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  • 1
    Monograph available for loan
    Monograph available for loan
    Mathematical methods for financial markets (2009)
    Dordrecht : Springer
    Details Availability
    Call number: PIK B 020-20-94151
    Type of Medium: Monograph available for loan
    Pages: XXV, 732 Seiten
    ISBN: 9781852333768 , 9781447125242
    Series Statement: Springer Finance
    Language: English
    Note: Contents: Continuous Path Processes ; Continuous-Path Random Processes: Mathematical Prerequisites ; Basic Concepts and Examples in Finance ; Hitting Times: A Mix of Mathematics and Finance ; Complements on Brownian Motion ; Complements on Continuous Path Processes ; A Special Family of Diffusions: Bessel Processes ; Jump Processes ; Default Risk: An Enlargement of Filtration Approach ; Poisson Processes and Ruin Theory ; General Processes: Mathematical Facts ; Mixed Processes ; Lévy Processes
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Electronic Resource
    Electronic Resource
    PRICING AND HEDGING DOUBLE-BARRIER OPTIONS: A PROBABILISTIC APPROACH (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 6 (1996), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Barrier options have become increasingly popular over the last few years. Less expensive than standard options, they may provide the appropriate hedge in a number of risk management strategies. In the case of a single-barrier option, the valuation problem is not very difficult (see Merton 1973 and Goldman, Sosin, and Gatto 1979). the situation where the option gets knocked out when the underlying instrument hits either of two well-defined boundaries is less straightforward. Kunitomo and Ikeda (1992) provide a pricing formula expressed as the sum of an infinite series whose convergence is studied through numerical procedures and suggested to be rapid. We follow a methodology which proved quite successful in the case of Asian options (see Geman and Yor 1992,1993) and which has its roots in some fundamental properties of Brownian motion. This methodology permits the derivation of a simple expression of the Laplace transform of the double-barrir price with respect to its maturity date. the inversion of the Laplace transform using techniques developed by Geman and Eydeland (1995), is then fairly easy to perform.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1996.tb00122.x
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  • 3
    Electronic Resource
    Electronic Resource
    On Some Exponential-Integral Functionals of Bessel Processes (1993)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 3 (1993), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper studies the moments of some exponential-integral functionals of Bessel processes, which are of interest in some questions of mathematical finance, including the valuation of perpetuities and Asian options.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1993.tb00090.x
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  • 4
    Electronic Resource
    Electronic Resource
    BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES (1993)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 3 (1993), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Using Bessel processes, one can solve several open problems involving the integral of an exponential of Brownian motion. This point will be illustrated with three examples. The first one is a formula for the Laplace transform of an Asian option which is “out of the money.”The second example concerns volatility misspecification in portfolio insurance strategies, when the stochastic volatility is represented by the Hull and White model. The third one is the valuation of perpetuities or annuities under stochastic interest rates within the Cox-Ingersoll-Ross framework. Moreover, without using time changes or Bessel processes, but only simple probabilistic methods, we obtain further results about Asian options: the computation of the moments of all orders of an arithmetic average of geometric Brownian motion; the property that, in contrast with most of what has been written so far, the Asian option may be more expensive than the standard option (e.g., options on currencies or oil spreads); and a simple, closed-form expression of the Asian option price when the option is “in the money,” thereby illuminating the impact on the Asian option price of the revealed underlying asset price as time goes by. This formula has an interesting resemblance with the Black-Scholes formula, even though the comparison cannot be carried too far.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.1993.tb00092.x
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  • 5
    Electronic Resource
    Electronic Resource
    Stochastic Volatility for Lévy Processes (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that are solutions to Ornstein-Uhlenbeck equations driven by one-sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean-corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean-corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one-dimensional marginal distributions of the level of the process at each future date.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00020
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  • 6
    Electronic Resource
    Electronic Resource
    Time Changes for Lévy Processes (2001)
    Boston, USA and Oxford, UK : Blackwell Publishers Inc
    Mathematical finance 11 (2001), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The goal of this paper is to consider pure jump Lévy processes of finite variation with an infinite arrival rate of jumps as models for the logarithm of asset prices. These processes may be written as time-changed Brownian motion. We exhibit the explicit time change for each of a wide class of Lévy processes and show that the time change is a weighted price move measure of time. Additionally, we present a number of Lévy processes that are analytically tractable, in their characteristic functions and Lévy densities, and hence are relevant for option pricing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00108
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  • 7
    Electronic Resource
    Electronic Resource
    PASSPORT OPTIONS (2002)
    Oxford, UK : Blackwell Publishing Ltd
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We relate the theory of passport options with general principles from martingale theory as well as with the theory of Bessel processcs. The calculation of the price of a passport option leads to an equality between two norms on continuous martingales. We also solve the discrete time case for passport options.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9965.2002.tb00126.x
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  • 8
    Electronic Resource
    Electronic Resource
    Some independence results related to the arc-sine law (1996)
    Springer
    Journal of theoretical probability 9 (1996), S. 447-458 
    Details
    ISSN: 1572-9230
    Keywords: Arc-sine law ; Lévy process ; local time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide proofs for recent results of Getoor and Sharpe on the distribution of local times on rays for certain planar Lévy processes which were invalidated by an appeal to an incorrect assertion. Our arguments rely on independence properties related to the arc-sine law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02214659
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  • 9
    Electronic Resource
    Electronic Resource
    Lévy processes in finance: a remedy to the non-stationarity of continuous martingales (1998)
    Springer
    Finance and stochastics 2 (1998), S. 399-408 
    Details
    ISSN: 1432-1122
    Keywords: Key words:Levy processes, martingales with stationary increments, forward-start-options JEL classification: G13 Mathematics Subject Classification (1991):90A09, 60J60, 60H30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. In this note, we prove that under some minor conditions on $\sigma$ , if a martingale $X_t = \int_0^t \sigma_u dW_u $ satisfies, for every given pair $u \geq 0, \, \xi \geq 0$ , $X_{u+\xi}-X_u{\mathop{=}^{\mathrm{(law)}}} X_{\xi},$ then necessarily, $|\sigma_u|$ is a constant and X is a constant multiple of a Brownian motion, thus providing a partial analogue of Lévy's characterisation of Brownian motion. In the introduction we explain why this theorem is a reason for considering Lévy processes in finance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007800050047
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  • 10
    Electronic Resource
    Electronic Resource
    A decomposition of Bessel Bridges (1982)
    Springer
    Probability theory and related fields 59 (1982), S. 425-457 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00532802
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