This paper studies stock options pricing in the presence of the stochastic deviations in bond prices. The martingale measure is not unique for this market, and there are non-replicable claims. It is shown that arbitrarily small deviations cause significant changes in the market properties. In particular, the martingale prices and the second moment of the hedging error can vary significantly and take extreme values, for some extreme choices of the  martingale measures. The paper suggests ad discusses some choices of the martingale measures .
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the num\'eraire process causes significant changes in the market properties. In particular, an equivalent martingale measure is not unique for this market, and there are non-replicable claims. The martingale prices and the hedging error can vary significantly and take extreme values, for some extreme choices of the equivalent martingale measures. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from observed bond prices. This allows to calculate the implied market price of risk process .
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paper studies stock options pricing in
papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that
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the
arbitrarily small
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bond prices. The
the evolution of the num\'eraire process causes significant changes in the market properties. In particular, an equivalent
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It is shown that arbitrarily small deviations cause significant changes in the market properties. In particular, the
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second moment of the
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equivalent
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The paper suggests ad discusses some
Some rational
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martingale measures
equivalent martingale measures are suggested and discussed, including implied measures calculated from observed bond prices. This allows to calculate the implied market price of risk process