Was having a debate with a coworker and he made the comment that between quant finance and actuaries, there is no structure for an option that cannot be given a numerical fair value. I disagreed with him (gut reaction). After stewing for a few minutes, I couldnt think of an example of an option with a fair value that can be reasonably estimated. Stupid question, but it got me thinking. So I put this trivial question to you. Is there anything that anybody could think of adding to a option's structure that makes it so complex that no lattice/monte carlo/actuary could give it a fair value?A

It's a fun question.Here are some very simple structures: Option 1: pays $10^11 or 0based on SETI making a valid contact or not in the next 10 years. Option2: same contingencies, but instead of zero, you get apayoff based upon the factors of very large numbers that are currently not factorable. For example, the sum of the factors of RSA-2048 (Oh yeah, forgot to mentionthat the second option matures when the factors are determined and the prize is paid.)awaiting word from the actuary -- risk management only needs 3 sig. digits

What about the St Petersberg paradox - where you toss a coin, and each time, if heads you get the money, and if tails you toss again for double.I don't know that anyone would put a single fair value on this.

How about the parity option: pays $1 if S&P ends up on an even number and -$1 if is ends on an odd number on given date ... any practical hedging scheme would cost more than the option, so quant finance must remain silent on the value (until a liquid market exists in such deals)

Even under the quite gentle conditions of vanilla american options where the allowed exercise is over a range can be a bit hard. This is "solved" by making assumptions about the utility function of the holder, with respect to money and time.But what if the utility function for some contract is unknown to you ?How about assuming an option where the holder can demand physical delivery of the stock, with no provision to settle in cash ?Chapter one of any derivatives books says that an call option can expire worthless, and trivially proportional to the difference if in the money.But what if an unknown % of the holders are involved in a closely fought takeover battle ?Sometimes the number of "loose" shares can be both small and important to the two sides.If you've written that option, you must extract shares by force of money from others. You cannot easily know which side the option holder is on, or if he is on either side.One pathological case is where the cheapest thing to do is buy the shares from the option holder, then give them back.

QuoteOriginally posted by: skrappyWas having a debate with a coworker and he made the comment that between quant finance and actuaries, there is no structure for an option that cannot be given a numerical fair value. I disagreed with him (gut reaction). After stewing for a few minutes, I couldnt think of an example of an option with a fair value that can be reasonably estimated. Stupid question, but it got me thinking. So I put this trivial question to you. Is there anything that anybody could think of adding to a option's structure that makes it so complex that no lattice/monte carlo/actuary could give it a fair value?AHow about an option with american exercise type, where underlying is a multidimensional basket (N~1000). Imagine some version where the underlying used in payoff calculations has nonlinear dependence, like Max, Min etc..

> What about the St Petersberg paradox - where you toss a coin, and each time, if heads you get the money, and if tails you toss again for double.Sometime ago someone on Dr Risk's website posed a question based on exactly this option:Derivative GamesScan down for the 'Bernoulli Option'.Like Pat's example it's an alligator option; the transaction costs on the hedging strategy will eat you alive.

I think I could put a value on most of the options mentioned. For example, I would quote the odd/even digit one at -a/+a with a between $0.01 and $.50 and depending on the expected flow and my utility fucntion. I would not hedge but I might do something in the market if the position is big enough. The St Petersburg one is more about agency structure at modern banks than about quant finance: I am indifferent between losses of $2bn and $20bn, bank shareholders are indiffirent between $50bn and $500bn. Once the payoff is bounded, it is easy to put a price on this option.But there exist assets that quant and actuaries fail to price. Those exotic beasts are called "equities". Can anyone show me a model that would really epxlain why GOOG is worth $299 and not $99 or $399?

QuoteOriginally posted by: PatHow about the parity option: pays $1 if S&P ends up on an even number and -$1 if is ends on an odd number on given date ... any practical hedging scheme would cost more than the option, so quant finance must remain silent on the value (until a liquid market exists in such deals)Since there is no reason to believe that the index will end up on even number more often than on an odd number then this option should have no value. But apart from gambling i cant see any economic rationale behind such a contract> At least in standard options its supposed that a hedger meets an a speculator and some risk is transfered for a price.