The choose of copula depends on the nature of the multivariate study and fitting objectives to an underlying data.</p>100528Wed, 29 Dec 2010 05:00:00 ZI. HlivkaI. HlivkaGeneration of correlated random numbers
http://www.maplesoft.com/applications/view.aspx?SID=99806&ref=Feed
<p>This application is an extension of an earlier document on multivariate distributions and demonstrates how Maple can be used to generate random samples from such distribution. In a narrow sense, it presents the tool for generation of correlated samples. The sampling need for multi-factor random variables (RV) with a given correlation structure arises in many applications in economics, finance, but also in natural sciences such as genetics, physics etc. and here we show that such task can be accomplished with ease using Maple’s <em>Statistic</em>s and <em>Linear Algebra</em> packages.</p><img src="/view.aspx?si=99806/maple_icon.jpg" alt="Generation of correlated random numbers" align="left"/><p>This application is an extension of an earlier document on multivariate distributions and demonstrates how Maple can be used to generate random samples from such distribution. In a narrow sense, it presents the tool for generation of correlated samples. The sampling need for multi-factor random variables (RV) with a given correlation structure arises in many applications in economics, finance, but also in natural sciences such as genetics, physics etc. and here we show that such task can be accomplished with ease using Maple’s <em>Statistic</em>s and <em>Linear Algebra</em> packages.</p>99806Fri, 03 Dec 2010 05:00:00 ZI. HlivkaI. HlivkaMaple for Commodity Finance
http://www.maplesoft.com/applications/view.aspx?SID=35126&ref=Feed
<p>In this application we show how Maple can handle financial options models that have become popular in commodity finance. The financial trading of commodities has dramatically increased over past years as finance community started to look for non-standard instruments uncorrelated with the traditional financial products such as stocks, bonds, rates and currencies. Commodities, unlike their financial counterparts, require different approach to the process modeling: (i) commodities exhibit seasonality effects, (ii) commodity futures are exposed to many deformation modes, (iii) futures volatility is driven by the "Samuelson" effect that causes its drop as the expiry time shortens.</p><img src="/view.aspx?si=35126/thumb.jpg" alt="Maple for Commodity Finance" align="left"/><p>In this application we show how Maple can handle financial options models that have become popular in commodity finance. The financial trading of commodities has dramatically increased over past years as finance community started to look for non-standard instruments uncorrelated with the traditional financial products such as stocks, bonds, rates and currencies. Commodities, unlike their financial counterparts, require different approach to the process modeling: (i) commodities exhibit seasonality effects, (ii) commodity futures are exposed to many deformation modes, (iii) futures volatility is driven by the "Samuelson" effect that causes its drop as the expiry time shortens.</p>35126Mon, 01 Feb 2010 05:00:00 ZI. HlivkaI. HlivkaOptimal Portfolio Allocation and Economic Utility
http://www.maplesoft.com/applications/view.aspx?SID=4860&ref=Feed
<p>Show how the risk and reward set of a portfolio of two or three securities whose returns are jointly normally distributed is calculated from standard theorems about the mean and variance of linear combinations of the random variables. Use ideas from multivariable calculus to show how the feasible set is derived. Visualize the efficient frontier of the risk and reward set. Visualize the economic utility of the portfolio. Show how the concept of economic utility selects a unique optimal portfolio on the efficient frontier.</p><img src="/view.aspx?si=4860/thumb2.jpg" alt="Optimal Portfolio Allocation and Economic Utility" align="left"/><p>Show how the risk and reward set of a portfolio of two or three securities whose returns are jointly normally distributed is calculated from standard theorems about the mean and variance of linear combinations of the random variables. Use ideas from multivariable calculus to show how the feasible set is derived. Visualize the efficient frontier of the risk and reward set. Visualize the economic utility of the portfolio. Show how the concept of economic utility selects a unique optimal portfolio on the efficient frontier.</p>4860Mon, 14 Sep 2009 04:00:00 ZShengjie GuoShengjie Guo