Could anyone advice on the following problem, please?:
The US company BLUECHIP INC has a stock whose price (in USD) evolves according to
dS(t)/S(t)= μdt + σdz(t);
where μ and σ are constants, and z(t) is a standard Brownian motion.
A broker firm has introduced a new type of derivative, which they call a "quadratic log." At maturity (T), the holder of a quadratic log will receive the amount USD ln[S(T)^2].
Determine the arbitrage free price (in USD) at time t that belongs to[0; T) of a quadratic log, given that the price of the BLUECHIP stock is USD s. Assume a constant instantaneous US interest rate r.
Start "from scratch" by forming a replicating portfolio and show every
step in your calculations.
thanks in advance.