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# CPPI

### Constant Proportion Portfolio Insurance

This simple CPPI trading strategy has a horizon of n steps over `T` years and results in a portfolio `Pi` which denotes the money in each simulated scenario path. This simple case manages a portfolio consisting of `d` stocks and a money market account. The CPPI strategy chooses `d` such that the portfolio value `Pi` never drops below the bond floor `F`. At each time step, the portfolio is updated according to the position `d` in stock `S` and the gain difference between the next stock price `S!` and its previous value `S`.

The underlying 'S' and the discount numeraire 'EUR' are processes simulated externally. For example, the process 'S' can be a stock price process that follows a Geometric Brownian Motion or a Heston Volatility process. The discount numeraire 'EUR' can be a constant discount curve as implemented in Discounting, or a stochastic process that has a dynamics as defined in the CIR model.

model CPPI import S "Stock price process" import EUR "Discount numeraire" import m "Multiplier" import F "Bond floor" import Pi_0 "Initial Portfolio value" import T "Maturity time" import n "Number of time steps" export Pi "Portfolio value in EUR" d = (m * (100-F))/S Pi = Pi_0 loop n Pi = Pi + d*(S!-S) %the ThetaML command 'Theta' passes time by 'T/n' years Theta T/n d = max( 0,(m*(Pi-F))/S ) end end