Call Option Strategies     a continuation of Part II

Here's what we'll do:

  1. Assume a Return R = 0.10 (meaning 10%) and Standard Deviation S = 0.25 (meaning 25%) for some stock.
  2. Assume we're interested in some strategy (Bull Spread? Butterfly? Condor?) involving Call Options
    which expire in N = 180 days.
  3. We calculate the losing range of stock prices: the range of stock prices where we lose money.
  4. With these three parameters (R, S and N) - and some assumption concerning the distribution of returns (normal? lognormal?) - we create a probability distribution for the stock prices after N days (at expiry).
  5. From this distribution of prices (at expiry of our Option) we determine the probability that the
    stock price lies in the losing range.
  6. We change the strategy (Bull Spread? Butterfly? Condor?) and keep our eye on the Probability of Losing.
>Example, please.
Okay. Suppose the distribution of prices, at expiry, is as shown in Fig. 1 and suppose, further, that stock prices below $27 will cause us to lose money.
From this Cumulative Distribution chart
note that stock prices will be in this losing range 29% of the time.
So, we'll go through some popular strategies

Bull Spread, Butterfly and Condor: See Option stuff

and see what the probabilities are, for success ...

Figure 1

>And the probability of losing, eh?
Yes, and in particular ...

>Go for it!

Okay, here's a picture (Fig. 2) with a Bull Spread:

  • The stock currently trades at $100.
  • We Buy a Call with a Strike Price of $95 and pay $11.65.
  • We Write an (uncovered) Call with Strike at $105 and receive $7.10. So far we've paid an initial cost of $11.65 - $7.10 = $4.55.
  • If the stock price is $99.55 we exercise our option (receiving a $99.55 stock for $95) thereby making $99.55 - $95.00 = $4.55 which exactly covers our initial cost.
  • We stare at the pertinent cumulative distribution and note that this Break Even price will be attained 38% of the time.
  • We conclude that, 38% of the time, we will lose money.
Figure 2

>You invented the option premiums, the $11.65 and $7.10?
Well, I'm assuming a 10% Annual Return, a 20% Standard Deviation, a 4% Risk-free Rate, 200 days to expiration and I've used Black-Scholes and ...
>And the distribution?
I've assumed a Normal distribution and ...
>Is that valid? I mean, doesn't Black-Scholes assume a Log-normal distribution?
Well ... yes, but I'm trying to demonstrate the idea of superimposing the Gain/Loss chart (for a Bull Spread, for example) with some Cumulative Distribution so that we can identify some probability of a loss.
>Why not assume a Log-normal distribution?
Yes, we could do that, but remember that everybody stares at Black-Scholes when trading in options so we accept Black-Scholes when calculating the option premium but we can assume any distribution we like for the future distribution of stock prices. It could be Normal or Log-normal or something else.
>And the probability is 38% ... for a Bull Spread?
Of course, not! It depends upon so many parameters. For example, if the Standard Deviation is increased to 25% and the time-to-expiry decreased to 100 days (and we keep the Normal distribution) we'd get a higher probability of loss ... like so:

>I assume those "Gains" are for 100-share contracts?
Yes and ...
>Do you have a spreadsheet to do all this?
Uh ... give me some time ... but the spreadsheet will probably look like this with an explanation which looks like this.

>Can I try it?
Sure ... such as it is!

Just RIGHT-click here and select "Save Target".

See also more on Call Options and Black-Scholes.