| Library: | finance |
| See also: | bitree IBTdk IBTbc IBTlocsigma IBTvolaplot |
| Quantlet: | IBTsdisplot | |
| Description: | plots a smoothed estimation of the implied probability distribution estimated by implied binomial tree |
| Usage: | mf = IBTsdisplot(dat, bandwidth) | |
| Input: | ||
| dat | matrix: two columns, the first column contains the stock prices of different nodes at a given level, the second column the probability taken at the corresponding nodes | |
| bandwidth | scalar: the bandwidth for estimating the density function | |
| Output: | ||
| mf | matrix: two columns, the first column is a grid and the second column contains the density estimation on that grid | |
library("finance")
proc(sigma)=volafunc(K, S, time)
sigma=0.1+(S-K)/S/10*0.5
endp
r=0.03 ; riskless annual interest rate
S=100 ; the underlying asset price
lev=20 ; the number of time steps
expiration=5 ; time to expiration
ibtree=IBTbc(S, r, lev, expiration, "volafunc")
dat=ibtree.Tree[,lev+1]~ibtree.lb[,lev+1]*exp(r*expiration)
bandwidth=10
mf=IBTsdisplot(dat, bandwidth)
Output is a density estimation plot of the implied risk-neutral stock price distribution at fifth year, which is computed from the implied binomial tree.