# Option Pricing using Monte Carlo Simulation – Course Outline

 The “Option Pricing using Monte Carlo Simulation” combines both theory and practice and uses model building and option pricing exercises as learning tools to tie in a number of essential topics such as:
• the difference between and the significance of the risk-adjusted probabilities of the Black Scholes option pricing model,
• the intuition behind the Black Scholes European call option formula,
• a preliminary overview of how to create a Monte Carlo simulation model of the Black Scholes solution in Excel,
• Estimating errors of and improving results generated from the Monte Carlo simulation model
• Pricing vanilla and exotic options using the Monte Carlo simulation model

The course splits the time evenly across 135 minutes between building a model step by step in EXCEL and working with the model to price and value derivative products.

# Course Prerequisites

Familiarity with derivative products and comfortable with basic mathematics, numbers and EXCEL.

# Course Audience

The course is targeted at intermediate and advance users and is aimed at professionals who deal with pricing, valuation and risk issues related to structured fixed income and foreign exchange transactions.

# Course Guide

Here is the structure of the course.

 Title Duration Session 1 – Black Scholes, N(d1) and N(d2), Monte Carlo Simulator – Theory and Model Review 37:16 mins Session 2 – Monte Carlo Simulator – Basic Model Walkthrough 10:39 mins Session 3 – Understanding N(d1) and N(d2) and Option Exercise using Monte Carlo 15:45 mins Session 4 – Building a Monte Carlo simulator – Foundations 28:37 mins Session 5 – Using data tables to store Monte Carlo simulation results 11:52 mins Session 6 – Estimating errors and improving results accuracy 18:46 mins Session 7 – Pricing Exotic Option using Monte Carlo 18:43 mins

### Session One – Black Scholes, N(d1) and N(d2), Monte Carlo Simulator – Theory and Model Review

The risk training course for understanding risk adjusted probabilities of the Black Scholes equation, N(d1) and N(d2), begins with a power point presentation of the theory setting the foundation for appreciating the difference between N(d1) and N(d2). We start with the Black Scholes European call option formula and move on to primary elements of the underlying process behind the generator function for stock prices, drift and diffusion. We address the concept of risk neutrality and conduct various thought experiments around drift and diffusion to understand their impacts on the plot of stock prices over time. We present three interpretations of the intuition behind the Black Scholes European call option formula and then given a preliminary overview of how to create a Monte Carlo simulation model of the Black Scholes solution in Excel.

View a sample of session one

### Session Two: Monte Carlo Simulator – Basic Model Walkthrough

In this part we move from our the theory presented in the power point presentation earlier to the practical application of the understanding the difference between N(d1) and N(d2). We given an overview of the Monte Carlo Simulation model built discussing the input cells including the price path generated, the results from the simulation model and the Black Scholes formula, and the results warehouse where results of 30 simulated runs of the model are stored.

A brief review of how the simulator can be used to generate and store results and how results could be updated by running multiple iterations.

View a sample of session two

### Session Three: Understanding N(d1) and N(d2) and Option Exercise using Monte Carlo

After having presented the theory behind the process and a general overview of the various elements of the Monte Carlo simulation model together with the procedure for running the model and updating results in our previous finance videos, we now give a thorough walkthrough of the EXCEL sheet of our Monte Carlo simulation model. We begin with how the results of the payment of exercise price and contingent receipt of stock components of the closed form Black Scholes European call option formula are calculated in the model. Each calculation cell is described in detail, stating precedent and dependent cells, to help with an understanding of:

• How the model is built,
• Difference between N(d1) & N(d2),
• Calculation of the call option value by using Black Scholes formula within the Monte Carlo simulation approach

View a sample of session three

### Session Four: Building a Monte Carlo simulator – Foundations

After reviewing the model in earlier session we finally start building the Monte Carlo simulation model for simulating the price path of an equity security and use that path to estimate the value of a call option, a put option and the probability N(d2) of the event ST > X. The session starts with a blank sheet and ends with 10 step simulator that can be used for pricing European call and put options.

Building a foundation for Monte Carlo model building with Vanilla options that is later extend to more exotic options. This video includes the procedure for generating:

• A randomly generated path of stock prices
• Average, minimum, maximum and terminal values for the stock price
• European call and put option payoffs and their respective premiums

View a sample of session four

### Session Five: Using data tables to store Monte Carlo simulation results

We start by storing results of MC iterations using EXCEL’s “Data Table” function. We then use the stored results to determine the probability of exercise, and values of the call and put options.We use data tables to store results from our option pricing Monte Carlo Simulator and review the sequence of steps required to extend the simulator to support multiple iterations.

View a sample of session five

### Session Six: Estimating errors and improving results accuracy

We look at the accuracy of results by comparing our Monte Carlo simulation model option prices with theoretical prices generated by the closed form Black Scholes formula. We introduce the concept of forecasting errors and the impact of increasing iterations on the accuracy and convergence of simulation results.

View a sample of session six

### Session Seven: Pricing Exotic Options using Monte Carlo

Now that we have a working Monte Carlo simulation model we extend it to price a number of exotic contracts such as Asian options, barrier options, binary options and lookback options. We take a quick look at the relationship between Vanilla Calls and

• Knock In and Knock Outs calls,
• Asset or nothing options and cash or nothing options
• Look back calls

The approach used here can be further extended to price contingent premium options, balloon exercise, participating forwards and other exotic contracts. Pricing for these contracts will be covered in later courses.

View a sample of session seven

## Random Testimonial

• ~ Corporate Training Testimonials

"A most amazing training - hands down the best, most useful, and most relevant I had during my tenure. Simply put, I loved it and will continue to build on the models.

Financial Modeling Course Participant
First Gulf Bank, Abu Dhabi, UAE

I have attended a number of training courses conducted by Alchemy technologies. Broadly, the areas covered have been Financial Risk Management aspects, Basel II implementation in Pakistan, as well as product knowledge for relatively new products in the our market for instance Financial Derivatives. As trainers, Mr. Jawwad Farid and his team bring in a wealth of conceptual knowledge entwined with their own professional experiences, adapting and honing it to our local market needs. The training courses are very informative and are delivered in a witty and energetic manner. The learning needs of the participants are kept in focus, and they are kept involved by interactive discussions and queries. Personally, I have always left these sessions with a much better understanding and grasp over the subjects delivered, which has helped me professionally.”

Senior Manager & Team Leader
Treasury Middle Office
Habib Bank Limited

“Jawwad Farid has admirably led the training piece on the Treasury side covering Treasury risk, Treausury products, Derivatives (basic & Advanced), Fixed income securities (Basic & Advanced) and ALM training modules. Jawwad in our opinion is an “Outstanding Senior Trainer” who has deep subject matter knowledge and an uncanny ability to keep the participants engaged in the training process. So far our clients have expressed maximum level of satisfaction in Jawwad’s capability to deliver high value training programs, that have tangibly enhanced their staff’s skill sets.

Based on our direct more than satisfactory experience, Jawwad’s otherwise exceptional track record on the training side with over 90 technical skill building courses in South Asia, Middle Eastern and Far Easterm markets, we have no hesitation in strongly recommending Jawwad Farid for the training that for participants based out of Malaysia or the adjoining Far Eastern Markets.”