In this appendix we provide a very brief description of how VBA functions are

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1 Option Pricing Models and Volatility Using Excel VBA By Fabrice Douglas Rouah and Gregory Vainberg Copyright 2007 by Fabrice Douglas Rouah and Gregory Vainberg APPENDIX A A VBA Primer In this appendix we provide a very brief description of how VBA functions are written with the VBA editor. The VBA editor is accessed under the Tools menu in Excel, by selecting Macro, and then Visual Basic Editor, or simply by pressing ALT and F11. The first step to writing VBA code is to insert a VBA module by selecting Module from the Insert menu. A VBA function always begins with the declaration statement Function and always ends with the statement End Function. The Function statement includes all parameters that are passed to the function. Funct i on SumNum( a, b) SumNum = a + b To use the function in Excel, the function name is typed into any cell, preceded by an equal sign ( ). Hence, in any cell we type =SumNum(5,4), which produces 9. If the numbers are in, say, cells A1 and A2, then we type =SumNum(A1,A2). Using built-in functions in Excel requires that the function name be preceded by Application. Hence, the built-in Sum function in Excel could be used, so that the function would be Funct i on SumNum2( a) SumNum = Appl i cat i on. Sum( a) If the numbers that need to be summed are in cells A1:A5, then in any cell we type =SumNum(A1:A5). SumNum2(A1:A5) It is sometimes useful to create VBA functions to apply built-in functions, to save space. The following function returns the standard normal cumulative distribution function: Funct i on Gauss( X) Gauss = Appl i cat i on. Nor msdi st ( X) 404

2 A VBA Primer 405 If there are many such Excel functions to invoke within the VBA function, we could use the With Application statement and precede each function with a period. Funct i on Gauss( X) Wi t h Appl i cat i on Gauss =. Nor msdi st ( X) End Wi t h Parameters can also be text strings, in which case the parameter name must be followed by As String in the function declaration. This is used often in the option pricing formulas, to incorporate the call and put price into a single function, as is the case with the BlackScholes() function. Funct i on Bl ackschol es( S, K, r, T, v, Put Cal l As St r i ng) d = ( Log( S / K) + T * ( r * v ^ 2) ) / ( v * Sqr ( T) ) bs_cal l = S * Gauss( d) - Exp( - r * T) * K * Gauss( d - v * Sqr ( T) ) I f Put Cal l = " Cal l " Then Bl ackschol es = bs_cal l El sei f Put Cal l = " Put " Then Bl ackschol es = bs_cal l - S + K * Exp( - r * T) Instead of the If-ElseIf-EndIf statements, we could use the Select statement, which is better than nesting If statements when there are many cases to choose from Sel ect Case Put Cal l Case " Cal l " Bl ackschol es = bs_cal l Case " Put " Bl ackschol es = bs_cal l - S + K * Exp( - r * T) End Sel ect Iterative processing in VBA is done analogously to other programming languages. The For loop, for example, processes a loop a given number of times. Funct i on Repeat ( n) For i = 1 To n MsgBox " I t er at i on Number i s " & i The iteration can also be run backwards from i n to i 1. This is accomplished with the Step statement, which specifies a step size of 1inthisexample: Funct i on Repeat 2( n) For i = n To 1 St ep - 1 MsgBox " I t er at i on Number i s " & i

