[an error occurred while processing this directive]
[an error occurred while processing this directive]

###
Problem Statement

A stock price is currently $40. It is known that at the end
of 3 months, it will either $45 or $34. The risk-free rate of
interest with quarterly compounding on a $1 bond is 8% per
annum. Calculate the value of a 3-month European put option
on the stock with a strike price of $40, and find the
replicating portfolio.

###
Solution

The payoffs are f(SU) = max(40 -SU, 0)
= 0 and f(SD) = max(40 -SD, 0)
= 6.

A replicating portfolio must satisfy:

Solving this system we obtain that = -0.54545 and = 24.06, so we short -0.54545
shares of stock, and own 24.06
worth of bonds. The value of the portfolio and therefore the
option is then phiS + = 2.25.

We can also figure the value from the risk-neutral measure,
namely

and

and so

Back to main section with
problem statement

[an error occurred while processing this directive]
[an error occurred while processing this directive]

Last modified: [an error occurred while processing this directive]