Reference no: EM131307035
Binomial Trees and Black-Scholes-Merton Model
The goal of the project is to explore the topics of binomial trees and the Black-Scholes-Merton model. Project requires to work in Excel with the provided spreadsheet.
Fill in the yellow boxes in the Excel file. In addition, type up a report in Word with an introduction (description of the mini project), findings (answer assignment questions, plots, etc.), and conclusion (summary).
Binomial Trees and Black-Scholes-Merton Model
Part 1: One-Step Binomial Tree
A stock price is currently $50. It is known that at the end of six months it will be either $60 or $42. The risk-free rate of interest with continuous compounding is 12% per annum. Calculate the value of a six-month European call option on the stock with an exercise price of $48.
A) Calculate/list the values of K, u, d, r, Δt, and p.
B) Calculate the value of the call option.
Part 2: Two-Step Binomial Tree
A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding.
C) Calculate the values of K, u, d, r, Δt, and p.
D) What is the value of a six-month European put option with a strike price of $42?
E) What is the value of a six-month American put option with a strike price of $42?
Part 3: Black-Scholes-Merton Model a European call option on a non-dividend paying stock. The current price of the stock underlying the option is $42. The strike price of the option is $40. The risk-free rate is 10% per year. The volatility is 20% per year. The option expires in 6 months.
F) Fill in the table for the variables needed to apply the Black-Scholes-Merton model. Calculate d1 and d2. Be sure to use excel function to calculate the natural log, square root, and exponential terms. Calculate N(d1) and N(d2) using the excel function "=normsdist". Calculate the price of the call option.
G) Fill in the tables and create a plot of strike price vs. option price, risk-free rate vs. option price, volatility vs. option price, and time to expiration vs. option price. Comment on the relation between the variable and call option price for each plot in your report.
See https://support.office.com/en-us/article/MAX-function-e0012414-9ac8-4b34-9a47-73e662c08098 for more information on the Excel Max function. To keep a cell constant in a formula reference, apply a dollar sign before and after the letter in the reference (e.g., $A$20).
Attachment:- Project-.rar
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