Question: The trinomial tree is an improvement over the binomial tree model, where the stock price can transition into three states S { dS,S,uS } .
The trinomial tree is an improvement over the binomial tree model, where
the stock price can transition into three states
S
{
dS,S,uS
}
. See page
466 in Hull. The relevant equations are reproduced below.
Trinomial tree model.
The trinomial tree model allows a transition into
three possible price states:
S
(
uS,S,dS
), where
(1)
u
=
e
3
t
, d
=
e
3
t
with probabilities
(2)
p
d
=
t
12
2
(
r
q
1
2
2
) +
1
6
, p
m
=
2
3
, p
u
=
t
12
2
(
r
q
1
2
2
) +
1
6
.
Consider a 3-month American put option on a non-dividend-paying stock
when the stock price is $60, the strike price is $60, the risk-free interest rate
is 5% per annum (continuously compounded) and the volatility is 25%.
Price the option on a trinomial tree with time interval 1 month. (3 steps)
You can implement the tree for example in Excel.
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