volatility for use in bsm

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mlh97

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I'm putting together a black-scholes-merton option model for a private technology company. i'm trying to get to a good volatility number. does anyone have any suggestions?

as i look at the public comps, i get a volatility based on three years history or 63%. frank fabozzi in the handbook of fixed income securities that when pricing convertible debt, the volatility should be capped at 60% due to mean reversion. so, based on that, 60% seems to be a ceiling.

however, someone mentioned to me that if i'm looking at an option with a five-year life, i should use five years of history to calculate volatility. is this right? the volatility seems to me to be the bigest "art v. science" number out there, and if you don't believe the past doesn't represent the future, you could use a shorter time fram (especially since a five-year history puts you into the tech bust).

any thoughts would be appreciated.
 
forgive my ignorance (as i've just graduated)...what is the difference between the Black Scholes formula and your black-scholes-merton model?
 
Cut a sheet of paper into 100 pieces.

Number them from 1 to 100.

Fold each piece and then put them in a pot.

Shake the pot vigorously. (This step is important. If you miss this out then the model is violated.)

Close your eyes and pick a number from the pot.

Add the "%" symbol to the end of the number.

The end.
 
I would use implied vol on a similar option of a public comp long before I would do any historical volatility calculations and the calculation that says you should use 5 years of data to estimate 5-yr vol sounds fishy to me.

Is this for pricing a convert for a venture capital investment? There might be some important issues here beyond just getting a decent implied vol. In general, in convert modelling the credit issue and the implied vol are confounded together with uique convert risks (i.e., cash take-out). Suggest that you start by looking at implied vols of public comp options (if available) and then try to do some modelling of public comp converts. You need some decent software though.
 
i work at a valuation firm, and we're valuing common for a private company that has an equity structure with about 90-95% preferred and the rest common. its a long story as to why we're using it, but effectively a valuation partner at one of the big 4 likes to use bsm as a back check to the other methods we're using. the "option" value is the value of the common. i know its sounds realy strange; i don't understand all of the theory as to why he thinks it works. what i do know is that if we can justify a volatility in the 40% range, he'll be ok, because the value using bsm is pretty close to all the other work we did.

we're trying to find the implied volatilities for the comps, but if that doesn't work, we've basically just got a laundry list of qualitative arguments as to why 40% makes sense.
 
It doesn't sound even a bit strange. Viewing equity as a call option on the assets of the firm is the standard "Merton" model for valuing equity. The partner is probably a smart guy you should hang around with. In his classic 1974 paper, Merton pointed out that you can value equity by looking at it as a call option with the total liabilities of the company as the strike and the value of the firm's assets as the underlying asset. Ponder that sentence for awhile....

There is a little problem here - the Merton view requires the implied vol of the assets, not the implied vol of the equity. Fortunately they are related, but you need to use Solver or something to turn one into the other and you need more info. Specifically, you need the market value of the assets and the value of the equity. The formula must be on the web in lots of places. If you can't find it, I will help.

That means that to get equity valuation of the firm from comps, you need to get the implied vol of the assets of the comps not just their equity implied vol. So you need to do more work. On the bright side, it might be that you get a more stable answer for the implied vol of the assets because you have taken financing out of the equation (equity on a highly leveraged company is more volatile than a non-highly leveraged company).

I would almost certainly not be impressed by a laundry list.
 
bmwhype Wrote:
-------------------------------------------------------
> forgive my ignorance (as i've just
> graduated)...what is the difference between the
> Black Scholes formula and your
> black-scholes-merton model?


merton added a constant dividend yield
 
you, sir, are smarter than i am.

i don't understand everything you're saying; however, he isn't (or at least i don't think he isn't) viewing equity as a call on the assets. he's viewing common equity as a call on the preferred.

what we were engaged to do is value the common of this company with an equity structure of 19+ million shrs of preferred and 5.5+ million shares of common. its an early stage tech company. we got a bev from dcf and market comps. then we have to determine how much each preferred is worth and how much each common is worth. the way the aicpa has recommended doing that is to try to estimate/approximate a discount from preferred to common based on the dividend rights, voting rights, liquidation rights, etc. kind of difficult to do, but we feel pretty good about what you come up with. from there you just solve for the values that add up to your value of total equity.

