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MathGroup Archive 2005

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Re: Newbie question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54193] Re: Newbie question
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Sun, 13 Feb 2005 00:21:24 -0500 (EST)
  • References: <cukb9l$lns$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Have a look at "Optional arguments" in the Help Browser.

Steve Luttrell

<Email address removed at author's request> wrote in message 
news:cukb9l$lns$1 at smc.vnet.net...
>I use the Mathematica package below. The function that I call is
> HestonVanilla. This function has 13 arguments that I need to provide. I 
> want
> to change the programm, so that I do not have to give "lambda", "rf", "cp"
> and "G" each time I use the function. Instead I want that these arguments
> are always set to specific values, namely:
>
> lambda = 0
> rf =0
> cp = 1
> G = 0
>
> The reason for that is that, when I call the function from Excel I can 
> only
> have 9 arguments.
> I guess this is a piece of cake for someone familar with Mathematica.
>
> It would be great if someone could help me with that, since I need it
> urgently for my diploma thesis. Thank you!
>
>
>
>
> BeginPackage["Options`HestonVanilla`"]
>
> (************************************************************************************
> author: Uwe Wystup, wystup at mathfinance.de
> date  : November 1999
> *************************************************************************************)
> AuxFunc::usage = "computing the ingredients for HestonVanilla"
> HestonVanilla::usage = "Steven Heston's Stochastic Volatility Model\n
> to price European put and call options\n
> HestonVanilla[k,o,sigma,rho,lambda,r,rf,v,S,K,tau,cp,G]\n
> The input parameters are:\n
> k:      MeanReversion\n
> o:      LongRunVariance\n
> sigma:  VolaVolatility\n
> rho:    Correlation\n
> lambda: VolaRiskPremium\n
> r:      domestic RiskFreeRate\n
> rf:     foreign RiskFreeRate\n
> v:      CurrentVariance\n
> S:      AssetPrice\n
> K:      ExercisePrice\n
> tau:    ExpirationTime\n
> cp :    1 for call, -1 for put\n
> G:      Greek\n
>  0 : value\n
>  1 : spot delta\n
>  2 : spot gamma\n
>  3 : theta (in years)\n
>  4 : vega (wrt v)\n
>  5 : domestic rho\n
>  6 : foreign rho\n
>  7 : vomma (wrt v)\n
>  21: dual delta (wrt K)\n
>  22: dual gamma (wrt K)"
>
>
> Begin["`Private`"]
>
> AuxFunc[k_,o_,sigma_,rho_,lambda_,
> r_,rf_,v_,S_,K_,tau_,fi_] :=
>  Block[{u,a,b,x,rsf,d,g,cl,dl,f},
>  u = {0.5,-0.5};
>  a = k*o;
>  b = {k+lambda-rho*sigma, k+lambda};
>  x = Log[S];
>  rsf = rho*sigma*fi;
>
>  d = Table [
> Sqrt[(I*rsf - b[[j]])^2 -
> sigma^2*(2*I*u[[j]]*fi - fi^2)],
> {j,2}];
>
>  g = Table [
>  (b[[j]] - I*rsf + d[[j]]) /
> (b[[j]] - I*rsf - d[[j]]),
> {j,2}];
>
>  cl = Table [
> I*(r-rf)*fi*tau +
> (a/sigma^2)*((b[[j]]-I*rsf+d[[j]])*tau -
> 2*Log[(1-g[[j]]*Exp[d[[j]]*tau])/(1-g[[j]])]),
> {j,2}];
>
>  dl = Table [
> ((b[[j]] - I*rsf + d[[j]])/sigma^2) *
> ((1-Exp[d[[j]]*tau])/
