Calculating Implied Volatility Implied volatility is possibly the most important concept in options trading. All traders should learn to calculate the implied volatility or know of websites which offer implied volatilities of the indices and individual stocks. One of the methods of calculating implied volatilities is described below. This calculator is a part of the options strategy evaluation Excel spreadsheet available at www.hoadley.com/options. For example, if we need to calculate the implied volatility of the Satyam 320 call option, the inputs required are: Ͱ Risk Free Rate: This can be the prevailing interest rates on bank deposits, annually 6%. Ͱ Dividends: These need to be included if it’s a dividend month. Generally options of stock which go ex-dividend in the current month should be avoided. Ͱ Option Type: Call Ͱ Option Market Price: This is available from the broker. Ͱ Strike Price: 320 Ͱ Value Date: It’s the date on which the valuation is being done. Ͱ Expiration Date: This is the date where the contracts in question expire. (The number of days to expiry is calculated automatically.) All dates need to be entered in the American date format which is mm/dd/yy. Once all the inputs are entered, you get the following output on your computer screen. Implied Volatility Calculator Risk Free Interest Rate: 6.00% Underlying Asset: Market price (Ͳ): 318.00 Dividends: Ex date Amount Or Continuous rate Option:
Option type: Option market price: 20 Strike price: 320.00 Value Date 5/7/04 Expiration date: 5/27/04 Days to expiration: 20 Pricing: Pricing model: Number of steps for binomial model: 100 Implied Volatility: 68.91% Now this implied volatility needs to be compared with the historical volatility in order determine if higher volatility is priced into the option than what is historically appropriate.
Appendix-III Using the Peter Hoadley Options Strategy Software This software can be used to test various strategies and construct profit diagrams. Below we will go through an example of a selling a straddle and how the software is used with this strategy. More help is available at www.hoadley.com/options. The software is available free of cost from the above site. There are a number of inputs which you need to change in the default screen. This should be done very carefully as a mistake here can spoil the calculation. Step 1 When you open the options strategy software, you see the first screen as shown below. We’ll consider the example of Nifty options for the purpose of this illustration.
Step 2 Now the inputs to this main screen need to be set up. This can be done by clicking on the underlying assets settings module. As you can see that the Nifty option is added at the end. The historical volatility of 17% is available at various websites with information on Indian derivatives and with some big brokers as well. Another change that is to be made here is the risk-free interest rate which we will change to 6%.
Step 3 The next step is changing the inputs on the main screen which are fairly simple with explanations on cells which are not immediately clear. Deal Details — This is a pulldown menu which will now show the new addition to the sample list. Stock Price — The prevailing stock price, or in this case the index value, i.e. 1800 is entered here. The deal date and the expiration date of the options are entered here. These dates are entered in the mm/dd/yy format. Price in the centrer of graph can be the price around which we would like to study the impact of the movement of underlying. This can vary from case to case. The graph increment can be adjusted to get maximum relevant movement on the graph. The option details are fed into action, buy/sell, number and strike cells. Now the next 3 entries are not used all the time but only when there is a particular situation: (i) Implied volatility needs be entered if it’s different from the volatility set up of the stock under the “underlying assets settings” sheet. (ii) Trade expiry date needs to be entered if it’s different from the deal expiry date, for example, in a calendar spread. (iii) Override price — Enter an option price here if it’s different from the option price calculated by the option model. In the case of Nifty they are and so those different prices are entered.
Right next to the foregoing screen is the profit diagram which shows profit/loss position on the deal date as well as at the expiry date.