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  • Blackwell Publishers Inc.  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Arbitrage with Fractional Brownian Motion (1997)
    Oxford, UK and Boston, USA : Blackwell Publishers Inc.
    Mathematical finance 7 (1997), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model long–range dependence of returns while avoiding arbitrage.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00025
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Complete Models with Stochastic Volatility (1998)
    Oxford, UK and Boston, USA : Blackwell Publishers Inc.
    Mathematical finance 8 (1998), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent options prices.We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00043
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  • 3
    Electronic Resource
    Electronic Resource
    The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates (1997)
    Oxford, UK and Boston, USA : Blackwell Publishers Inc.
    Mathematical finance 7 (1997), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: It is possible to specify a model for interest rates in various ways, by giving the dynamics of the spot rate or of the forward rates, for example. A less well–developed approach is to specify the law of the state–price density process directly. In abstract, the state–price density process is a positive supermartingale, and the theory of Markov processes provides a rich framework for the generation of examples of such things. We show how this can be done, and provide simple examples (some familiar, some new) where prices of derivatives can be computed very easily. One benefit of the potential approach is that it becomes very easy to model the yield curve in many countries at once, together with the exchange rates between them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00029
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    Paper (German National Licenses)
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