What are the types of pricing models?
- The Binomial Model:
There are two main models used in the Australian market for pricing equity options: the binomial model and the Black Scholes model. For most traders these two models will give accurate results. The binomial option-pricing model was first proposed by Cox, Ross and Rubinstein in a paper published in 1979. This solution to pricing as an option is probably the most common model used for equity calls.
The model divides the time to an option’s expiry into a large number of intervals, or steps. At each interval it calculates that the stock price will move either up or down with a given probability and also by an amount calculated with reference to the stock’s volatility, the time to expiry and the risk free interest rate. A binomial distribution of prices for the underlying stock or index is thus produced.
On expiry the option values for each possible stock price are known as they are equal to their intrinsic values. The model then works backwards through each time interval, calculating the value of the option at each step. At the point where a dividend is paid (or other capital adjustment made) the model takes this into account. The final step is at the current time and stock price, where the current theoretical fair value of the option is calculated.
2. The Black Scholes Model:
First proposed by Black and Scholes in a paper published in 1973, this analytical solution to pricing a European option on a non-dividend paying asset formed the foundation for much theory in derivatives finance. The Black Scholes formula is a continuous time analogue of the binomial model.
The Black Scholes formula uses the pricing inputs to analytically produce a theoretical fair value for an option. The model has many variations that attempt, with varying levels of accuracy, to incorporate dividends and American style exercise conditions. However, with computing power these days the binomial solution is more widely used.