Intrinsic value can't go negative?

zzaxx99

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I've been reading Sheldon Natenberg's Option Volatility and Pricing book, which was recommended in a couple of threads on T2W that I read recently (bv robertral and RogerM, to name but two)

So far, so good - it's a very thorough book and has already cleared up several misunderstandings I had about option (and by implication, covered warrant) pricing.

However, there's one comment in one of the early chapters that stopped me in my tracks, where he says that "intrinsic value can't be negative" or words to that effect.

So, if I have an underlying a 1000p Call on an underlying at 980, which is currently trading at 27p, this would be 20p intrinsic with 7p time value.

But if in the same set-up, but with the underlying at 1020 and the option at say 4p, he would have the intrinsic as 0p and the time value as -16p. I have always thought that this situation would have an intrinsic of -20p and time value of 4p.

His view seems illogical to me - surely if the time value is negative, this is saying that the chance of the option finishing in profit is less than zero? Which seems, at best, counter-intuitive, and at worst, plain wrong.

So, bearing in mind that he's a well-respected author, and I know nothing, which of us is "right"? :)

If he's is "right" (ie the generally accepted view), can someone please explain the logic of this view?

(On another tack entirely, for anyone reading this book, I would also recommend a copy of Buying and selling volatility by Kevin Connolly - there is a throw-away comment about hedging that isn't (yet?) covered in the Natenberg book which is covered in exhaustive detail in the Connolly book. Generally, the two books complement each other well, without too much duplication. Advert over)
 
zzaxx99 said:
So, if I have an underlying a 1000p Call on an underlying at 980, which is currently trading at 27p, this would be 20p intrinsic with 7p time value.

But if in the same set-up, but with the underlying at 1020 and the option at say 4p, he would have the intrinsic as 0p and the time value as -16p. I have always thought that this situation would have an intrinsic of -20p and time value of 4p.


In your first example, you are saying that the underlying is 1000p and the strike price of the Call option is 980. The call option trades at 27p. In this case, you are correct in that 20p of the premium would be intrinsic, and 7p would be time value.

Your 2nd example is confusing because you refer to the underlying being 1020. Do you really mean the underlying, or the strike price being 1020?

If you mean the underlying is at 1020 (which I don't think you do), then the 980 call option would be trading for a premium higher than the 27 stated above.

If on the other hand you mean that the underlying remains at 1000p but the strike price of the Call option is 1020 (and therefore out of the money), and the premium trades at 4p, then there is no intrinsic value, and 4p of time value.

Basically ,in the money options will have intrinsic value and perhaps some time value, while out of the money options will have 0 intrinsic and time value only in the premium.

Hope thats clear.

If not, pm me.
 
option value = time value + intrinsic

intrinsic_call = max (S-K, 0) >=0
intrinsic_put = max(K-S, 0) >=0

Intrinsic can't be negative
 
Yes, it would rather have helped my case if I'd got the example the right way round.

So 1000p call, underlying at 1020p, option at 27p = intrinsic of 20p, time value of 7p
And 1000p call, underlying at 980, option at 4p = intrinsic of 0p, time value of -16p

I suppose it's logical that the value of the option can't go to less than zero, so in that case, when the time value has eroded the option expires with no value. But why should a slightly out of the money option have negative time value? Is this just a result of the "intrinsic can't go below zero" rule, or is there some deeper logic to it?
 
zzaxx99 said:
Yes, it would rather have helped my case if I'd got the example the right way round.

So 1000p call, underlying at 1020p, option at 27p = intrinsic of 20p, time value of 7p
And 1000p call, underlying at 980, option at 4p = intrinsic of 0p, time value of -16p

I suppose it's logical that the value of the option can't go to less than zero, so in that case, when the time value has eroded the option expires with no value. But why should a slightly out of the money option have negative time value? Is this just a result of the "intrinsic can't go below zero" rule, or is there some deeper logic to it?

"And 1000p call, underlying at 980, option at 4p = intrinsic of 0p, time value of -16p" - You are wrong here....the answer is intrinsic = 0p, and time is 4p

remember the option price is = intrinisic + time value, and in the above case there is no instrinsic as S<K
 
Robertral said:
"And 1000p call, underlying at 980, option at 4p = intrinsic of 0p, time value of -16p" - You are wrong here....the answer is intrinsic = 0p, and time is 4p

You are of course right - that was a pretty dumb mathematical transition from have -16p "out of the moneyness" to making it time value.
 
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