question on BSM model

Baozi

Baozi

Hi all,

I am trying to calculate the expected value of an option at a certain point in time when the value of the underlying in that point is known.

I am looking for something that is not too intensive in terms of calculations because this formula would be part of a more complex function with thousands of iterations, therefore I decided to stick with the BSM model without going for any other fancy stuff. I have however a few doubts about the inputs. Any of the pros would like to help me out?

time > this one should be the DTE at the specific exit time/360, correct?
underlying & strike > no problems here
freerate & dividend > not knowing the rates is it ok just to use the rates at the entry point? The influence should be marginal, right?
IV> Can I use the forward volatility as per taleb's formula?

If you want to point out another (lightweight) model that I can use then free to let me know!
 
Baozi said:
time > this one should be the DTE at the specific exit time/360, correct?
More...

252, if you want to be exact.

Baozi said:
freerate & dividend > not knowing the rates is it ok just to use the rates at the entry point? The influence should be marginal, right?
More...

Risk free rate and dividend absolutely alter the pay off. The modifications are necessary (often times 3% is used as a baseline but you should adjust it to the actual rate). But you can probably project and/or guess here. Just know your expected value won't be robust against spikes and drops in these.

Baozi said:
IV> Can I use the forward volatility as per taleb's formula?
More...

As for IV this should also be forecasted, probably using something like GARCH(1, 1), EWA, etc. Since IV has a significant effect on the value of an option (especially of the ATM straddle), you will want this to be as accurate of a "guess" as possible.
 
BSBH.jpg
Buy a copy if you can find one - money well spent.
 
Strike: Agreed. No mystery there.

Underlying: Depends: If you are dealing with an index, you may be better off deriving this from the chains if you desire accuracy.

It would be wise to consider what precision will be adequate for your longer term goals.
BSM formulas typically expect the time input to be in years (use a real or double). Consider your desired finest resolution (60 second?, 5min?) Don't forget to account for the proper AM /PM expiry times.

interest free rate: For expirations less than 6 months away, the adjusted nearest term LIBOR rate is a fairly good fit. Longer durations may be better fit with other instrument. Shorter durations become less sensitive, so sticking with the LIBOR may be close enough.

Dividends: If you ignore dividends, you introduce error. There are clever techniques for dealing with Indexes like RUT / SPX to compensate.

IV: IMHO: the most critical input. (the most common flawed input) Best to think of this being your responsibility to provide the proper input value!
 
Baozi said:
time > this one should be the DTE at the specific exit time/360, correct?
More...
BSM sez "360:24:60:60" IIRC. Yes, "to the second."
But papers on the interwebs (from a variety of contexts) seemed split 50|50 about 5{?} years ago, when I was working up this detail myself.
In practice, I'm with gaussian: 252 is how I see the indexes behave, *mostly*. A lot of data sins (in theta) get washed away with a dose of bumpy vol. "Oops. :rolleyes:"

Baozi said:
freerate & dividend > not knowing the rates is it ok just to use the rates at the entry point? The influence should be marginal, right?
More...
Totally with you. A lot of places (including World Class Interactive Brokers) don't even quote rho. The BMS model (and its forbears) were developed when inflation was 2x-3x what it is now, and inflation was NOT stable. Thus, a "rho" needed to be there, and so it was. Now? It is, has been, and deserves to be, our lost vagrant BSM cousin.

stepandfetchit said:
IV: IMHO: the most critical input. (the most common flawed input) Best to think of this being your responsibility to provide the proper input value!
More...
Didn't someone mention Monte Carlo? Was that another thread? In any event, I would NOT trap myself into thinking that either my IV estimate, or my results and prospective trading agenda, matter a whit to the market. My practice is to take a fair guess, and then bracket that with 2σ or 3σ guesses on either side, and see how sensitive my intended path is. EASY to do, if you're setting it up beforehand. (And for that matter, you could run it through a table, and graph your own, true, Monte Carlo results. "Sweet!")
 
>> underlying & strike > no problems here

Not that simple. You should use the "forward" price instead of just the spot underlier price. If you get that right, you can ignore interest and dividend yield (set them to zero).
You need to derive the forward price from the option prices using the call-put parity.

IV> Can I use the forward volatility as per taleb's formula?

You need to use options's impled vol using the prices on the market. You know all the other parameters (including the crucial forward which you also derived from the prices), then you can do a bisection search for the volatility which matches the observed option price. Prefer the OTM option if it's got quotes, otherwise you can use the ITM option and call-put parity to compute the OTM price which you can further use to derive the implied vol.
 
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