Option Tools

This gadget uses yahoo.com historical data, therefore symbols for indexes are non-standard.

S&P500 = ^gspc, RUT = ^rut, NDX = ^ ndx, NASD Comp = ^ixic, OEX = ^oex.

A word about volatility - Volatility for these purposes is defined as the annualized standard

deviation of the log of the returns. The assumption for options pricing and for these calculations

is that returns are log-normally distributed. In reality, stock returns only approximate the normal

distribution. Generally their distribution results in "fat tails", which means that prices have a higher

variance from the mean due to prices becoming over-bought or over-sold during extreme moves.

Normally distributed log returns implies that prices will be log-normally distributed. Prices are

log-normally distributed due to the upward bias in stock prices, and price return compounding.

Distribution of Returns -

The distribution of returns below is determined by calculating the daily returns over several years

of historical data and tabulating the data over the various % values. Each day's return is

"bucketized" into a range and the total number of each bucket is plotted. The graph of the

returns approximates the normal distribution. As can be seen by observing stocks with a

wide range of volatilities, those with a high volatility will have a larger dispersion of values

centered about the zero return point.

Enter a symbol in the textbox above to display the distribution of returns or the Normal Distribution

Curve graph. To change the volatility used in the calculations, click on the "volatility" button and

enter the volatility you want to use. Right click on the graph for more options.

The X axis scale is measured in % return. The distribution bar counts are normalized to the value of the

0% return bar. This allows for an easy comparison to a wide range of prices and returns.

How to calculate the Standard Deviation of a future price and the probability of

exceeding that price.

Enter a stock symbol in the text box below to get the current historical volatility and closing price.

Enter a future price and the number of calendar days in the future to calculate the probability of

exceeding that price. Click on "Calculate" to perform the calculation. The calculation is based on

the concept that stock prices follow a log-normal distribution over time. This means the probability

of the stock closing at the current price any time in the future is 50% and there is an equal chance of

closing above or below the current price.

Select the appropriate radio buttons to change the volatility or closing price, respectively.

Expected Value Calculator -

What is "Expected Value"? Expected value is a resulting value of a series of repeatable events

that you would expect to achieve based on the probabilities of the event occurring. As an example,

consider a coin toss, The probability of heads or tails showing is 50%. if you bet $1 for each

outcome of heads, and lost $1 for each outcome of tails, you would eventually expect to break

even, if you flip a coin many times. This is calculated by multiplying each probability by the profit

or loss and adding the results.

( probability of heads) * ( heads profit) + (probability of tails) * ( tails loss)

= (.5 * $1) + (.5 * -$1) = 0

Although it's possible to flip many heads in a row, if you flip it enough times you will eventually

break even. The only way to assure a profit is to have either a higher payout for a win, or a higher

probability of a win. In any game of chance, you need to have a positive expected value if you

want to make money.

Now let's apply this concept to options trading. Consider the below bear call credit spread. With the stock

trading at 24.71 we establish a short 26 call and a long 28 call with 43 days till expiration. We receive

a credit of $0.39 for the spread. With this spread, the break even price is 26.39. The max profit is $39 when the underlying is below 26 and the max loss is $161 when the price is above 28. Theprofit and loss between these strikes varies depend-ing on the stock price. Using the odds tool above we know that the probability of closing below 26 is 67.4% ( the probability of greater than 26 is 32.6 so the probability of less than 26 is 100 - 32.6). The probability of closing above 28 is 13.4%. In order to calculate the expected value we have to multiply the profit/loss by the respective probabilities. The calculation is easy below 26 and above 28, but between 26 and 28 the profit or loss varies with the price. In order to calculate the expected values between these 2 prices, we would have to divide the range into small intervals and calculate the probabilities and profits at those points. We then add up all the expected values

for the price ranges to get a total expected value. Putting the strike and prices into the application results in an

expected value of -0.11. This trade has a negative expected value and if we repeatedly executed this trade we

would lose money. Is it possible to make money on this trade? The answer is maybe. There are a lot of variables

that can change during the life of the trade. The volatilities (and therefore the probabilities of reaching any future

price) can change, or we can adjust the trade if it moves against us. Having a negative expected value alone

doesn't mean a losing trade, just as having a positive expected value doesn't guarantee a winning trade, but

starting out with a positive expected value gives us a statistical edge.

Option Pricing Calculator:

Calculate the fair value of an option. This gadget uses the Cox, Ross, Rubinstein

binomial tree pricing model. Max Time Steps = 2000.