# BLACK SCHOLES MERTON ASSIGNMENT HELP

## What is Black Scholes Merton Assignment Help Services Online?

Black-Scholes-Merton assignment help services online are specialized academic assistance services that provide support to students studying finance or related fields who need help with assignments related to the Black-Scholes-Merton (BSM) model. The BSM model is a mathematical formula used to estimate the theoretical price of European-style options, which are financial derivatives commonly used in stock markets and other financial markets.

The Black-Scholes-Merton model, named after its developers Fischer Black, Myron Scholes, and Robert Merton, is a widely used model in quantitative finance. It takes into account various factors such as the current stock price, the option’s strike price, the time to expiration, the volatility of the stock price, and the risk-free interest rate to calculate the fair value of options. However, the mathematical calculations involved in the BSM model can be complex and require a deep understanding of financial concepts and mathematical techniques.

Black-Scholes-Merton assignment help services online provide assistance to students who may struggle with understanding the underlying concepts and calculations involved in the BSM model. These services typically offer expert guidance, step-by-step explanations, and examples to help students grasp the key concepts and apply them to their assignments. They also ensure that the assignments are plagiarism-free, meaning that the work provided is original and not copied from any other source.

Using Black-Scholes-Merton assignment help services online can be beneficial for students who want to improve their understanding of the BSM model, enhance their analytical skills, and achieve better grades in their assignments. However, it’s important for students to use these services responsibly, as they are meant to be supplementary to their own learning and should not be used as a substitute for independent study and effort.

## Various Topics or Fundamentals Covered in Black Scholes Merton Assignment

The Black-Scholes-Merton model, commonly known as the Black-Scholes model, is a widely used mathematical model for pricing options, which are financial derivatives that give the holder the right, but not the obligation, to buy or sell an underlying asset at a specified price within a certain period of time. When working on a Black-Scholes-Merton assignment, there are several fundamental topics that are typically covered. These topics include:

Option Pricing Theory: The Black-Scholes-Merton model is based on the concept of option pricing theory, which involves using mathematical equations to estimate the fair value of an option. This theory is fundamental to understanding how options are priced and how the Black-Scholes-Merton model works.

Option Greeks: The Black-Scholes-Merton model incorporates various factors that affect the price of an option, which are commonly referred to as “Greeks.” These Greeks include delta, gamma, theta, vega, and rho, and they represent the sensitivity of the option price to changes in the underlying asset price, time decay, volatility, and interest rates. Understanding the concept of option Greeks and how they are used in the Black-Scholes-Merton model is essential in comprehending how different factors affect option prices.

Black-Scholes-Merton Equation: The Black-Scholes-Merton model is based on a partial differential equation known as the Black-Scholes-Merton equation. This equation is a mathematical representation of the relationship between the price of the option, the price of the underlying asset, time, and other relevant parameters. An understanding of the Black-Scholes-Merton equation and how it is used to derive option prices is crucial in working with the model.

Assumptions of the Black-Scholes-Merton Model: The Black-Scholes-Merton model is based on a set of assumptions, including the assumption of a continuous and frictionless market, constant volatility, and no dividends on the underlying asset. Understanding these assumptions and their implications is vital in interpreting the results obtained from the Black-Scholes-Merton model.

Sensitivity Analysis: Sensitivity analysis is a crucial aspect of working with the Black-Scholes-Merton model. It involves analyzing how changes in various parameters, such as the underlying asset price, volatility, time to expiration, and interest rates, impact the price of the option. Sensitivity analysis allows for a better understanding of the risks and uncertainties associated with options and helps in making informed investment decisions.

Applications of the Black-Scholes-Merton Model: The Black-Scholes-Merton model has numerous applications in finance and investment management. These applications include option pricing, risk management, and portfolio optimization. Understanding the practical applications of the Black-Scholes-Merton model is important in comprehending its relevance in the financial industry.

In conclusion, a Black-Scholes-Merton assignment typically covers various fundamental topics, including option pricing theory, option Greeks, the Black-Scholes-Merton equation, assumptions of the model, sensitivity analysis, and applications of the model. A solid understanding of these topics is crucial in comprehending the Black-Scholes-Merton model and its applications in finance and investment management. It is important to ensure that any written work related to Black-Scholes-Merton is plagiarism-free and properly cited to acknowledge the original sources of information.