well, as a back check, this partner has been using the bsm to get comfortable with the common value. what you do is assume the calculated value of the preferred is the underlying (lets say $2). then, to get the exercise price, you give yourself the stated annual cumulative dividends for the preferred stock (in this case 15%) over what you believe will be the life of the company (they assume a strategic sale in five years). That gives an exercise price of about $4.02.

now you need interest rates (easy) and volatility (not so easy).

if it still makes sense to you, like i said, you're smarter than i am.

what appears to be a problem to me is that 1) it doesn't consider the breakout between preferred and common (50-50 or 95-5; it doesn't seem to matter), 2) it doesn't consider the rights of the preferred compared to those of common, and 3) how is the calculated "strike price" really a strike price?

and he's a partner in another firm, which precludes us from hanging out much. i've never even met him. his firm is reviewing my firm's work.

i really appreciate you help.
 
"It doesn't sound even a bit strange. Viewing equity as a call option on the assets of the firm is the standard "Merton" model for valuing equity. The partner is probably a smart guy you should hang around with. In his classic 1974 paper, Merton pointed out that you can value equity by looking at it as a call option with the total liabilities of the company as the strike and the value of the firm's assets as the underlying asset. Ponder that sentence for awhile...."

interesting, never thought about this. I've actually argued with Joey D on here before about using BSM to value non-publicly traded assets. The problem is, BSM assumes that you can value an option from a "risk-neutral" standpoint, because in a liquid market you can continuouslly hedge your exposure to hte underlying by buying/selling stock. In the case of a private company, this clearly isn't the case. IMHO, this leaves you with three alternatives:

1) Price the options as a "Real Option" (see chapter 28 if you have Hull lying around, I'd imagine someone in your office does). In a sense, this involves building a binomial tree and calculating the expected present value of the option. You'll still need volatility for this so I'd reccommend using a combination of historical volatility, comps, and a subjective element factoring changing catalysts for the company that the historical volatility won't account for. (this is the 2nd best method IMO)

2) When Merton generalized the BSM model, he relaxed the liquidity assumptiong and assumed that in illiquid stocks you could hedge exposure to the underlying by trading a correlated instrument. In other words, find a correlated index or company and calulate the historical volatility of the correlated security adjusted for the beta you give it. Use this vol in the BSM formula. (a lot of assumptions used in this one...)

3) Throw out estimating vol and use the values for SE, L, and Assets as BS inputs, and then calculate the implied volatility from the BSM (or some other option pricing formula) in order to understand whether the optionality would be expensive or cheap. This is actually how traders evaluate options, and as long as you have a reasonable understanding of the implications of the vol level, involves the least assumptions. The downside is that this spits out a number for volatility instead of a dollar amount which may not be the desired effect. (I'd recommend this method)

to throw in two more cents, general thoughts on the street is that once you get into the 60 vol and up range, historical vol tends to lose value. For example, quite a few Biotechs trade in the 100s in vol terms due to the nature of their business. If I sold options in one of these names because it was currently realizing somewhere in the 30's I think my boss would lose his mind...

"however, someone mentioned to me that if i'm looking at an option with a five-year life, i should use five years of history to calculate volatility"
As your gut told you, this is probably not the best way to look at historical vol, Especially in a private company. This may hold for something in a less volatile product like an index or bonds, but I wouldn't do it in this case...
 
fyi, some of the people on Wilmott consider your question one of the most "cutting edge" problems in finance...
 
didn't see your post, I still reccomend the third approach using what he gave you for S, X, R, T and the implied current value of the option, or make a chart/graph showing the relationship between call value and volatility...
 
as far as using the assets, liabilities and equity in the bsm and solving for volatility: you aren't saying use book values are you? the book value of equity is in the $8 million range while the value we calculated is close to $42 million. should i just make assets a plug? assuming liabilities are close enough to market value?

and i did read that volatilities higher than 60% should be avoided due to mean reversion.

and i'm sorry i don't know abuot hull. i looked it up on barne and noble. is it "Options, Futures and Other Derviatives" or "Fundamentals of Futures and Options Markets" that you're referring to?

thanks.
 
mlh97 Wrote:
-------------------------------------------------------
> as far as using the assets, liabilities and equity
> in the bsm and solving for volatility: you aren't
> saying use book values are you? the book value of
> equity is in the $8 million range while the value
> we calculated is close to $42 million. should i
> just make assets a plug? assuming liabilities are
> close enough to market value?

