# Monte Carlo Simulation - Package

#### About the Course

The course begins with a walkthrough of the construction of a basic simulator in EXCEL for stock prices. It discusses how the model may be extended for simulating currency rates and commodity prices and why it cannot be used for simulating interest rates. The similarities between the Monte Carlo simulation model, the Black Scholes model and the Binomial Tree Approach are considered.

Next, a hybrid model that randomly picks returns from the actual historical return distribution instead of using the normal distribution assumption that the original simulator utilizes is constructed and back testing is performed to compare the results with the original model.

Basic option terminology and the Black Scholes option pricing formula are reviewed before an in depth analysis of the Black Scholes model risk adjusted probabilities is conducted using a Monte Carlo simulator.

The Monte simulation model is then used in a variety of applications such as pricing vanilla and exotic options (including using convergence and variance reduction techniques to improve the accuracy of and time to convergence to the true results), calculating Value at Risk for derivative instruments, analyzing hedge effectiveness for fuel costs for the aviation industry, simulating interest rate term structure and forecasting monetary policy rates.

The course also consists of three EXCEL files that simulate the terminal price for a commodity, a currency and an equity respectively. The methodology used in these files is as follows:

- Simulating prices generated using Black Schole’s Terminal Price formula
- Deriving random numbers, zts, by normally scaling Excel’s RAND() function NORMINV(RAND())
- Generating a path of prices, St, for 10 time steps, up to and including the Terminal price, ST
- Data warehousing terminal prices for 25 different scenarios using Excel’s DATA Table functionality
- Averaging terminal price across the 25 scenarios to arrive at the result

#### Learning Objectives

After taking this course you will be able to:

- Construct a basic Monte Carlo simulator in EXCEL to determine possible future price paths for equities, commodities or currencies
- Build a hybrid Monte Carlo simulation model that uses the actual historical return distribution instead of the normal distribution assumption used in the original version
- Explain and analyze Black Scholes risk adjusted probabilities using a Monte Carlo simulation model
- Price vanilla and exotic options using a Monte Carlo simulation model
- Apply convergence and variance reduction techniques to improve the accuracy of Monte Carlo simulation results
- Calculate Value at Risk (VaR) for futures and options using the Monte Carlo simulation approach
- Calculate Value at Risk using the Monte Carlo simulation model that makes use of the actual historical return distribution and compare the result to results from the original Monte Carlo simulation and Historical Simulation VaR approaches
- Analyze the effectiveness of entering a hedging program for the aviation industry using Monte Carlo simulation
- Simulate the term structure of interest rates using the Cox-Ingersoll Ross (CIR) interest rate model & the Heath-Jarrow-Merton (HJM) multifactor interest rate model
- Forecast the monetary policy rate using a simplified Monte Carlo simulation model

#### Prerequisites

The candidate should have some familiarity with basic derivative products and their pricing and be comfortable with basic mathematics, statistics, probability and EXCEL.

#### Target Audience

The course is aimed at professionals who deal with pricing, valuation and risk issues related to structured fixed income and foreign exchange transactions, as well as individuals responsible for capital allocation, limit setting and risk management within banks, insurance companies, mutual funds, as well as finance departments of non-financial organizations.