>  (1-g[[j]]*Exp[d[[j]]*tau])),
> {j,2}];
>
>  f = Table [
> Exp[cl[[j]] + dl[[j]]*v + I*fi*x], {j,2}];
>
>  Table [{
>    Re[(Exp[-I*fi*Log[K]] * f[[j]])/(I*fi)],
>    Re[(Exp[-I*fi*Log[K]] * f[[j]])],
>    Re[(dl[[j]]*Exp[-I*fi*Log[K]] * f[[j]])/(I*fi)],
>    Re[(dl[[j]]*dl[[j]]*Exp[-I*fi*Log[K]] * f[[j]])/(I*fi)],
>    d[[j]],
>    f[[j]]
>    },{j,2}]];
>
>
> HestonVanilla[k_,o_,sigma_,rho_,lambda_,
> r_,rf_,v_,S_,K_,tau_,cp_,G_] :=
> Switch[G,
> 0, (*value*)
>     Block[{p,j},
>  p = Table[
>  0.5+(1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,1]], {fi,0.,100}],
>  {j,2}];
> S*Exp[-Log[1+rf]*tau]*(p[[1]]-(1-cp)/2)
> - K*Exp[-Log[1+r]*tau]*(p[[2]]-(1-cp)/2)],
> 1, (*delta*)
>     Block[{p,j},
>  p = Table[
>  0.5+(1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,1]], {fi,0.,100}],
>  {j,1}];
> Exp[-Log[1+rf]*tau]*(p[[1]]-(1-cp)/2)],
> 2, (*gamma*)
> Block[{dp,j},
>      dp=Table[
>  (1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,2]], {fi,0.,100}],
>  {j,1}];
> Exp[-Log[1+rf]*tau]/S*dp[[1]]],
> 3, (*theta*)
> 50000*
> (HestonVanilla[k,o,sigma,rho,lambda,r,rf,v,S,K,tau-0.00001,cp,0]
> -HestonVanilla[k,o,sigma,rho,lambda,r,rf,v,S,K,tau+0.00001,cp,0]),
> 4, (*vega*)
> Block[{dpv,j},
>   dpv=Table[
>  (1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,3]], {fi,0.,100}],
>  {j,2}];
> S*Exp[-Log[1+rf]*tau]*dpv[[1]]
> - K*Exp[-Log[1+r]*tau]*dpv[[2]]],
> 5, (*rho*)
> Block[{p,j},
>     p = Table[
>  0.5+(1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,1]], {fi,0.,100}],
>  {j,2,2}];
>     K*tau*Exp[-Log[1+r]*tau]*(p[[1]]-(1-cp)/2)/(1+r)],
> 6, (*rhof*)
> Block[{p,j},
>     p = Table[
>  0.5+(1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,1]], {fi,0.,100}],
>  {j,1}];
>     S*tau*Exp[-Log[1+rf]*tau]*((1-cp)/2-p[[1]])/(1+rf)],
> 7, (*vomma*)
> Block[{d2pv,j},
>  d2pv=Table[
>  (1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,4]], {fi,0.,100}],
>  {j,2}];
> S*Exp[-Log[1+rf]*tau]*d2pv[[1]]
> - K*Exp[-Log[1+r]*tau]*d2pv[[2]]],
> 21, (*dual delta*)
> Block[{p,j},
>     p = Table[
>  0.5+(1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,1]], {fi,0.,100}],
>  {j,2,2}];
> Exp[-Log[1+r]*tau]*((1-cp)/2-p[[1]])],
> 22, (*dual gamma*)
> Block[{dp,j},
>      dp=Table[
>  (1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,2]], {fi,0.,100}],
>  {j,2,2}];
> Exp[-Log[1+r]*tau]/K*dp[[1]]],
> 101, (* Real part *)
> Block[{dp,j},
>      dp=Table[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  2][[j,1]],
>  {j,2}];
> dp[[2]]],
> 111, (* d *)
> Block[{dp,j},
>      dp=Table[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  2][[j,5]],
>  {j,2}];
> dp[[2]]],
> 112, (*probability factors*)
>     Block[{p,j},
>  p = Table[
>  0.5+(1/N[Pi])*NIntegrate[
>  AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,
>  fi][[j,1]], {fi,0.,100}],
>  {j,2}];
> p[[1]]],
> 30, (*the Heston Integrand*)
> AuxFunc[k,o,sigma,rho,lambda,Log[1+r],Log[1+rf],v,S,K,tau,cp][[1,1]],
> _,0];
>
> End[]
>
> EndPackage[]
>
> 



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