Call Option Strategies a continuation of
Here's what we'll do:
- Assume a Return R = 0.10 (meaning 10%) and Standard Deviation S = 0.25
(meaning 25%) for some stock.
- Assume we're interested in some strategy (Bull Spread? Butterfly? Condor?) involving
which expire in N = 180 days.
- We calculate the losing range of stock prices: the range of stock prices
where we lose money.
- 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).
- From this distribution of prices (at expiry of our Option) we determine the probability that
stock price lies in the losing range.
- We change the strategy (Bull Spread? Butterfly? Condor?)
and keep our eye on the Probability of Losing.
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.
>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.
>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
with an explanation which looks like
>Can I try it?
Sure ... such as it is!
RIGHT-click here and select
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