| Library: | finance |
| See also: | bitree IBTdk BlackScholes IBTsdisplot IBTlocsigma IBTvolaplot IBTresort IBTnicemat |
| Quantlet: | IBTbc | |
| Description: | starting program to calculate the stock price on the nodes in the implied binomial tree, the tree of transition probabilities and the tree of Arrow-Debreu prices using Barle and Cakici's method. |
| Usage: | z = IBTbc(S, r, lev, expiration, volafunc) | |
| Input: | ||
| S | scalar: the underlying asset price | |
| r | scalar: riskless interest rate | |
| lev | scalar: the number of time levels to be chosen | |
| expiration | scalar: time to expiration of the stock | |
| volafunc | text string: name of procedure where the function is used to define how the Black Scholes implied volatilities change with time to expiration and strike price | |
| Output: | ||
| z.Tree | Matrix: (lev+1)x(lev+1), the first j elements at jth column are corresponding to the stock prices of the nodes at jth level in the implied tree | |
| z.prob | Matrix: (lev)x(lev), the first j elements at jth column are corresponding to the transition probability of the nodes at (j-1)th level in the implied tree, only can be obtained up to (lev)th level | |
| z.lb | Matrix: (lev+1)x(lev+1), the first j elements at jth column are corresponding to the Arrow-Debreu price of the nodes at jth level in the implied tree | |
library("finance")
proc(sigma)=volafunc(K, S, time)
sigma=0.1+(S-K)/S/10*0.5
endp
r=0.03
S=100
lev=4
expiration=4
ibtree=IBTbc(S, r, lev, expiration, "volafunc")
ptree=IBTresort(ibtree.Tree)
prob=IBTresort(ibtree.prob)
lb=IBTresort(ibtree.lb)
IBTnicemat("stock price", ptree, 3)
IBTnicemat("transition probability", prob, 3)
IBTnicemat("Arrow-Debreu price", lb, 3)
Output is an implied binomial tree for the price process of the underlying, a tree of transition probabilities and a tree of Arrow-Debreu prices stock price . 151.418 . 138.725 . 127.046 132.058 . 111.470 119.328 . 100.000 106.184 112.750 . 95.258 100.330 . 84.056 92.559 . 79.529 . 71.138 transition probability . 0.563 . 0.597 . 0.416 0.529 . 0.480 0.478 . 0.637 0.536 . 0.341 . 0.505 Arrow-Debreu price . 0.060 . 0.109 . 0.188 0.221 . 0.466 0.341 . 1.000 0.576 0.338 . 0.504 0.350 . 0.177 0.213 . 0.114 . 0.055