1. Lectures 3 – Monte Carlo method in finance: Lab
The goals:
create a VBA package/framework to price exotic options via Monte Carlo method and its modifications (i.e. variance reduction techniques).
create an excel file to be used as a front end for pricing options.
11/22/2018

2. Lecture 3 – MC Lab: library design
Create separate modules, containing functions with similar goals (reading input, writing output, core Monte Carlo functions etc.).
Isolate contract dependent code in dedicated modules (e.g. one for plain vanilla, one for asian option etc.).
Make the code easily extensible
11/22/2018

3. Lecture 3 – MC Lab: Excel as a front end (I).
define sheets to manage Monte Carlo parameters (input):
scenario numbers (N)
flag for: activate antithetic sampling or control variates
define sheets to store market data (input)
Yield curves
Equity data (current stock price, dividends, volatility)
11/22/2018

4. Lecture 3 – MC Lab: Excel as a front end (II).
define sheets to store some general contract descriptions (input)
Fixing dates
define sheets to store specific contract descriptions (input) and option price (output). This sheet is strictly related to option typology
e.g. for plain vanilla option:
Strike price
Option sub-type (e.g. call or put)
Option price
11/22/2018

5. Lecture 3 – MC Lab: Excel as a front end (III).
define sheets to store equity path evolution (output)
printing the N paths generated by Monte Carlo (for debug only).
printing the pay-off for each path.
11/22/2018

6. Lecture 3 – MC Lab: VBA library (I).
Structures to manage:
Fixing: future fixing dates
Yield curve market data (rates for different maturities),
Equity market data: price, dividend yield and volatility.
Function to read from excel data to initialize the structures defined above.
11/22/2018

7. Lecture 3 – MC Lab: VBA library (II).
Core functions
Path generation
Compute option price (using pay-off function – see next slide)
Output functions
Printing path and pay-off
Printing statistics
11/22/2018

8. Lecture 3 – MC Lab: VBA library (III).
Structure and functions related to contract typology (e.g. plain vanilla, asian, reverse cliquet)
Structure containing specific contract characteristics
Function to read (initialize) structure from excel sheet
Function to write outputs: e.g. the option price
Function for pay-off computation along a specific path (it depends from contract typology!)
Remember: the Compute_price function must be customized in order to treat a new type of option (select case)
11/22/2018

9. Lecture 3 – MC Lab: VBA library organization (I).
For each of the above points we define a specific bas file:
Module_cons: constants definitions.
Module_struct: containing the structures definition
Module_read_struct: to read main structures
Module_core_functions: the core Monte Carlo functions (path generation and MC option pricing).
Module_output_functions: to manage the output
Module_util: utility functions
11/22/2018

10. Lecture 3 – MC Lab: VBA library organization (II).
Module_pv: containing structure and functions to manage plain vanilla options
Module_asian: containing structure and functions to manage asian options
Module_reverse_cliquet: containing structure and functions to manage reverse cliquet options
11/22/2018

11. Lecture 3 – MC Lab: Exercises
Ex. 1: verify that Monte Carlo error scales with N (the scenario’s number) as 1/sqrt(N). Suggestion: compute option prices with different values of N and plot the data in a log-log graph.
Ex. 2: within VBA library, implement the pay-off calculation for a reverse cliquet option and compute, via Monte Carlo simulation, its value.
Suggestion: take the following parameters values
H = 4%
L = 0%
M=12, i.e. twelve fixing dates (with delta_t = 1/12 year)
11/22/2018