What do you mean specifically by “crash risk”? Perhaps if you provided an example of a carry trade you are thinking about, you could describe the crash risk you associate with those particular instruments/assets involved in your trade.

As it stands, you haven’t given us enough information to answer your question–it’s far too generally stated. Without knowing more, I suspect that one could employ an options-based approach, generally speaking, but unless one employs a combination of puts and calls in a long/short options combination of some kind, which carries its own set of risks, you’ll be paying option premia in excess of your expected return on your underlying strategy.

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I have started by looking at the simplest naive carry trade strategy – taking a short position in the low interest rate currency and taking a long position.

Several academic papers have suggested that you can condition these types of models on indicators such as the VIX or TED spread in order to prevent against crash risk i.e. when there is greater uncertainty/volatility in the market and these indicators reach a certain target level, you take zero positions in all the currencies in anticipation of the carry trade unwinding so that you don’t lost your previous gains.

However, I have tested these strategies and have found the indicators either have very small or no statistical significance. I was wondering if anyone could suggest either alternative indicators or point me in the direction of literature which explores more sophisticated strategies. Any suggestions would be greatly appreciated as I am very new to this area of finance