Hi all ,I m working on cppi option but i don ' t have much papers on it :--(( I suppose i can use MC in order to price cppi option . I m about to implement it with VBA.But i am wondering if a closed formula has been derived ?Does somebody know where i could get any docs related to that field? (even book chapters!)Thanks a lotJeFF

closed form solution? I dont think there is one.It is all about simulation therefore MC is the way to go.QuoteOriginally posted by: jeanfranHi all ,I m working on cppi option but i don ' t have much papers on it :--(( I suppose i can use MC in order to price cppi option . I m about to implement it with VBA.But i am wondering if a closed formula has been derived ?Does somebody know where i could get any docs related to that field? (even book chapters!)Thanks a lotJeFF

is this an option on a cppi? or a cppi??

Hi,Thx for answers.I am talking about Option on CPPI !More precisly , suppose i run a cppi portfolio with a fund as risky asset and bonds as risk free asset .Maturity say 5 years .In five years i promess you ( :--) ) the following payoff : 100% + Max (0 ; perf CPPI) where perf CPPI= (CPPI value at time T / CPPI value at time 0 ) -1 .CPPI value is the portfolio value which include Fund & Bonds . A friend told me Peter Carr had been writen something about this issue but i m not able to find it .MC is a good way to price this product but a closed form fomula is good for computing Greeks !

Hi,Dr. Carr is effectively writing something on CPPIs, but not on options on CPPIs. As far I know, he's trying to release Prigent's approach on vol (they had Heston).But let me also point something on MC.If your underlyings are funds (MF or HF) as it is the case in most CPPI's on the market, you'll have to model the funds dynamics, and lognormality is not the way to go. Historical simulation might be also short given the small number of points you might have to value the empirical distribution. Add on top of this non-liquidity, and the greeks you'll get will be swinging around for no good reason...--------------------------------------Don't try to win, enjoy the run

QuoteOriginally posted by: hypersphereHi,Dr. Carr is effectively writing something on CPPIs, but not on options on CPPIs. As far I know, he's trying to release Prigent's approach on vol (they had Heston).But let me also point something on MC.If your underlyings are funds (MF or HF) as it is the case in most CPPI's on the market, you'll have to model the funds dynamics, and lognormality is not the way to go. Historical simulation might be also short given the small number of points you might have to value the empirical distribution. Add on top of this non-liquidity, and the greeks you'll get will be swinging around for no good reason...--------------------------------------Don't try to win, enjoy the runDo you have a good publications on CPPI? I want to understand how it works.

To get the understanding :- Bertand and Prigent, "OBPI vs CPPI"- Boulier and Kanniganti, "Expected performance and risk of various Portfolio insurance strategies".- Merton's paper (mentionned in Boulier)- Brennan and Schwarz's "PRICING OF EQUITY-LINKED LIFE INSURANCE POLICIES WITH AN ASSET VALUE GUARANTEE"

i 've ever read Lognormal is not the way for modelling paths for HF.Hypersphere do you have something related to CPPI option???Don't tell me nobody has never tried to write something about this issue !?!It s a real business ...

I've seen several products priced with usual log normal dynamics to model HF returns, and some ended up loosing a lot of money.Just because CPPI is ultra sensitive to down/up jumps whith the dynamic rebalancing component, and completely path dependant, you need to add jumps in your pricing method, no matter what is is. Funds have a tendancy to move 5 or 10% over a period without people being annoyed by it, that is just the way they behave. But when you consider a CPPI, these moves can trigger an up/down rebalance and affect your path up to maturity.I did not say MC is not the way to do it as long as we do not have anything else to do, but FYI have more reserves than usual on the prices if you do not include jumps in your underlying dynamics.Loosely speaking, compare the empirical dist of returns of a quaterly or even monthly fund to any liquid stock. I say they are not alike, not even mentionning the amount of data you have to evaluate it.I know CPPI option is real business, as if you choose your parameters correctly a bond+call on a CPPI replicates the payoff of the underlying CPPI. But maybe that fair modeling these things is not the easiest thing ever and people do not really disclose any paper. I never saw any good article about this, I just had discussions with traders/quants when I was dealing with CPPI and CPPI options. Also, as I mentionned in a previous post, Dr Carr is writing something on CPPI, but I am not sure of him mentionning options. He also wrote a paper late January on vanilla CPPI with jumps added in the diffusion.

