Put can have negative instrinsic value?

[mikhail]

I recently by chance discovered that put options can have a negative intrinsic value, which can be easily seen on this graph:

Call options, on the other hand, always have a positive intrinsic value.

The question is: why can puts have a negative intrinsic value? What is the easiest and intuitive explanation?

 

[rmorse]

An ITM call can be worth a little less than parity if the underlying is so hard to borrow, that being short the call is more beneficial than being long the call,to avoid a reg sho buy in(Your broker is failing on delivery of a short sale). This can also happen in events like a dutch tender offer where the long call gets no benefit and all the value is in the stock. Either event is very short term.

I can't think of a scenario where the ITM put is worth less than parity more than a few pennies. Any MM will buy a deep ITM put and buy the stock to make a small profit, then exercise the put.

I'm not sure what you are graphing, but it might not represent a current market or the spread maybe very wide and the midpoint is not where trades would occur.

 

[mikhail]

I'm not sure what you are graphing, but it might not represent a current market or the spread maybe very wide and the midpoint is not where trades would occur.

Hi Robert, if we look at a standard Black-Schole calculator, then we can easily see that a put can have a fair value smaller than the intrinsic value:

Intrinsic value = Max (Strike - Price; 0) = 100 - 50 = 50

Black-Scholes value = 45,1196

 

[rmorse]

This is assuming a 5.006% interest rate and no early exercise. Maybe a cash settled index options with no early exercise in a retail account would replicate this. In practice, all MM have a better cost of borrow right now than 5%, much better, and any american style option would not be accurate with your assumptions. The cost of carry is the issue here. If you can early exercise the values will all change. Dates are all old too. Plug in a 1 year option with today's date with the ability to exercise today. The value will move to near parity.

Anyone with a low cost structure would buy that put vs. the common for just under their clearing/commissions/early exercise cost. risk-less profits.

 

[mikhail]

This is assuming a 5.006% interest rate and no early exercise. Maybe a cash settled index options with no early exercise in a retail account would replicate this. In practice, all MM have a better cost of borrow right now than 5%, much better, and any american style option would not be accurate with your assumptions. The cost of carry is the issue here. If you can early exercise the values will all change. Dates are all old too. Plug in a 1 year option with today's date with the ability to exercise today. The value will move to near parity.

Robert, this is a European options calculator (because the Black-Scholes model works only for European options, not American ones).

I guess with American options there will be no negative time value.

As for the rate and the dates, since I am calculating the theoretical value of an option - the values and dates do not matter much.

So my question is about European puts.

 

[rmorse]

BS does not work well for this. Use Binomial.

 

[rmorse]

Robert, this is a European options calculator (because the Black-Scholes model works only for European options, not American ones).

I guess with American options there will be no negative time value.

As for the rate and the dates, since I am calculating the theoretical value of an option - the values and dates do not matter much.

So my question is about European puts.

You are correct. That makes a big difference. It is all cost of carry.

 

[mikhail]

For American put it is clear now.

Still a bit confused as to why time value can be negative for European puts...

 

[rmorse]

For American put it is clear now.

Still a bit confused as to why time value can be negative for European puts...

Option values always assume a hedge. The difference between parity and the value above is cost of carry of the put and the hedge.

 

[mikhail]

Option values always assume a hedge. The difference between parity and the value above is cost of carry of the put and the hedge

Thank you, Robert, I will think it over.