User manual MATLAB FINANCIAL DERIVATIVES TOOLBOX

[. . . ] Financial Derivatives Toolbox For Use with MATLAB ® Computation Visualization Programming User's Guide Version 2 How to Contact The MathWorks: www. mathworks. com comp. soft-sys. matlab support@mathworks. com suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Web Newsgroup Technical support Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information Phone Fax Mail 508-647-7000 508-647-7001 The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Financial Derivatives Toolbox User's Guide COPYRIGHT 2000 - 2001 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] PriceTree is a tree structure with a vector of instrument prices at each node. Examples Price a portfolio containing two cash flow instruments paying interest annually over the four year period from January 1, 2000 to January 1, 2004. HJMTree contains the time and forward rate information needed to price the instruments. 4-41 cfbyhjm load deriv CFlowAmounts =[5 NaN 5. 5 105;5 0 6 105]; CFlowDates = [730852, NaN, 731582, 731947; 730852, 731217, 731582, 731947]; [Price, PriceTree] = cfbyhjm(HJMTree, CFlowAmounts, . . . CFlowDates, HJMTree. RateSpec. ValuationDate) Price = 96. 7805 97. 2188 PriceTree = FinObj: 'HJMPriceTree' tObs: [0 1. 00 2. 00 3. 00 4. 00] PBush: {1x5 cell} You can visualize the prices of the two cash flow instruments with the treeviewer function. treeviewer(PriceTree) See Also cfamounts, hjmprice, hjmtree, instcf 4-42 cfbyzero Purpose Syntax Arguments 4cfbyzero Price cash flows by a set of zero curves Price = cfbyzero(RateSpec, CFlowAmounts, CFlowDates, Settle, Basis) RateSpec A structure encapsulating the properties of an interest rate structure. Number of instruments (NINST) by maximum number of cash flows (MOSTCFS) matrix with entries listing cash flow amounts corresponding to each date in CFlowDates. If an instrument has fewer than MOSTCFS cash flows, the end of the row is padded with NaNs. NINST-by-MOSTCFS matrix of cash flow dates. Each entry CFlowAmounts CFlowDates contains the serial date of the corresponding cash flow in CFlowAmounts. Settle Basis Settlement date on which the cash flows are priced. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365. Description Price = cfbyzero(RateSpec, CFlowAmounts, CFlowDates, Settle, Basis) computes Price, an NINST-by-NUMCURVES matrix of cash flows prices. Each column arises from one of the zero curves. Examples Price a portfolio containing two cash flow instruments paying interest annually over the four year period from January 1, 2000 to January 1, 2004. ZeroRateSpec contains the interest rate information needed to price the instruments. load deriv CFlowAmounts =[5 NaN 5. 5 105;5 0 6 105]; CFlowDates = [730852, NaN, 731582, 731947; 730852, 731217, 731582, 731947]; Settle = 730486; 4-43 cfbyzero Price = cfbyzero(ZeroRateSpec, CFlowAmounts, CFlowDates, Settle) Price = 96. 7804 97. 2187 See Also bondbyzero, fixedbyzero, floatbyzero, swapbyzero 4-44 classfin Purpose Syntax 4classfin Create financial structure or return financial structure class name Obj = classfin(ClassName) Obj = classfin(Struct, ClassName) ClassName = classfin(Obj) ClassName Struct Obj Arguments String containing name of financial structure class. Name of a financial structure. Description Obj = classfin(ClassName) and Obj = classfin(Struct, ClassName) create a financial structure of class ClassName. ClassName = classfin(Obj) returns a string containing a financial structure's class name. Examples Example 1. (Typically, the function hjmtimespec is used to create HJMTimeSpec structures). TimeSpec = classfin('HJMTimeSpec'); TimeSpec. ValuationDate = datenum('Dec-10-1999'); TimeSpec. Maturity = datenum('Dec-10-2002'); TimeSpec. Compounding = 2; TimeSpec. Basis = 0; TimeSpec. EndMonthRule = 1; TimeSpec = FinObj: ValuationDate: Maturity: Compounding: Basis: EndMonthRule: 'HJMTimeSpec' 730464 731560 2 0 1 4-45 classfin Example 2. Convert an existing MATLAB structure into a financial structure. TSpec. ValuationDate = datenum('Dec-10-1999'); TSpec. Maturity = datenum('Dec-10-2002'); TSpec. Compounding = 2; TSpec. Basis = 0; TSpec. EndMonthRule = 0; TimeSpec = classfin(TSpec, 'HJMTimeSpec') TimeSpec = ValuationDate: Maturity: Compounding: Basis: EndMonthRule: FinObj: 730464 731560 2 0 0 'HJMTimeSpec' Example 3. Obtain a financial structure's class name. load deriv. mat ClassName = classfin(HJMTree) ClassName = HJMFwdTree See Also isafin 4-46 date2time Purpose Syntax Arguments 4date2time Fixed income time and frequency from dates [Times, F] = date2time(Settle, Maturity, Compounding, Basis, EndMonthRule) Settle Settlement date. Settle must be earlier than or equal to Maturity. Maturity Compounding Maturity date. Scalar value representing the rate at which the input zero rates were compounded when annualized. This argument determines the formula for the discount factors: Compounding = 1, 2, 3, 4, 6, 12 Disc = (1 + Z/F)^(-T), where F is the compounding frequency, Z is the zero rate, and T is the time in periodic units, e. g. Compounding = 365 Disc = (1 + Z/F)^(-T), where F is the number of days in the basis year and T is a number of days elapsed computed by basis. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month. Basis EndMonthRule 4-47 date2time Description [Times, F] = date2time(Settle, Dates, Compounding, Basis, EndMonthRule) computes time factors appropriate to compounded rate quotes between Settle and Maturity dates. [. . . ] A portfolio. A-3 A Glossary inverse discount - A factor by which the present value of an asset is multiplied to find its future value. The reciprocal of the discount factor. least squares method - A mathematical method of determining the best fit of a curve to a series of observations by choosing the curve that minimizes the sum of the squares of all deviations from the curve. option - A right to buy or sell specific securities or commodities at a stated price (exercise or strike price) within a specified time. per-dollar sensitivity - The dollar sensitivity divided by the corresponding instrument price. [. . . ]