XploRe Help : spdbs

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	finance
See also:	spdbl greeks

Quantlet:		spdbs
Description:		Using the assumptions of the Black-Scholes call-option pricing formula this quantlet calculates the Black- Scholes State-Price Density, Delta and Gamma from call-options data

Reference(s):

Ait-Sahalia, Y. and Lo, A.W. (1998). "Nonparametric estimation of state-price densities implicit in financial asset prices," Journal of Finance 53:499-547; Hull, 1999: Options, Futures and other Derivatives, Longman Higher Education

Usage:	`bsspd=spdbs(X,s,r,div,sigma,tau)`
Input:
	`X`	N x 1 vector of the terminal stock price (use strike price)
	`s`	N x 1 vector of the spot price
	`r`	N x 1 vector of the interest rate
	`div`	N x 1 vector of the dividend process
	`sigma`	N x 1 vector of the implied volatility
	`tau`	N x 1 vector of the time-to-maturity
Output:
	`bsspd.fbs`	N x 1 vector of Black-Scholes SPD
	`bsspd.delta`	N x 1 vector of Black-Scholes option delta
	`bsspd.gamma`	N x 1 vector of Black-Scholes option gamma

Example:

library("finance") data=read("XFGJan1997.dat") names=readm("XFGkeyJan1997.dat") date=names.text[,1] type=names.text[,2] l=list(date,type,data) ind=(l.date=="02.01.1997")&&(l.data[,2]==0.25)&&(l.type=="C") smdata=paf(l.data,ind) vola=smdata[,1] tau=smdata[,2] m=smdata[,3] r=smdata[,4]./100 s=smdata[,5] F=s.*exp(r.*tau) K=m.*F data=m~vola div=0 ;create a finer grid to match local polynomial SPD bw=0.001 m2=grid(min(m),bw,(max(m)-min(m))/bw+1) ;original strike grid only has 9 points ;the grid must be reconstructed to allow for the interpolated points ;multiply by the scalar mean(F) since for one day worth of options F remains constant k=m2.*mean(F) bsspd=spdbs(k,mean(s),mean(r),div,mean(vola),mean(tau)) ;rescaling SPD so it can be expressed in terms of moneyness r2=m2~(bsspd.fbs.*mean(F)) ;plotting Black-Scholes SPD res2 = setmask(r2, "line","blue") d=createdisplay(1,1) show(d,1,1,res2) title="Black-Scholes SPD: 02-01-1997 tau=0.25" xlabel="moneyness" ylabel="density" setgopt(d,1,1,"title",title,"xlabel",xlabel,"ylabel",ylabel)

Result:

Black-Scholes State-Price Density, Delta and Gamma for
January 2, 1997 with a time-to-maturity of 0.25 years
It also produces a plot of Black-Scholes SPD.

Author: K. Huynh, P. Kervella, W. Haerdle, 20010720 license MD*Tech