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 \si t is observed through an observation process Y t subject to random error. A price formula and a PDE are then derived regarding the stock price S t and the observation process Y t as parameters. Finally, we assume that S 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.
Applied Mathematics and Optimization – Springer Journals
Published: Jan 1, 2001
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