Hello,I am looking for an exotics desk who will sell me a somewhat unusual one touch ratchet option which I have designed to hedge some liquidity / gap risk on one of our trading books. The problem I have is that "Fair Value" is a rather abstract concept for this option as there is no liquidity this far out on the wings of the forward or spot vol surface. In short, it is a type of catastrophic, nth sigma risk. BSM etc would say that the price is fractions of a basis point but clearly it isn't.My question therefore is:1. How would you price the option detailed below if you HAD to sell it?2. How would you hedge it if you were short of it - indeed would you bother?Payoff / Parameters:The option pays 100% (immediately) if the market TOUCHES the price X% below the previous day's closing price, otherwise nothing. At the end of each day, the strike resets to X% below that day's closing price. As soon as the option pays out, the option expires (can't pay out more than once).Underlying: S&P 500 indexExpiry: 1 year, strike price resets dailyPayout: $300k minimumLiquidity: None, no two way market, hold to expiryI am interested in prices for all values of x% from 5% to 20%.For the little that it is worth, in the last 50 years (12,585 trading days), the market has fallen by > the amount's tabulated below, the corresponding number of times.5% - 11 times6% - 8 times7% - 6 times8% - 2 times9% - 2 times10% - 1 time11% - 1 time12% - 1 time13% - 1 time14% - 1 time15% - 1 time16% - 1 time17% - 1 time18% - 1 time19% - 1 time20% - 1 timeWhere October 1987 is the 1 time for all values over 10%, so, once in 50 years.So, given that I wish to buy this option, I need to find a seller. Thinking as if I am a seller: Why would I sell this and at what price? How could I hedge it?If I worked on an exotics desk at a bank I guess I would try to back the risk off via a structured note paying X bps over LIBOR if the gap event does not occur. Alternatively, perhaps the hedge fund desk could hawk it to a HF who wanted to make "probably" money for nothing ;-)To complicate things further, what effect would this have on the seller's internal capital capital requirements under different scenarios? I only asked one exotics desk to sell it to me so far but they have a strange set up and while they initially offered me a price, they said that it wouldn't represent a good return on internal capital budgeting. Though they had got happy with the return on risk at the price offered (they were going to 'go naked' on the risk), they couldn't make it work for them.Aside from backing the risk off, hedging would be too costly to be worth while I think, though I would like to be told otherwise. Any static hedge using vanillas or binaries would cost a lot and forget delta hedging this thing.OK, over to the floor... what do you think?Thanks.

For Put options, the possible reason why people are willing to buy an “expensive” deep OTM Puts are that they are viewed as a form of “insurance” against market crash. The lower cost in terms of dollar might also offer another reason for deep OTM Puts to serve as an insurance / protection tool of one’s portfolio.

For an unhedgeable trade like this, the other side would have to prop it. I would expect that if you call up a bank, they would try to find the other side and only intermediate it. Some desks might take it themselves, but I suspect they would have pretty limited appetite for this type of risk. Either way, expect to pay well above any TV (either risk-neutral or expectation based) for this type of an instrument.As far as hedging goes, you'd probably leave this unhedged until risk becomes real. I.e. start heding once you get to X% delta on these things. You would need a decent system to track this, since it would all be intraday (I guess I'm too used to less liquid markets these days). Also, for strike this far down, you know you'll be hedging in a market that's far from normal (shorting on an up tick etc). On the other side, with a binary, having positive gamma on a low strike isn't the worst thing to have. In general there is a lot of demand for this type of hedge and little supply out there. Sourcing these at a reasonable price would be great, since it would let you run a number of negative skew strategies without getting smoked in the tail event. Alas, in the absence of supply, this risk is too often hedged with the traders option. For what it's worth, I price gap options in my market a lot, but if somebody asked me to prop the other side of a structure as toxic as this, I'd tell them to take a hike.

Didn't Taleb write a whole book on this, The Black Swan, or something ?

what happens if the market has a rule that it shuts as soon as it falls Y% where Y% < X%?

What about using the superhedging price? Are there upper bounds on this or something?

QuoteOriginally posted by: mjwhat happens if the market has a rule that it shuts as soon as it falls Y% where Y% < X%?Or worse, the circuit breaker is defined in points, not % so that path dependencies define whether a given % loss triggers a trading halt.

Hi, I'm not concerned about a circuit breaker as the NYSE / NASDAQ (where the S&P 500 constituents trade) doesn't have one. Besides, it is obvious that if the market is closed, the touch can't trigger. The reference would be off Bloomberg or the official S&P index price.In any event, does anyone have any thoughts on my original question?StructCred - thanks for the input, how would you price it though if you had to?Thanks!

Just an idea: perhaps a combination of a volatility swap and a position in the implied vol index would begin to hedge this?

Honest question on the contract design. Is there really an "official" intraday high/low from S&P on the index?If so, how exactly is it calculated?

The index is calculated as per the documentation here http://www2.standardandpoors.com/portal ... es_usThere is always a question as to whether an index hit a given level at the high / low because the index providers only update the indices every X seconds (where X is 2 for the Dow, 15 for the FTSE etc). However, most traders calculate the index for themselves in real time using a feed of the constituent stocks and / or the futures. Having said that, you then have to be careful creating it like this as the stocks all need to trade very quickly for the index to be up to date or you get situations after bursts of volatility where a cash index that you calculate will trail the futures as not every stock will trade right away... a classic "tail wagging the dog" scenario between the cash index and the futures. The solution to this is to take an index feed, the futures and the constituents and blend a hybrid. Anyway, we digress, for the purpose of this contract that I wish to buy and am interested in pricing, we can assume that the prices quoted on Bloomberg are those to be used.Any thoughts on this series of ratchet forward starting far OTM One Touch options appreciated...Thanks!

Observations (some already mentioned):1. A ballpark value comes from looking at probability of the fall not happening each day, and raising that to the power of the number of days (and subtracting from one)2. Normally you might not delta hedge until delta reaches some critical level (it starts each day so small), but this might happen too quickly for you to put on a hedge3. Seller would probably take a punt4. Find someone for whom the principal is insignificant5. Is there enough profit margin between the theoretical value and the sale price, and where does that fit in w.r.t. time of year and people's bonuses6. You could buy OTM puts for less than they are worth as long as the seller thinks that short-term gain beats long-term survival7. You have to find a seller still using normal distributions (getting hard thanks to NNT)P

Thank you for your thoughts Paul, much appreciated and all valid I think. Point 1 is how I did it but problem with this is of course the quantification of probability.As you say, the delta would probably just move too fast with all that gamma and I don't think we will find anyone who hasn't read Taleb's books and assumes a normal dist!I would love for us to take this bet on one of our books but in a smaller size than I want to buy it and the net position is we just have to hedge some things.You know a lot of people in the market... if you can PM me any suggestions I would be grateful.Cheers!

Ok, I guess what worrys me is that if things get contentious (say S&P says the low for the day was -4.97% and Bloombergsay -5.02%), then you and the counter-party may get into a dispute about whether or not Bloomberg made an error. Regarding pricing, I would first try to price the close-to-close version of this option say by studying all the S&P500 optionexpirations with one day to go. Take the -5% option. Perhaps the existing option data will allow you to estimatethe risk-adjusted probability p that the daily return is < -5%. Then, as a rough approx., assuming independence, the close-to-close option is worth 1 - (1 - p)^252, ignoring cost-of-carry issues.p.s. This crossed with Paul's identical suggestion. I will add that you probably want to distinguish between theunconditional and conditional p, the latter conditional on the current volatility of the index (and the circuit breaker rules)

Pricing such an instrument may require brushing up on the theory of large deviations.