Understanding N(d1) & N(d2) - EXCEL Example

About the Course

The course consists of an EXCEL file which is also the supporting EXCEL file to the “Understanding N(d1) and N(d2)” online course.

It derives the solution of the closed-form Black Scholes European call option price formula using a Monte Carlo Simulator. The purpose is to build an intuition of how the formula works, in particular, what the risk adjusted probabilities N(d1) and N(d2) mean.

The worksheet consists of three elements:

1. Inputs which are primarily inputs required for the Black Scholes formula, i.e. spot price, strike price, volatility, time to maturity, risk free rate; and the number of time-steps to be considered for the Monte Carlo simulator.

2. Outputs:

• True values of N(d1), N(d2) and call premium using the closed form Black Scholes formula
• Path dependent prices including terminal price generated using the MC simulator with a graphical representation of price path
• Logical test for terminal price exceeding strike price that returns one if the condition is met or zero if it is not, unconditional expected terminal price, conditional expected terminal price, minimum, maximum and average terminal price

3. Results warehouse to store the results for 30 simulated iterations including averages of outcomes across iterations for:

• Terminal price.
• Logical test, which gives the risk adjusted probability N(d2)
• Conditional terminal price given that it is greater than strike price
• SN(d1), which is the expected conditional term price times the probability that the terminal price is greater than the strike price times the present value factor, and
• Call premiums (i.e. discounted intrinsic value)

Learning Objectives

After taking this course you will be able to:

• Understand the intuition behind the Black Scholes European call option price formula and the related risk adjusted probabilities with the help of a Monte Carlo simulator
• Simulate the value of the option using this intuition and first principles

Prerequisites

The candidate should be comfortable with basic mathematics, statistics, probability and EXCEL.

Target Audience

This course is for beginners in the finance field.