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How is gap risk (i.e. due to the Nav dropping below the threshold/ZCB level) on CPPI-type products usually calculated/managed?I've seen Monte Carlo simulations and short-puts mentioned elsewhere. Would anyone like to elaborate on these or suggest any other ideas/methods?Many thanks!

if the bank does not want to run the gap risk, they sell it on to investors through notes which pay an above market coupon and have repayment risk linked to the underlying 'gapping' or sell the risk to a reinsurance company. As the underlying of the CPPI portfolios are usually illiquid (the normal capital protected structure for liquid underlyings is a zero and call), hedging the crash-puts would be sensles as one could not manage the deltas. If the underlying was very liquid (ie equity index) one could actually hedge by rolling a deep out of the money put.for pricing the gap risk, the most common practice would be through MC simulations. Key is the jump assumption, especially when pricing for underlyings such as FoF's which have higher risk then would be implied from the historic vols (event risk, etc)

Thanks Donyoshi.When you say that the jump assumption is key, if a Merton-type jump diffusion were to be added to the MC simulation, then the jump parameters would need to be calibrated somehow. If historical data were available and used to calibrate, then it wouldn't take into account expectations about future jumps.But if the underlying is illiquid, then also there may not exist options in the market which could be used for calibration to take into account forward-looking estimates of jump parameters. Is that what you mean?

yes exaclty, so you have to make an [big] assumption here, which usually is derived from barganing with the risk management group

Appart from model assumptions and calibration your underlying, the CPPI gap risk is simply the probability that the cushion become negative (wich is normally impossible because as CPPI structurers, investment banks prevent from it). As the cushion is calculated as :CPPI Net Asset Value-Zero Coupon Curve, we get : CPPI Net Asset Value-Zero Coupon Curve < 0 <=> CPPI Net Asset Value (i+1) < 1/Leverage * CPPI Net Asset Value (i)...therefore you'll find a huge gap risk with jump models, and a very small gap risx with other model assumptions, which consider the NAV to be "continuous"rgds,

for the hedging of cppi, do you think seller should buy short-term otm put & roll out OR just long-term put?many thanks

as mentioned below, if the underlying is something utterly unhedgeable, then it is almost pointless trying to hedge gap risk. better to try and mitigate it by using a lower multiple, or try and lay it off with someone else...if the underlying is a vaguely market-like thing, such as an actively managed fund, then giant market moves will usually result in very highly correlated market moves. therefore you may as well buy deep OTM puts on the most liquid related index.in terms of short vs long dated puts, i would say shorter dated. your actual contingent liability is like a daily deep OTM put cliquet, with the added feature that all future cliquets knock out once the first cliquet has paid off.the closest you can get is shorter dated far OTM puts, somewhere around the minimum value puts with the highest strike (offers for every strike below a certain value tend to be the same).probably quarterly puts is a good target as mar/jun/sep/dec options tend to be most liquid due to futures expiring on the same date.