Many Many Thanks Hypersphere for replying me !Yeah Jumps is important issue : when i simulated with log normal dynamics , Fund Paths never broke the Floor... it s not realistic !That 's why i run simulation using Jumps (as Merton's paper) to get some case where paths go through the floor .In fact my problem is to compute a price for the CPPI option i described below :"In five years i promess you ( :--) ) the following payoff : 100% + Max (0 ; perf CPPI) where perf CPPI= (CPPI value at time T / CPPI value at time 0 ) -1 .CPPI value is the portfolio value which include Fund & Bonds . "I proceed as follow :1/ i run simulations including jumps2/i compute the final payoff at maturity dateI know i must calculate an average of all payoff at maturity I get but i find prices which are weird ::--))Anyway Thanks for your help Hypersphere , i keep working on it !

I know what you want to compute, and maybe I can explain a bit on the "weird" prices.Say your CPPI starts at 100 and guarantees 100 (which is a common feature of the CPPIs out there in the market), and your option is floored at 100 (as per your example). Hence you supposingly cannot have CPPI_T<CPPI_0 because of the floor in the CPPI, so you have CPPI_T=100. your whole option's terminal payoff is 100. On the other hand, if CPPI_T>CPPI_0, then 100%+Max(0,perf CPPI) = perf CPPI.This is what I said when I mentionned the option replicates the underlying. You get weird prices because of that path dependancy that translates into the option, something which I am sure you are aware of, else you would have no use doing options on CPPIs. Pricing these with MC requires a lot (like really a lot) simulations to get a converging price.And if you still get weird prices, then it might be because of the fees (i guess your jump process, vol, etc are well calibrated). Indeed, the very use of the option on the CPPI is to get completely different greeks behaviours overtime, on top of some interesting others things. Then usually, when dealing with options on CPPI, one would not use the same level of fees as he would when trading the underlying itself as the risk you're bearing is not the same.good luck.

It's absolutely essential to put transaction costs, jumps and market sized transactions into this modelling. If possible get an historical data set to run your model through.The likelihood of a floor failure is small, if properly managed, so we can estimate the probability of being close to the floor at various horizons (using LN assumptions), and then compound with the probability of a jump, and jump size to give an estimate of failure severity and associated probability. Then check the sensitivity of the answers to the assumptions. Put proper bounds on your knowledge of assumptions and choose the appropriate confidence level on your estimate of payoff.

Well as per the transaction costs, it depends how you run you algorithm, and it depends on legal issues as per the redemption/subscription notice to the fund. Indeed, usually the weights used are t-1, meaning when you notice a change in weights to occur at t, you need the fill of the price to do so, and the lag enables you to enter/leave the fund without any cost at this very price (on top of the fact that investment banks usually get rebates on the fund fees...), as the algo frequency is based on the underlying liquidity. So if your algo is properly set up, i would not worry about the transaction costs.And Frashe, about the floor violation, it is not about management at all, in the case of the main players on CPPIs. Crash risk is not dependant on the writer, rather the underlyer. The thing about the probability theory is that usually you do not have enough data to estimate it. It is a bit like when traders say they hedge the CPPI crash risk with CDOs. Well what if a crash does not correspond to a default event, or a default is triggered on the CDO while the CPPI valuke does not go below the floor ?

How you implement transactions costs does depend on the algorithm, but they must be there. If I understand you properly on how you implement your algorithm, then you are able to see what the price change will be and (mechanically) execute at this price. If this price is a NAV for both buying and selling units then the residual holders of the portfolio wear all the transaction costs. If the underlying fund is purely inhouse then the transaction costs are just being delayed and showing up in a downward drift to the underlying unit price. Better to make it clear up front by having different prices for buying and selling units.Your point on not having enough data is exactly why you have to test the sensitivity to your assumptions and put reasonable bounds on the assumptions, which give a distribution for option cost. Then you choose an option price at the higher end of that distribution to cover the cost of extra capital you need to cover this uncertainty.Your statement that crash risk is not dependent on the write is exactly what I mean when I say if the CPPI is properly managed then probability of being close to boundary is small. I'm presuming that the expected drift away from the floor is positive.