I was reffrring to Joey's comment about the interpretation of equity. My assumption was that somewhere out there, there are options that someone is paying for. What I'd recommend is find the asking price of those options, and use the current value of equity and strike price to back out what vol you WOULD have to use if you wanted to arrive at that price... and then compare that to a set of reasonable assumptions i.e., if it's 100% it's too high, but if it's 25%, the options may be dirt cheap... In other words, it's like talking about a bond in terms of its yield as opposed to its dollar price...


> and i did read that volatilities higher than 60%
> should be avoided due to mean reversion.

While stocks trade higher than 60, it's ussually a sign of expected fundamental events in the future, such as the outcome of a drug trial, as opposed to the normal standard deviation of returns.

> and i'm sorry i don't know abuot hull. i looked it
> up on barne and noble. is it "Options, Futures and
> Other Derviatives" or "Fundamentals of Futures and
> Options Markets" that you're referring to?

Options futures and other Derivatives, If you don't have it, I wouldn't bother buying it though...

> thanks.



Edited 1 time(s). Last edit at Friday, September 15, 2006 at 01:00PM by ahahah.
 
Options, Futures, and Other Derivatives needs to be on everyone's bookshelf. That's such a neat book (but freakin expensive)

ahaha - I think the question here is not valuing equity options but valuing the equity as option. We can carry on our debate about valuing options in non-traded assets some other place. It is an interesting debate, dramatically more interesting than some of the stuff on OT. I completely agree with "to throw in two more cents, general thoughts on the street is that once you get into the 60 vol and up range, historical vol tends to lose value. For example, quite a few Biotechs trade in the 100s in vol terms due to the nature of their business. If I sold options in one of these names because it was currently realizing somewhere in the 30's I think my boss would lose his mind... "

mlh97 - Well, I don't like what aicpa is telling you to do. If preferred stock was always worth more than common stock, there would be no such thing as convertible preferred stock. Preferred stock isn't really equity when viewed alongside common; it's debt. If you own the preferred, you're never getting more than par + dividends (well, usually). Obviously, with common stock the skie's the limit to what you might make. Thus, it's not appropriate to view common as a call on preferred because the the call on the preferred can only be worth a well-defined maximum amount.

I think where this got lost in the translation is that the preferred stock is the liability of the company so the strike of the option in the Merton model is the value of the preferred. An option whose strike is the value of the preferred is not the same as an option on the preferred, but they sure sound close.
 
"I think the question here is not valuing equity options but valuing the equity as option. We can carry on our debate about valuing options in non-traded assets some other place. It is an interesting debate, dramatically more interesting than some of the stuff on OT."

If I remember correctly, we pretty much finished it last time... You were certainly right about the quality of stuff on OT lately. Some decent sports talk, but it looks like a lot of people have gone crazy over there...
 
one of you can correct me if i'm wrong, but i was told that when a pe or vc firm invests in a company, many times they make the investment preferred stock. that way they can offer stock or options to executives etc and still have preference in the event the company has to liquidate or something. the preferred is convertible to the common so if the company is acquired or goes public, they can get the full value of the common.

as far as the discount from preferred to common thing goes, the assumption (which is correct in this case) is that the preferred is just like the common except that it has preferences, etc. it will never be worth less than common due to its convertability.
 
Convertible preferred is different than plain vanilla preferred. I agree that convertible preferred stock can never be worth less than its conversion ratio times the stock price. You are correct the vc firms like to invest in convertible preferred or even convertible debt if they can get it. Most preferred is not convertible.

This problem is tougher now. The convert represents either a liability of the company or outstanding equity. I'll have to think about Merton in this context. Hmm... Give me a day.
 
happy to.

sorry its taken awhile to get much of the specifics out. i appreciate your help and thoughts.

did you learn your stuff from a masters of phd? or have you picked it up from work?
 
This thread is great. Makes me more sure about going back to university. I hope I'll be able to pursue this kind of stuff then.
 
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