Question

Post by Day 3 a 3- to 6-paragraph comparison of the Black-Scholes and Binomial Tree option pricing models. Make sure to include responses to the following specific questions:

(1) What are the distinct advantages and disadvantages of each model? List 2–3 advantages and disadvantages for each.

(2) Who might use one model over the other more often? (Suggest specific users, such as banks, speculators, hedge fund managers, etc.).

(3) Why do you think that the selected preferred users of each model make such choice(s)?

Clearly address each of the questions with 1–2 paragraphs. Make sure you use APA style for your response(s) and properly cite any resources you have used.

Answer 1

Black Scholes Model

The black scholes model is a model to determine the fair prices of options. An option is an instrument which derives its price based on the price of an underlying asset.

The value of an option is based on six variables:

1. Whether the option is a call or a put
2. Current underlying stock price
3. Time left under the option’s expiration
4. Strike price of the option
5. Volatility of the stock
6. Risk free rate

It makes an assumption that stock prices follow a lognormal distribution since asset prices cannot be negative. An assumption is made that there are no transaction costs or taxes.

Advantages:

1. Speed: It calculates the prices of a large number of options in very less time.
2. Simplicity: The model is simple and only requires the input of the variables to determine the option price.

Disadvantages:

1. It cannot accurately price an American style option. This is because it only calculates the option price at one point in time- at expiration.
2. The model makes several assumptions that are not true in reality.
3. The model does not take account of transaction costs, dividends and taxes.
4. The market is assumed to be complete which is not true in case of some options like weather options.

Users of Black Scholes model:

1. Option traders
2. Large companies. They prefer to use black scholes to determine the prices of options to using other methods like the binomial model for its simplicity.

Binomial Tree Option Pricing Model

The binomial tree option-pricing model is used for determining the prices of options. It uses a binomial distribution to calculate the price of an option. It assumes that the price of an option can only increase or decrease with time until the option expires. It is based on the assumption of no arbitrage.

Advantages:

1. Simplicity: It is quite easy to use the binomial model.
2. It is used for valuing American style options in which the option can be exercised at any time before expiration.

Disadvantages:

1. The model is very slow in speed. The complexity in computing increases in multi period binomial models.
2. Trading times are not discrete times. Trading goes on continuously.
3. The model is complex and requires a vast amount of time.

Users of Binomial tree option model:

1. Option traders for option pricing.

I hope that was helpful :)