3 406 A VBA PRIMER In both functions, the statements could both be changed to Next. When there are multiple loops nested within one another, however, including the looping variable with the Next statement makes the code easier to read. The Do-While loop executes a loop until a certain condition is met. The BisMet() function of Chapter 1, for example, finds the root of a function using a Do-While loop. The Do-While loop continues the bisection algorithm until a tolerance of EPS is met. Funct i on Bi smet ( f name As St r i ng, a, b) EPS = I f ( Run( f name, a) < Run( f name, b) ) Then tmp = b b = a a = t mp Do Whi l e ( Run( f name, a) - Run( f name, b) > EPS) mi dpt = ( b + a) / 2 I f Run( f name, mi dpt ) < 0 Then b = mi dpt El se a = mi dpt Loop Bi smet = ( b + a) / 2 Sometimes the VBA function needs to return an array of numbers rather than just a single value. In this case, it is convenient to define an array within VBA and assign the function value to the array name once the array is filled with the values to output. In this example, terminal values from the CRR binomial tree of Chapter 3 are transferred to the array Out(). The dimensions of an array are set by the Dim statement, and can later be redimensioned using the ReDim statement. When using the ReDim statement, the values contained in the array can be preserved using the Preserve option. The Option Base 1 statement sets the first element of the arrayto be indexed as 1 instead of as 0. The latter value is the default value, but in our opinion it is more intuitive to index array elements starting with 1. Opt i on Base 1 Funct i on CRRTr ee( Spot, T, si gma, n) dt = T / n u = Exp( si gma * ( dt ^ 0. 5) ) d = 1 / u p = ( Exp( r * dt ) - d) / ( u - d) Di m S( ) As Doubl e, Out ( ) As Doubl e ReDi m S( n + 1, n + 1) As Doubl e ReDi m Out ( n + 1) As Doubl e For j = i To n + 1 S( i, j ) = Spot * u ^ ( j - i ) * d ^ ( i - 1) I f j = n + 1 Then Out ( i ) = S( i, j )

4 A VBA Primer 407 FIGURE A.1 The CRR Binomial Tree CRRTr ee = Appl i cat i on. Tr anspose( Out ) The Out() array produces a row vector, so the array must be transposed if the terminal prices are to be outputted as a column vector. To output the n 1terminal values, we must use the combination of the keys SHIFT, CTRL, and ENTER. This is illustrated with the Excel file Appendix and Figure A.1 below, using a spot price of S 100, a time to maturity of T 0 5 years, an annual volatility of 0 30, and n 5steps. In cell E4, we type CRRTree(C4,C5,C6,C7) and press ENTER, which produces the terminal price S(1, n 1) Next, since n 1 6 cells are needed for the output, we highlight cells E4:E9, press F2 (EDIT), and then CTRL-SHIFT-ENTER simultaneously. To output the entire tree values, it is convenient to Dim the Out() array as Variant, so that blank values can be outputted to cells where there is no price (the lower diagonal of the array), rather than zeros. The output is achieved in the second loop. Funct i on CRRTr ee2( Spot, T, si gma, n) dt = T / n u = Exp( si gma * ( dt ^ 0. 5) )

5 408 A VBA PRIMER d = 1 / u p = ( Exp( r * dt ) - d) / ( u - d) Di m S( ) As Doubl e, Out ( ) As Var i ant ReDi m S( n + 1, n + 1) As Doubl e ReDi m Out ( n + 1, n + 1) As Var i ant For j = i To n + 1 S( i, j ) = Spot * u ^ ( j - i ) * d ^ ( i - 1) For j = 1 To n + 1 I f j >= i Then Out ( i, j ) = S( i, j ) El se Out ( i, j ) = " " CRRTr ee2 = Out Referring to Figure A.1, to output the entire CRR binomial tree in cell C13 we type CRRTree2(C4,C5,C6,C7) and press ENTER, which produces S(1, 1) 100. Since a six-by-six array is needed for the output, we highlight cells C13:H18, press F2, and press CTRL-SHIFT- ENTER simultaneously. If a tree with more steps is required, we change the value of n 1 in cell C7, and we select a larger number of cells to highlight.

3. (1.0 point) To quickly switch to the Visual Basic Editor, press on your keyboard. a. Esc + F1 b. Ctrl + F7 c. Alt + F11 d.

3. (1.0 point) To quickly switch to the Visual Basic Editor, press on your keyboard. a. Esc + F1 b. Ctrl + F7 c. Alt + F11 d. Excel Tutorial 12 1. (1.0 point) Excel macros are written in the programming language. a. Perl b. JavaScript c. HTML d. VBA 2. (1.0 point) To edit a VBA macro, you need to use the Visual Basic. a. Manager