EUROPEAN_FFT

Syntax

EUROPEAN_FFT(characteristicFunction,S0,spot,R,rate,T,expiry,ALPHA,damping,N,gridSize,ETA,spacing,...parameters)

Example

CF=SYM(EXP(i*U*((R-0.5*SIG^2)*T)-0.5*SIG^2*U^2*T))
F=EUROPEAN_FFT(CF,S0,100,R,0.03,T,1,ALPHA,1.5,N,4096,ETA,0.25,SIG,0.2,CF_RETURN,1)
EXTRACT(F,"diagnostics")
SLIDE(F)

Details

Pass a symbolic characteristic function first, followed by parameter/value pairs. Required keys in the inspected result implementation: S0, R, T, ALPHA, N, ETA; rates and volatility use decimals, N must be a power of two. Additional model parameters are passed to the characteristic function; CF_RETURN=1 denotes a return characteristic function. The active dispatcher constructs EuropeanFFTOperator(tool,args); this wrapper preserves that constructor rather than replacing the installed pricing engine. Named extracts below were verified against the supplied result source. Results include strike, call, put, implied volatility, raw/normalized density and CDF. Review diagnostics: finite grid, filtering and density clipping/normalization affect interpretation.

Available extracts

Save the command result in a variable, then use EXTRACT(result, "key"). Availability can depend on the input form and fitted model.

• matrix
• data
• all
• strike
• strikes
• call
• calls
• put
• puts
• price
• prices
• vol
• volatility
• impliedvolatility
• smile
• rawdensity
• density
• pdf
• cdf
• cumdensity
• cumulativedensity
• moments
• diagnostics
• stats
• summary
• parameters
• params
• cf
• characteristicfunction
• latex
• cflatex
• json
• tojson

In indexed patterns such as beta:n, replace n with the required index.