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I have a simple replication pricing implementation for 1st gen exotics (digitals, single and double barriers, etc.). In order to effectively test strategies I want to price "like" strikes across securities and products. Where "like" just infers that I've normalized the likelihood of touch for each security, product, etc.

Some options I could use are:

  • % from spot: this won't scale well across markets, securities, products.
  • SDs from spot: That uses historic data instead of the implied volatility to generate strikes.
  • Same delta as vanilla: This seems like a reasonable approach but only under BS assumptions.

Since exotics are normally quoted in %TV (theoretical value) I was hoping there was a standard "solve for strike" given a specific %TV value. If not, are there any other common strategies? References appreciated.

Edit: TV is theoretical value. Also for reference a bit about option contracts in FX from a text I'm referencing:

Exotic option contracts are priced in premium terms and the pricing is anchored by Theoretical Value (TV)—the CCY1% value of the exotic contract under Black-Scholes assumptions, specifically:

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  • $\begingroup$ I honestly don't know what you intend to do. What does TV stand for (total value, theoretical value?). You cannot solve a barrier option (given premium) for strike, unless you fix the barrier which will have a major impact on the value of the option. In terms of probability, if you want real world prob., the underlying doesn't care if you look at digitals, vanillas, touches or whatever else (it's simply the prob. of spot touching a value with whatever logic you use). For risk neutral implied prob. you can just use N(d2) from Black Scholes. $\endgroup$
    – AKdemy
    Sep 22, 2021 at 8:17
  • $\begingroup$ @Akdemy thanks for the response. Literature I have from banks reports on strikes chosen "binaries are selected such that their barriers are equidistant from spot on either side, and cost 20% TV". I'm trying to determine how they go about finding those strikes. $\endgroup$
    – TCopple
    Sep 22, 2021 at 14:09
  • $\begingroup$ More specifically. In vanilla space we say a 25D option has ~25% chance of finishing in the money and we can pull a particular strike for that probability. I imagine if the premium on a one touch is marked at 10% of the payout then there's a strike that corresponds to that specific premium value which seems equivalent to the probability of touch. I just don't know which bits I should use to find said strike. $\endgroup$
    – TCopple
    Sep 22, 2021 at 14:21
  • $\begingroup$ Delta is not the probability of finishing in the money (see my link above). Ignoring overhedging, fair values of touches or digitals are always probabilities. It's like tossing a coin. Not sure where exotic FX options are anchored by theoretical values. I have seen a fair bit of exotic FX options and none were quoted in %TV. Digitals are usually priced as tight call spreads, touches and most exotics with SLV (stochastic local vol). Premium is simply in percent of notional or pips. $\endgroup$
    – AKdemy
    Sep 22, 2021 at 18:39
  • $\begingroup$ If you want to solve for strike, you can use the model of choice, which provides a price, and solve for the strike that gives the price you desire (root solver). To go from delta to strike in FX pairs that are quoted with premium included (most pairs), are also solved with root solvers (vanilla European options) because there are no closed form solutions. $\endgroup$
    – AKdemy
    Sep 22, 2021 at 18:40

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