## Explanation of Black Scholes Merton Assignment with the help of General Motors by showing all formulas

Black-Scholes-Merton (BSM) is a mathematical model used to calculate the theoretical price of European-style options, which are financial derivatives that give the owner the right, but not the obligation, to buy or sell an underlying asset at a predetermined price (strike price) on a specified date (expiration date). Let’s explore how BSM can be applied to General Motors (GM) to determine the price of options.

The BSM model involves several key formulas:

Black-Scholes Option Pricing Formula: This formula calculates the theoretical price of a call option, which gives the owner the right to buy the underlying asset. The formula is as follows:

C = SN(d1) – Xe^(-r*t)*N(d2)

Where:

C = Theoretical price of the call option

S = Current stock price of GM

X = Strike price of the option

r = Risk-free interest rate

t = Time until expiration of the option

N(d1) and N(d2) = Cumulative distribution function of standard normal distribution

d1 = (ln(S/X) + (r + (σ^2)/2)t) / (σsqrt(t))

d2 = d1 – σ*sqrt(t)

σ = Volatility of GM’s stock price

Put-Call Parity Formula: This formula relates the prices of call and put options with the stock price and risk-free interest rate. It is used to calculate the theoretical price of a put option, which gives the owner the right to sell the underlying asset. The formula is as follows:

P = Xe^(-rt)N(-d2) – SN(-d1)

Where:

P = Theoretical price of the put option

S, X, r, t, N(d1), and N(d2) are the same as in the call option formula

-d1 and -d2 = Negative values of d1 and d2 from the call option formula

Now let’s consider an example of how BSM can be applied to GM. Suppose GM’s current stock price (S) is \$50, the strike price (X) of the call option is \$55, the risk-free interest rate (r) is 3%, the time until expiration (t) is 6 months, and the volatility (σ) of GM’s stock price is 20%.

Using the formulas mentioned above, we can calculate the theoretical price of the call option (C) and put option (P) as follows:

Call Option:

d1 = (ln(50/55) + (0.03 + (0.2^2)/2)0.5) / (0.2sqrt(0.5))

d2 = d1 – 0.2sqrt(0.5)

N(d1) = 0.331

N(d2) = 0.266

C = 500.331 – 55e^(-0.030.5)*0.266

C = \$1.67

Put Option:

-d1 = -0.331

-d2 = -0.266

N(-d1) = 0.169

N(-d2) = 0.366

P = 55e^(-0.030.5)0.366 – 500.169

P = \$3.16

Therefore, the theoretical price of the call option for GM is \$1.67 and the theoretical price of the put option is \$3.16.

Based on these calculations, an investor can use the BSM model to make decisions regarding buying or selling options on GM stock. For example, if an investor believes that GM’s stock price will increase in the future, they may decide to buy a call option at the calculated theoretical price of \$1.67 to potentially profit from the expected price increase. On the other hand, if an investor expects GM’s stock price to decrease, they may decide to sell a put option at the calculated theoretical price of \$3.16 to potentially benefit from the expected price decrease.

It’s important to note that the BSM model has some assumptions, including that stock prices follow a log-normal distribution, there are no transaction costs or taxes, and the risk-free interest rate and volatility remain constant throughout the option’s life. In reality, these assumptions may not always hold true, and actual option prices may deviate from the calculated theoretical prices.

Furthermore, it’s crucial to consider other factors such as market conditions, company-specific news, and overall risk tolerance when making investment decisions. The BSM model is just one tool among many used in option pricing, and it’s essential to conduct comprehensive research and analysis before making any investment decisions.

In conclusion, the Black-Scholes-Merton (BSM) model is a widely used mathematical formula to calculate the theoretical prices of options, including call and put options, based on various inputs such as stock price, strike price, risk-free interest rate, time until expiration, and volatility. By applying the BSM model to General Motors (GM), investors can estimate the theoretical prices of options and make informed investment decisions. However, it’s essential to consider the model’s assumptions, market conditions, and other factors before making any investment decisions.

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