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Anup Menon

IN the purest sense, trading is a gamble, more so in the derivative markets. For instance an option price is derived from the movement of the underlying asset, which by itself is a random process. There are several strategies that one can use to profit from option trading.

Those who are willing to absorb a considerable amount of risk can consider selling naked calls or puts. Traders who are, to some extent, risk averse can consider writing covered calls. But all these positions involve a certain risk that the position would go against the traders. Is there something that can be done about this? Can investors protect themselves to some extent when being short in the options market? The answer is yes.

Success in trading depends on probabilities. Taking a view on how the underlying asset moves and the accuracy of the view determines the final pay off to the trader. The development of option pricing models assumes certain statistical properties that the underlying asset price should follow. To be a successful trader it helps to understand the likelihood of the stock moving in the direction it is expected to. This is where a basic understanding of probability theory might help.

The log normal distribution has been cited in literature as being one among the better distributions to model asset prices. Intuitively the natural logarithm of the return series is expected to follow a normal (Gaussian) distribution.

The distribution has some interesting properties. A look at the graph of the normal curve will give us some interesting insights. The probabilities are highest at the mean values of the distribution. Further as we move away from the mean, the probabilities are lower. Further the curve is symmetrical on either side. This means that there is an equal chance of the event moving either way. While this is the basic idea, what does this have to do with options?

Options and probabilities

Lets take a real-life example. One of the factors that all traders look is the returns and the risk factor in stocks when an investment is made. Take the case of the Sensex. On an average, we know that the sensex will move around `x' points in a day. It is very rarely that we may see movement to the scale of "x+y" where y is significantly above the historical standard deviation. Therefore, this conforms to the normal distribution then the probability of the sensex moving in and around the mean values will be much higher.

Therefore, consider options on the Sensex. Lets say that we have a host of OTM options and they are OTM by the range of x%, y%, z% and so on. The pricing of the options and the probability of the underlying asset moving jointly determine the probability of the trade being successful. For instance assume that the Sensex is at 3000. You have to choose from different options with strikes of say 3020, 3030, 3040 and 3050, all calls. Now as the strike increases the premium comes down. Therefore the 3050 calls will be priced lower than the 3030 calls.

Now assume the case of the write of the option. The question is whether he wants to write the 3030 calls or the 3050 calls. Obviously writing the 3050 calls will be less risky. But the 3030 calls is more profitable. Now using the probabilities he can determine whether it is worth taking the risk of writing the 3030 calls as against the 3050 calls. The significance of assessing the probabilities is more important when writing naked positions as the risks are higher. But there are several questions when using probabilities

Implementation

The first thing that comes to mind is implementation. For a small trader how easy is it to implement such models. Spreadsheets are armed with functions that can help calculate the probabilities. In terms of data, all that is required is stock prices and options data, which is available. Therefore implementing these models is not difficult.

Validity

The validity of the probabilities is even more questionable than implementation. In noisy processes (such as what we see in stock prices), where volatilities are very high, the normal distribution might not be the best of distributions to characterize the market. But it is the easiest to use. This increases the comfort level for small investors.

But ultimately irrespective of the model used, in the long run, the probabilities do add up.

(The author is a Research Scholar and Graduate Student with the department of Agricultural Economics at Kansas State University. Feedback is invited to amenon@agecon.ksu.edu)

If you have any queries relating to the futures/options markets and strategies that can be used in these markets, please mail them to Futures & Options, Kasturi & sons, 859-860, Anna Salai, Chennai 600 002 or email them to vaidy@thehindu.co.in with a mention of futures/options in the subject line of the mail.

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