A Barrier Option of American.

In this paper we study the asset pricing problem when the volatility is random. First, we derive a PDE for the risk-minimizing price of any contingent claim. Secondly, we assume that the volatility process at is observed through an observation process Y[sub t] subject to random error. A price formula and a PDE are then derived regarding the stock price S[sub t] and the observation process Y[sub t] as parameters. Finally, we assume that S[sub t] is observed. In this case we have a complete market and any contingent claim is then priced by an arbitrage argument instead of by risk-minimizing. [ABSTRACT FROM AUTHOR]