Hedging fx barrier options

But why is that? The partial derivative doesn't exist or the magnitude is very large? What are the work arounds if any?

I assume this is the property of the function and has nothing to do with a numerical method used to calculate the solution. As you know, Barrier options are extensions of vanilla options in the sense that they have a barrier level which activates or deactivates the option's pay-off upon hitting the barrier. The barrier can be hit when the option is in-the-money or out-of-money. Barrier options which are activated upon hitting the barrier are called Knock-in barrier options or simply Ins and those that are instead deactivated are known as Knock-out barrier options or Outs.

In knock-out options, if the barrier is not hit by the underlying price from the time of issuance of the option to its maturity, then the option holder receives an equivalent pay-off of a vanilla option. Knock-in options only provide a possibility of a positive pay-off after the barrier has been hit.

When a barrier option knocks-in, it becomes an equivalent vanilla option and thus, offers the same pay-off whereas a knock-out is equivalent to the corresponding vanilla option as long as the barrier is not hit until maturity exercise time. Since you have tagged your question with delta-hedging I assume we delta hedge the option with the underlying.

Here difficulties would arise if the amount of underlying contracts we need to exchange to keep the delta near zero is large compared to illiquidity and transaction costs.

Use Knock-Out Options To Lower The Cost of Hedging | Investopedia

With these together with volatility about constant, transaction costs would increase with gamma. As gamma gets very high, typically but not only, for plain vanilla options at the money near expiry, delta hedging gets very expensive.

hedging barrier options - Quantitative Finance Stack Exchange

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Join them; it only takes a minute: Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top. Please determine your model.

Without the model , we can not talk about this issue. By no means does this constitute a proper answer but did you have a look at this paper by Derman: Michael Suchaneck, The Pricing and Hedging of Barrier Options and Their Applications in Finance and Life Insurance , Nassim Taleb, Dynamic Hedging: Managing Vanilla and Exotic Options.

But I think I can find an answer in the links you have provided.

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