Created by Dr. Jan-Frederik Mai

Cap struct arb hedging: the delta-to-jump ratio

Regarding the hedge of a capital structure arbitrage position, we focus on both the jump-to-default risk and the delta risk at the same time. In an earlier article we pointed out that when a put option is used to hedge a long credit investment, not only the number of puts but also the strike price is determined by these two targets. Slightly reformulating this observation, in the present article we find that the essential criterion for the choice of strike price is that the delta-to-jump ratio of the put equals the delta-to-jump ratio of the long investment, thereby uniting both targets in a single quantity. If one uses two short instruments for hedging, for instance a shorter-dated CDS and a put or two puts with different strikes, then it is important to make sure that the delta-to-jump ratio of the long investment lies in between the delta-to-jump ratios of the two hedging instruments. The appropriate hedge can then conveniently be interpreted in terms of a convex combination of the two delta-to-jump ratios of the hedging instruments.


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