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VBA
Q2 2012
Vincent JEANNIN – ESGF 4IFM

vinzjeannin@hotmail.com ESGF 4IFM Q2 2012
1

ESGF 4IFM Q2 2012
Summary of the session

• Introduction: from BASIC to VBA
• Think Algorithmic First: π
• First VBA Program: a formula

vinzjeannin@hotmail.com
• Alternatives to π estimation
• Formula using Excel References
• Advanced Formula: CRR

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Introduction: from BASIC to VBA
Beginner's All-purpose Symbolic Instruction Code

Created in 1964 by students for students

ESGF 4IFM Q2 2012
Spread because free

Succeed because easy and base to most of languages

If you’re old enough to know what is a 80-386 or to have played with an
Apple II you may have heard of: Applesoft BASIC, GW BASIC, QBASIC

BASIC extended to event driven programming: Visual BASIC
The flow of the program is determined by events: sensor
outputs, user actions (mouse clicks, key presses)…

Visual BASIC integrated in Microsoft Office: VBA
Visual BASIC for Applications enables building user defined 3
functions, automating processes,…

Think Algorithmic First: π

ESGF 4IFM Q2 2012
Let’s approximate pi

Think first about “How to” regardless of any programming

Draw a chart of the program then the “translation” is easier

4

Let’s pick 2 random numbers

Using a uniform distribution

ESGF 4IFM Q2 2012
How do you determine if (x,y) is inside or outside the circle?
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Right Triangle properties

ESGF 4IFM Q2 2012
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 2 = 𝐴𝑗𝑎𝑐𝑒𝑛𝑡 2 + 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 2
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Repeat Repeat

Generate x and y

ESGF 4IFM Q2 2012
Calculate the hypotenuse

Is the hypotenuse shorter than the radius?

Yes No

Count

7

Surface of the square: 1
𝜋
Surface of the circle:
4
𝜋
Surface of the rest: 1 −
4

ESGF 4IFM Q2 2012
Let’s make i trials, count the n points inside the circle

Randomisation has been done uniformly 8
𝑛
Proportions will be respected 𝜋≅
𝑖 ∗ 𝑅𝑎𝑑𝑖𝑢𝑠 2

First VBA Program: a formula
VBA can be sued to create custom Excel Functions

ESGF 4IFM Q2 2012
Display the Visual Basic Editor

Right Click on your file and insert a module

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Let’s call our function EstmPi

What are the arguments?

ESGF 4IFM Q2 2012
Only one argument

The number of simulations to make

Let’s call the variable Simu

Compulsory to define the type of variable

String: Text

Integer: Natural Number

Double: 64-bits number

Boolean: True/False 10

What type is Simu?

Basic structure of the function

ESGF 4IFM Q2 2012
Used in Excel

=EstmPi(100)

Result will be the value stored in the variable Result

Time to be reminded the algorithmic fundamentals of our
program and learn the corresponding BASIC functions
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Repeat Repeat

Generate x and y

ESGF 4IFM Q2 2012
For… To… Next Calculate the hypotenuse
or
Do While/Until… Loop


If… Then… Else… End If
Yes No

Count

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For… To… Next
Full syntax
For counter = start To end [Step step]
[statements]

ESGF 4IFM Q2 2012
Next [counter]

The program will repeat instructions a specified number of time

Step is optional and by default 1

For i = 1 To Variable
Example Variable2= Variable2+1
Next i
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Full syntax

Do [{While | Until} condition]
[statements]

ESGF 4IFM Q2 2012
Loop

The program will repeat instructions while or until a condition is met

Do {While | Until} Variable<>0
Example Variable= Variable-1
Loop

Careful to potentially endless loop

What if in the Do While case Variable is negative at the start of the loop?
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Full syntax
If condition Then
statements

ESGF 4IFM Q2 2012
[Else]
[statements]
End If
The program will launch instructions if condition is met

Else statements are optional

The program will lunch instructions if condition is not met if
Else is specified
The program won’t do anything if condition is not met if Else is
not specified
If Variable > 0 Then
Variable2=1
Variable3=-1 15
Example
Else
Variable= Variable+1
End If

Repeat Repeat

Generate x and y

ESGF 4IFM Q2 2012
For… To… Next Calculate the hypotenuse
or


Yes No

Count
For i=1 to Simu If Hypo<=Radius then
VariableCount= VariableCount+1
Next i End If 16
Could have use Do Until Variable=Simu…. Loop…
But manual increment needed of Variable

Reminder: basic structure of the function

ESGF 4IFM Q2 2012
We know we have to use For/Next and If/Then/End If

What do we miss?

