Pricing rule based on non-arbitrage arguments for random volatility and volatility smile

@article{Dokuchaev2002PricingRB,
  title={Pricing rule based on non-arbitrage arguments for random volatility and volatility smile},
  author={Nikolai Dokuchaev},
  journal={Social Science Research Network},
  year={2002}
}
  • N. Dokuchaev
  • Published 10 May 2002
  • Economics, Mathematics
  • Social Science Research Network
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that gives Black-Scholes price for at-money options and such that the market is arbitrage free for any number of tradable options, even if there are two Brownian motions only: one drives the stock price, the other drives the volatility process. This problem is… 
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