In the options pricing methods we learned so far, a number of parameters are assumed to be constant: interest rates, strike prices, dividends, and volatility. Here, the parameter of interest is volatility. In quantitative research, the volatility ratio is used to forecast price trends.
To derive implied volatilities, we need to refer to Chapter 3, Nonlinearity in Finance where we discussed root-finding methods of nonlinear functions. We will use the bisection method of numerical procedures in our next example to create an implied volatility curve.
Let's consider the option data of the stock Apple (AAPL) gathered at the end of day on October 3, 2014, given in the following table. The option expires on December 20, 2014. The prices listed are the mid-points of the bid and ask prices:
|
Strike price |
Call price |
Put price |
|---|---|---|
|
75 |
30 |
0.16 |
|
80 |
24.55 |
0.32 |
|
85 |
20.1 |
0.6 |
|
90 |
15.37 |
1.22 |
|
92.5 |
10... |