John Hull Derivatives

Strengths and weaknesses of the binomial and Black and Scholes pricing models and their applications:

Introduction:

The binomial model and the Black and Schole option valuation models are the binomial model is to value the options using a tree as the format in which the value of the option is determined by the time of expiration of the option and the volatility for the Black and Schole model of option value is determined simply by obtaining a derivative that helps to obtain discount rate options.

binomial pricing model:

The binomial pricing model was presented by Ross, Cox and Rubinstein in 1979, but it provides a numerical method, in which the evaluation of options can be undertaken.

Application:

This model decomposes the option of many possible outcomes during the period of the option, these steps form a tree like format where the model assumes that the option value will increase or decrease, this value is computed and is determined by the date of expiration and volatility. Finally, at the end of the shaft of the option value is determined final possible because the value is equal to the intrinsic value.

Assumed

• The model also assumes that the market is effective because people can not predict the direction of change in stock prices.
• Interest rates are constant and known, and therefore they do not change over time we consider as an option.
• The model assumes that no dividends paid during the period when we consider the option.
• The model assumes that the returns on stocks are normally distributed.
• It also assumes that no commission is paid on the purchase or sale of shares.

Strengths:

• This evaluation method is simple mathematics and therefore it is used in integrated software for the evaluation of options making it easy to use the model.
• This model is considered more accurate than the Black Schole, it is considered more accurate especially when evaluating options for a long period of time.
• The binomial model solves an option using a calculation method, so that black and solves Schole the same option, using a method of analysis. Therefore, the binomial method is much easier to use.

Weaknesses

• The binomial model is too slow compared to the Black-Scholes model and takes much longer to calculate using the options on this model.

The Black-Scholes model:

The Black-Scholes model was introduced by Fisher Black and Myron Scholes in the year 1973, this model involves calculation of a derivative that helps show how the discount rate for different options vary with time and share price at the same time.

Application:

The black and Schole involves calculating a theoretical price for ignoring the presence of dividends and the value of options is determined by the share price, volatility, expiration period and interest rates.

Model:

C = SN (d1) - Ke (-rt) N (d2)

When C is the premium

S is the current share price

T is the period under study

K is the option striking price

R is the risk of lower interest

N is the cumulative normal distribution

E is the exponential

The model can be divided into two parts and where the first step is SN (d1) is the expected benefits and the second part is Ke (-rt) N (d2) is the present value of the value paid to the expiry time of the option.

Assumed

• The model assumes that no dividends paid during the period when we consider the option.
• The model also.