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  • Articles  (5)
  • Other Sources
  • Blackwell Publishers, Inc.,  (5)
  • 2000-2004  (5)
  • 1985-1989
  • 2002  (5)
  • Mathematics  (5)
  • 1
    Electronic Resource
    Electronic Resource
    A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options (2002)
    Oxford, UK : Blackwell Publishers, Inc.,
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we consider a Black and Scholes economy and show how the Malliavin calculus approach can be extended to cover hedging of any square integrable contingent claim. As an application we derive the replicating portfolios of some barrier and partial barrier options.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.02007
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    [ohne Titel] (2002)
    Oxford, UK : Blackwell Publishers, Inc.,
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound is sharp for the optimal choice of Lagrangian martingale. As a first exploration of this method, four examples are investigated numerically; the accuracy achieved with even very simple choices of Lagrangian martingale is surprising. The method also leads naturally to candidate hedging policies for the option, and estimates of the risk involved in using them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.02010
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  • 3
    Electronic Resource
    Electronic Resource
    [ohne Titel] (2002)
    Oxford, UK : Blackwell Publishers, Inc.,
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The paper presents some security market pricing results in the setting of a security market equilibrium in continuous time. The theme of the paper is financial valuation theory when the primitive assets pay out real dividends represented by processes of unbounded variation. In continuous time, when the models are also continuous, this is the most general representation of real dividends, and it can be of practical interest to analyze such models. 
Taking as the starting point an extension to continuous time of the Lucas consumption-based model, we derive the equilibrium short-term interest rate, present a new derivation of the consumption-based capital asset pricing model, demonstrate how equilibrium forward and futures prices can be derived, including several examples, and finally we derive the equilibrium price of a European call option in a situation where the underlying asset pays dividends according to an Itô process of unbounded variation. In the latter case we demonstrate how this pricing formula simplifies to known results in special cases, among them the famous Black–Scholes formula and the Merton formula for a special dividend rate process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.02006
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  • 4
    Electronic Resource
    Electronic Resource
    [ohne Titel] (2002)
    Oxford, UK : Blackwell Publishers, Inc.,
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the delta-gamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution. Because the quadratic approximation may not always yield accurate VAR estimates, we also develop a low variance Monte Carlo method. This method uses the quadratic approximation to guide the selection of an effective importance sampling distribution that samples risk factors so that large losses occur more often. Variance is further reduced by combining the importance sampling with stratified sampling. Numerical results on a variety of test portfolios indicate that large variance reductions are typically obtained. Both methods developed in this paper overcome difficulties associated with VAR calculation with heavy-tailed risk factors. The Monte Carlo method also extends to the problem of estimating the conditional excess, sometimes known as the conditional VAR.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00141
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  • 5
    Electronic Resource
    Electronic Resource
    [ohne Titel] (2002)
    Oxford, UK : Blackwell Publishers, Inc.,
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate D to the interest rate r. For D〉r the put boundary near expiry tends parabolically to the value rK/D where K is the strike price, while for D≤r the boundary tends to K in the parabolic-logarithmic form found for the case D=0 by Barles et al. (1995) and by Kuske and Keller (1998). For the call, these two behaviors are interchanged: parabolic and tending to rK/D for D〈r, as was shown by Wilmott, Dewynne, and Howison (1993), and parabolic-logarithmic and tending to K for D≥r. The results are derived twice: once by solving an integral equation, and again by constructing matched asymptotic expansions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.02008
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