## Learning Roadmap – Monte Carlo Simulation

If you would like to jump directly to the Monte Carlo master training reference please see Monte Carlo Simulations – How to reference.  In addition to the master reference, we have also included links to the following Monte Carlo Simulation Training Courses:

a) Using Monte Carlo Simulation to price Exotic Options
b) Tweaking and Hacking Monte Carlo Simulation for more robust results.

The first focuses on application of Monte Carlo Simulation in Option pricing. The second suggests solutions for addressing the normality assumption challenge by replacing the normal distribution with the historical distribution.  Click on any of the images to jump to the relevant course pages.

Courses linked to the first three images are free.

### Option pricing using Monte Carlo Simulation

Exotic Option pricing using Monte Carlo Simulation

The Derivative and Option pricing package guide includes the following EXCEL files:

a. The supporting excel file for the alternate binomial tree methodology for the products mentioned above

b. Option pricing using the Traditional Binomial Tree approach

c. Option pricing using the Black-Scholes option pricing formula

d. Ladder call option priced using Monte Carlo simulation in EXCEL (standalone Excel file)

e. Derivative Pricing using Monte Carlo Simulation  EXCEL file calculates the option prices for a number of vanilla and exotic options including Asian, Barrier, Lookback & Chooser Options.  The “Exotic Option Pricing using Monte Carlo Simulation” EXCEL file calculates option prices  using Monte Carlo Simulation:

1.  Vanilla European Call and Put options are priced for model calibration and tweaking
2. Out of Money Call and Put options are priced to compared cost savings between vanilla and exotic option contracts
3. Asian Call and Put options that replace the terminal price with the average of prices across the simulated path,
4. Look-back Call option are priced to simulate maximum payoffs
5. Barrier or Sudden Death Call option which has both in and out barriers above and below the strike,
6. Ladder Call option with two rungs (high water marks) in addition to the original strike, and
7. Chooser options which allow the owner to choose between a 9-month call or put option three months down the line.

## Monte Carlo Simulation & risk exposure for fuel oil hedging

The fuel oil hedging is two cases rolled up in one. The first deals with the question of fuel expense volatility for an airline (easily extendable to logistics and supply chain businesses). The second deals with the inventory write down issues faced by refineries on fuel stock and processed supplied in storage and in pipelines.

Monte Carlo Simulation – Fuel hedging example and illustration

## My love affair with Monte Carlo Simulation – Switching out the Normal Distribution

A simulation is an experiment, and a MC simulator may be considered a machine that can churn out a series of experiments. The simulator will behave in a certain fashion (i.e. produce symmetric, asymmetric, normal and skewed, with thin tails or long fat tails) depending on the tool used to build the machine (i.e. the choice of distribution). By definition it will always be inaccurate and an approximation to the real world.

EXCEL files:

The basic Monte Carlo Simulation course package has now been updated to include:

1. Simulated prices generated using Black Schole’s Terminal Price formula St=S0*exp[(r-q-0.5?2)t+??tzt]
2. Random numbers, zts, obtained by normally scaling Excel’s RAND() function NORMINV(RAND())
3. A path of prices, St, for 10 time steps, up to and including the Terminal price, ST
4. Terminal Prices for 25 different scenarios using Excel’s DATA Table functionality
5. Average Terminal Price across the 25 scenarios

What are the prerequisites?

### What are some applications of Monte Carlo simulations that I will learn about in this course?

In the next stage we consider Monte Carlo simulation applications: