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# chapter4/2 the significance of volatility

Chapter 4

#### The Significance of Volatility

We know the factors effecting the price of an option and a new set of definitions from reading Chapter 3. There are a handful of widely available mathematical models which compute the theoretical price of option given the five inputs: volatility, strike, term, interest rate, and dividend yield.

The strike, term, interest rate, and dividend yield are all fixed parameters. If these were the only factors used in computing option prices, then options for all stocks trading at the same price would have the same prices. Clearly, some stocks have a greater probability of changing in price and that probability has a direct impact on the option price. Historical changes in the price of the underlying stock are used to compute the Historical Volatility.

The historical volatility is the annualized standard deviation of price changes in the underlying stock. The result is a single measure of volatility that is applied across the stock's entire option chain. This should result in a very uniform distribution of option prices across the chain, since all options theoretically have the same volatility as the underlying stock, but prices rarely exhibit uniform pricing. One significant reason is the difference in supply and demand for different contracts on the same option chain. If there is more demand for a specific option contract, the cost of that contract will increase, regardless of the stock's volatility. This may make other contracts on the same chain appear relatively cheap, which may make certain trades, such as spreads, more desirable.

A method for identifying which options are trading at a relatively high premium is invaluable to the option trader. Simply comparing the prices of the option is not sufficient. Consider two call options with the same expiration date, one with a \$50 strike price and the other with a \$55 strike price. If the underlying stock is trading at \$53 and the options are trading at \$4.25 and \$1.75 respectively, which option is more expensive? The \$4.25 option is priced higher than the \$1.25 option, so it is more expensive right? But the \$4.25 option is in the money by \$3, and the time premium is only \$1.25. The \$1.75 option is out of the money and the time premium is \$1.75, therefore the \$1.75 option is more expensive, right? Not so fast.

The three factors that most significantly influence the option price are strike, term, and volatility. If the strike prices of the options and the expiration dates are fixed, then the only measure of the relative expense of the option is the volatility. An effective method of computing the relative expense of different options is to compute the implied volatility. The implied volatility is the measure of the likelihood that the underlying stock price will change based on the price of the option.

If the volatility represents how likely the underlying stock price will change, then all the options in the chain for the same stock will be priced using the same measure of volatility. In practice, this is not true. There are other factors that effect the trading price of an option. One of the more notable factors is supply and demand for the option and that can provide insight into supply and demand for the stock.

Spotting options with high premiums is not too difficult. Analyzing those options to determine sentiment towards the underlying stock is much more difficult. If calls are trading at a premium one might quickly assume that there is more demand for calls, and therefore there is a greater chance a stock will go up. But, because of put call parity, the price of a put will also rise in tandem with the call. If there is a simultaneous rise in the put and the call price, is the sentiment bullish or bearish? Another quick assumption might be to examine the volume. If the volume of calls is much greater than the volume of similar puts, then the activity must be in the calls, and therefore the sentiment is bullish. Again, not so fast...activity in an option simply means the contracts were traded. It is not apparent from published volumes and prices which side the initiator of the trade is on.

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