Random number: Rnd command

We Should have everything

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Looping to numbers of simulations

Generate 2 random variables

ESGF 4IFM Q2 2012
Calculate the length of the hypotenuse

Is the hypotenuse inside the circle?

Yes: count it

No: Don’t count it

Simulation finished, percentage of points inside the circle

The square area being 1, knowing the radius, you can extract Pi

𝜋 ≅ 3.14159 18

From how many simulations the estimation is correct?

𝜋 ≅ 3.14159

ESGF 4IFM Q2 2012
Test in Excel =EstmPi (xxx) for a few different numbers of simulations
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Why for a same number of simulations your results are different?
From how many simulations the estimation is correct?

Alternatives to π estimation
Reminder of our function

ESGF 4IFM Q2 2012
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Let’s use Do While / Loop

Don’t forget to fix the initial value of the variable

Don’t forget to increment the variable (beware the endless loop)

ESGF 4IFM Q2 2012
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Let’s use Do Until/ Loop

Don’t forget to fix the initial value of the variable

Don’t forget to increment the variable (beware the endless loop)

ESGF 4IFM Q2 2012
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What you CAN do but what you MUST NOT do

ESGF 4IFM Q2 2012
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Bad algorithmic method

“Before going into detail of how to use the
GoTo statement it is important to be aware
that the use of the GoTo statement is generally
considered to be bad programming practice.”
John Walkenbach

ESGF 4IFM Q2 2012
The program has been led into a corner and some way of getting to
another section of code is needed

Bad programming indeed…

Most of the time avoidable if program written carefully

Avoiding GoTo statement make the code easier to debug
and maintain

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Spaghetti code

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Formula using Excel References
Let’s build a formula pricing a Black & Scholes Call option

ESGF 4IFM Q2 2012
5 or 6 arguments

Time to maturity Or Start Date – End Date

S

r

K

σ

26

ESGF 4IFM Q2 2012
Easy, no reason to have and loops or conditional tests

Problem… Thee Standard Normal Cumulative distribution
is not available in VBA (and it’s not an analytic linear
formula so can’t recreate it) 27

Basic structure

ESGF 4IFM Q2 2012
Time to maturity, d1 and d2 easy to compute

How to compute N(D1) and N(D2)?

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In Excel, it would be NORMSDIST function

Excel formula can be used in VBA with the following

ESGF 4IFM Q2 2012
Final part of the formula can then be written

Use it in Excel

=CallBS(D4,D8,D9,D5,D6,D7)
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Full Formula

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Advanced Formula: CRR
Let’s build a formula pricing a CRR Call option

ESGF 4IFM Q2 2012
Challenges

Build a tree with a variable number of nodes

Enables American or European type

7 or 8 arguments

Time to maturity Or Start Date – End Date σ

S n
31
r A/E

K

Program steps

ESGF 4IFM Q2 2012
Build the tree for the price of the underlying

Calculate the price of the option at maturity

Do the backward induction

Differentiate American & European

32

ESGF 4IFM Q2 2012
How many nodes do you have at any given step?

𝑛+1
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Asymmetric matrix

2 dimension variable

Must be defined and re dimensioned

ESGF 4IFM Q2 2012
Use Dim and ReDim
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Why +1?

Matrix won’t be fully filled

Compute T, u, d & p

𝜎 𝑡
1 𝑒 𝑟𝑡 − 𝑑
𝑢= 𝑒 𝑑 = = 𝑒 −𝜎 𝑡
𝑝=
𝑢 𝑢− 𝑑

ESGF 4IFM Q2 2012
Allocate S to the first node

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Our first double loop…

ESGF 4IFM Q2 2012
Times
current
step+1

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Times the number of steps

One For/Next inside the other

ESGF 4IFM Q2 2012
Construct the tree

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Let’s check…
Introduction to Subs

Display results in Excel

ESGF 4IFM Q2 2012
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Tree seems properly built

ESGF 4IFM Q2 2012
Back to our function

Time for the backward induction
39

Same principle

Two loops one inside the other

ESGF 4IFM Q2 2012
Negative Step on the columns

Backward induction

Specific case on the last node

Specific case ITM or OTM

Specific cases American or European 40

A few if structures inside the other?

Structure

Yes… Early exercise or not?

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42

Final (Initial) Node

Same process

ESGF 4IFM Q2 2012
Compare intrinsic to binomial value

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1/3
We’re finished!

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3/3

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2/3

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Use it in Excel

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Conclusion

ESGF 4IFM Q2 2012
Functions & Subs

If Then Else

For Next

Do Loop

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