XploRe Help : plotITT

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:	grITTcrr grITTstsp grITTspd ITT

Quantlet:		plotITT
Description:		plots desired components of an implied trinomial tree

Reference(s):

Derman, E., Kani, I. and Chriss, N. (1996). Implied Trinomial Trees of the Volatility Smile. Journal of Derivatives, 4, pp. 7-22. Komorad, K. (2002). Implied Trinomial Trees and Their Implementation with XploRe.

Link:

Tutorial: ITT

Usage:	`plotITT(itree,what{,r{,text{,prtext}}})`
Input:
	`itree`	list; output of ITT(.) containing: Ttree - the Implied Trinomial Tree, P - the upper probabilities, Q - the lower probabilities, AD - the Arrow-Debreu prices, LocVol - the local volatilities, Onodes - the overwritten nodes, Oprobs - the overwritten probabilities and Time - the time vector.
	`what`	optional vector; with maximal 5 rows, the rows correspond to: (1) state space of the ITT, (2) transition probabilities, (3) tree of local volatilities, (4) the tree of the Arrow-Debreu prices and (5) the state price density. The row for each item which should be plotted must contain a non-zero element.
	`r`	optional scalar; interest rate, from interval (0,1), which is only needed when the state price density should be plotted.
	`text`	optional scalar; text = 1, the description of the tree nodes with the values of the underlying (default), text = 0 if no description is desired. Applicable only when the state space of the ITT should be plotted.
	`prtext`	optional scalar; prtext = 1, the description of the tree arrows with corresponding probabilities is shown, prtext = 0 for no description (default). Applicable only when the state space of the ITT should be plotted.

Note:

A plot of the corresponding implied trinomial tree will be returned. The tree is growing from the root on the left to the right hand side. Each tree node has a text label with the spot price. Any node which violates the forward condition is designated with a red rhombus. The tree arrows are denoted with the corresponding probability. If the original probability falls out of the interval (0,1) it will be overwritten and all three arrows are now magenta.

Example:

library("finance") library("plot") proc(sigma)=volafunc(S,K,time) sigma=0.15 +(S-K)/10 * 0.005 endp S = 100 ; current index level r = 0.1 ; compounded riskless interest rate div = 0.05 ; dividend yield time = 0|1|3|6 ; time vector t=ITT(S, r, div, time, "volafunc") plotITT(t,0|0|0|0|1,r) ; plot the state price density

Result:

A plot showing a blue state price density curve

Example:

library("finance") library("plot") proc(sigma)=volafunc(S,K,time) sigma=0.15 +(S-K)/10 * 0.01 endp S = 100 ; current index level r = 0.1 ; compounded riskless interest rate div = 0.05 ; dividend yield time = 0|3|5|6 ; time vector what = 0|1|1 ; plot the probabilities and loc. volatilities t=ITT(S, r, div, time, "volafunc") plotITT(t,what)

Result:

One display with the transition probabilities and
one display showing the local volatilities is plotted.

Author: K. Komorad, W. Haerdle, 20020326 license MD*Tech