FAQs

I would like to implement a covered-call writing strategy. How can I use your software to identify which calls on the equities I own will give me the best return?

   Here's one suggestion. Try to fit parameters for the
SVJ (Stochastic volatility + jumps) model for the options on a particular stock that you own. To do this, try to imitate the procedures in the tutorial for the S&P500 example found under "II.3 Working with the Calculator". You might want to start with
those S&P500 parameters and make adjustments from there. (This is not necessarily easy and may take a while).
    Then, once you have some reasonable parameters, look for particular call options whose bids are at least equal to or higher than the model prices.
     Of course, all else equal, the total position (stock + options) will tend to have an expected return commensurate with its risk. That is, the expected return will be higher if the options are out-of-the-money vs. selling an in-the-money position.

What parameters should be entered in case the average absolute value jump is around 5%, but negative and positive jumps mostly compensate each other giving an average of around 0 ?

You enter

(1) for the jump volatility: sigJ = (0.05) Sqrt[Pi/2], which is approx. 0.063.
(2)for the mean jump: muJ = -(1/2) sigJ^2 , which is approx. -0.002

The reason the mean jump muJ parameter is not exactly zero is explained in the tutorial at page 11 (Converting logarithmic jump sizes to percentage jump sizes). These entries will show a percentage jump size of zero in the status bar (lower right).
For some other absolute value jump, replace the 0.05 term above by the other absolute value. These formulas are obtained by standard calculations with the normal distribution.

Is there a clear definition of a jump? (after all, the prices move by "ticks", so it seems that any (non minimal?) move can be considered a jump).

You're right -- with real price data, there is an ambiguity in deciding what's a jump. (With the underlying theoretical models, it's clear: jumps are discontinuous moves). This ambiguity is inescapable, but our suggestion is to concentrate on the jumps that represent, large, infrequent moves over a short time.

For example, with a very lengthy historical data set of, say daily prices on stock, you might want to define a jump as any move greater than 10% or, perhaps any move greater than 5 times the historical daily standard deviation.

I am exploring two different jump models with the calculator, one with 4 jumps per year with a mean jump of zero and jump vol. of 0.05, the other with 2 jumps per year with a mean jump of zero and jump vol. of 0.10. They seem to give very different option values. Is this right?

When exploring different jump models on a particular stock, it's important to keep the "Total long-run volatility" constant. This quantity is explained on p. 11 of the tutorial and displayed in the status bar (lower right of the calculator). To keep this value constant, adjust the first stochastic volatility parameter (sigL). Doing that, you will find that these two jump models are not too much different in terms of their option fair values.

Will you please clarify the use of the "Half Life Parm" parameter? The help document say it relates to the time it takes for the volatility to drift to its long-term value. Is the initial volatility (from which the volatility tends to drift towards its long term value) some theoretical volatility, or is it the current volatility? And if it's the current volatility, then what should be entered if the current volatility happens to equal the long term volatility?

The initial volatility is the current volatility (the entry at the end of the first row of parameters). The half-life parameter still has an effect, although it's a smaller one, when the current volatility equals the long-term volatility. That's because the calculator models account for the fact that, in between now and the option expiration, the current volatility will change.
    There are statistical methods that can help with parameter estimation. One of them is a general class of methods called GARCH, that can start with a long data series of daily prices on a stock and then estimate the (historical) half-life parameter, among other parameters. OptionCity may provide some tools for this, later on.
     Even with an advanced statistical tool, such as GARCH, the half-life parameter can be a difficult parameter to estimate. Values of 3 to 12 are typical, corresponding to half-lives of 1/3 year = (4 months) and 1/12 year (= 1 month). Another complication is that the risk-aversion of investors typically shifts this parameter to a lower number than the statistical one (thereby raising the values and implied volatilities of longer-dated options).
    We use 4 for the default value, corresponding to a half-life of 1/4 year (= 3 months), which is the quarterly earnings cycle. Intuitively, you are trying to answer the question: "if the volatility unexpectedly jumps way up or down", how long will it take to get (half-way) back to normal? This question makes sense even when today's volatility equals the long-term volatility. For a given stock, the answer may involve a lot of judgment. For the S&P 500 index, take a look

at the volatility chart to get a very rough sense of mean-reversion of volatility.