This paper studies pricing of stock options for the case when the evolution of the risk-free assets or bond is stochastic . We show that, in the typical scenario, the martingale measure is not unique , that there are non-replicable claims , and that the martingale prices can vary significantly; for instance, for a European put option, any positive real number is a martingale price for some martingale measure. In addition, the second moment of the hedging error for a strategy calculated via a given martingale measure can take any arbitrary positive value under some equivalent measure. Some reasonable choices of martingale measures are suggested, including a measure that ensures local risk minimizing hedging strategy .
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 .
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pricing of stock options for the case when the evolution of the risk-free assets or bond is stochastic . We show that, in the typical scenario, the
stock options pricing in the presence of the stochastic deviations in bond prices. The
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, that
for this market, and
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, and that the martingale prices can vary significantly; for instance, for a European put option, any positive real number is a martingale price for some martingale measure. In addition, the
. It is shown that arbitrarily small deviations cause significant changes in the market properties. In particular, the martingale prices and the
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for a strategy calculated via a given martingale measure can take any arbitrary positive value under some equivalent measure. Some reasonable choices of martingale measures are suggested, including a measure that ensures local risk minimizing hedging strategy
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