We are asked to calculate the price of a 2 year euro put option with strike price .92 on a 1 year zero coupon bond using the following binomial tree with each period is one year.
---------------.14
-------.12
.1------------- .1
--------.08
---------------.06
They solve like this:
Premium = .25*((e^-.22)* value at uu + ((e^-.22) + (e^-.18)) * value at ud)
(we calculate that value at dd = 0).
I solved it the way we usually solve binomial tree problems, where I calculate the value at the 2nd period, upper value = .02977 (from .5*(e^-.12) * (value of uu + value of ud) and lower value = .007 (from .5*(e^-.08) * (value of ud + value of dd) , and then discount this back by e^0.1 to get the value.
I find that my answer is .01664, where their answer doing it their way is .016369.
Is the only difference due to rounding? Or is my approach incorrect?
---------------.14
-------.12
.1------------- .1
--------.08
---------------.06
They solve like this:
Premium = .25*((e^-.22)* value at uu + ((e^-.22) + (e^-.18)) * value at ud)
(we calculate that value at dd = 0).
I solved it the way we usually solve binomial tree problems, where I calculate the value at the 2nd period, upper value = .02977 (from .5*(e^-.12) * (value of uu + value of ud) and lower value = .007 (from .5*(e^-.08) * (value of ud + value of dd) , and then discount this back by e^0.1 to get the value.
I find that my answer is .01664, where their answer doing it their way is .016369.
Is the only difference due to rounding? Or is my approach incorrect?
ASM Exercise 25.5 Pricing Option from binomial tree of interest rates