00:01
We're given that the current future prices, if not, is 90.
00:05
The time to maturity is 0 .75 years because that's nine months, 9 out of 12.
00:12
The volatility, sigma, is 0 .28.
00:16
The risk -free rate r is 3%.
00:19
That's 0 .03 is a decimal with continuous compounding.
00:23
And the number of steps is 3.
00:26
Since it's a three -step tree over nine months, then the change in t would be 0 .75 over 3, which is 0 .25 years.
00:37
The up and down factors, u and d, are based on volatility.
00:41
U is equal to e to the sigma square root delta t, which would be e to the 0 .28 square root.
00:49
0 .25.
00:50
Let me get that in a calculator.
00:54
About 1 .15 and d is 1 over u.
01:08
So 1 over 1 .15 is about 0 .87.
01:17
Now, since it's a futures option, the formula for the risk neutral probability, p is e to the r delta t minus d over u minus d.
01:34
So that would be e to the 0 .03 times 0 .25 minus 0 .87 over 1 .15 minus 0 .87.
01:51
Get that in.
02:05
0 .491.
02:13
And if we build the price tree starting at f equals 90 and build up, up, down moves over three steps...