Lectures 3 – Monte Carlo method in finance: Lab

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.

2. Lecture 3 – MC Lab: library design 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

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)

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

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.

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.

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

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)

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

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. 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)