# Monte Carlo Simulation

Monte Carlo Simulation Training Courses offered on FinanceTrainingCourse.com  include

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

The first focuses on application of Monte Carlo Simulation in Option pricing. The second is a more generalized how to reference that include applications for financial as well as industrial customers. The third and final suggests solutions for addressing the normality assumption challenge.  Click on any of the images to jump to the relevant course pages.

Enjoy.

## Option pricing using Monte Carlo Simulation

Exotic Option pricing using Monte Carlo Simulation

The Derivatives & Option Pricing Package Guide includes the following topics:

a. Brief overview of relative pricing, risk neutral probabilities and the risk free rate with a focus on binomial trees (the PDF Guide)

b. Binomial option pricing basics (PDF Guide)

c. An alternative method of implementing a two-dimensional binomial tree that allows the extension of a simple 3 step tree to a 50 – 100 step option pricing tree in a few minutes (PDF Guide)

d. Pricing of options using this alternate methodology (PDF Guide)

The Derivative and Option pricing package guide also 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.

• The methodology uses a Monte Carlo simulator to first generate a path of monthly prices for a one year period. For the chooser option, the Black Scholes option pricing formula is used together with the simulated price of the 3rd month, to estimate the price of a 9-month call/ put option.
• An antithetic price series is also generated for each simulation to increase the speed of convergence
• Payoffs and discount values for each option are determined for both the regular and antithetic MC simulated prices
• Values (both regular and antithetic) are stored in a data table containing 500 simulated runs
• Average premiums across all runs are calculated for both regular and antithetic scenarios
• The average between the regular and antithetic average premiums is taken to arrive at the simulated price of the option.

## Using Monte Carlo Simulation to determine risk exposure for fuel oil hedging

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