# Asset Pricing with Stochastic Volatility

Asset Pricing with Stochastic Volatility 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Asset Pricing with Stochastic Volatility

, Volume 43 (1) – Jan 1, 2001
16 pages

/lp/springer_journal/asset-pricing-with-stochastic-volatility-xUeH63wlKI
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002450010018
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2001

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