| Library: | finance |
| See also: | bitree IBTdk IBTbc IBTlocsigma IBTsdisplot |
| Quantlet: | IBTvolaplot | |
| Description: | shows the implied local volatility surface sigma(S,tau) in the implied tree at different time and stock price levels |
| Usage: | IBTvolaplot(loc, step, startpoint, endpoint, m) | |
| Input: | ||
| loc | Matrix: 3 columns, which contain the stock prices, the time to expiration (by year), the estimated local implied volatility | |
| step | scalar: the bandwidth of the time interval | |
| startpoint | scalar: the startpoint giving the lowest limit in the strike dimension of the volatility surface | |
| endpoint | scalar: the startpoint giving the highest limit in the strike dimension of the volatility surface | |
| m | scalar: the number of the steps to be estimated | |
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=IBTdk(S, r, lev, expiration, "volafunc")
ptree=ibtree.Tree
prob=ibtree.prob
deltat=expiration/lev
m=20
loc=IBTlocsigma(ptree, prob,m, deltat)
startpoint=50
endpoint=150
n=10
step=0.5
IBTvolaplot(loc, step, startpoint, endpoint, n)
a surface plot to show the local implied volatility in implied tree changing with time and stock price levels