IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Efficient Path-Dependent Valuation Using Lattices: Fixed and Floating Strike Asian Options

Listed author(s):
  • Allen Abrahamson
Registered author(s):

    A lattice-based method is advanced for evaluating functionals of sequences of path-wise values of a lattice's state variable. For the Asian call valuations in this paper, the lattices discretely replicate the stochastic future states of conventionally prescribed, lognormally distributed, equity values. The Asian call valuations have the same level of precision as do valuations arising from numerical solutions based on the derivatives' governing partial differential equations or from high-confidence Monte Carlo, but are accomplished without the significant computer time and sophisticated software which attend those calculations. The method is termed SCEV induction, for "State Conditional Expected Value." By rolling forward through the lattice, expected values of prescribed functionals of the path-wise levels attained by the state variable are defined for all paths to every state individually. For Asian options, the method establishes the first few moments of the arithmetic average of a stock price, both conditionally for each expiry state, and unconditionally as well. These moments are used to define a proxy for the unspecifiable conditional distributions of the average, and applying the payoff rule numerically to the proxy ultimately provides the valuation. The results are compared with published values for options with continuous averaging over a range of strike, volatility, and riskless rate. To affect convergence of value from discrete-step lattices to the limiting case, an extrapolation method provides rapid convergence to the results in the continuous dynamic. Since state-conditional valuations are an intermediate step, then appropriate expiry state-dependent modification of the payoff rules provides floating strike Asian call valuation in the same framework, and the same precision, as for the fixed strike valuations. Application of SCEV induction to path-dependent cash flows of fixed income securities is discussed, particularly with regard to the valuation issues entailed in mortgage backed securities.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: no

    Paper provided by EconWPA in its series Finance with number 0305005.

    in new window

    Length: 39 pages
    Date of creation: 21 May 2003
    Handle: RePEc:wpa:wuwpfi:0305005
    Note: Type of Document - PDFLatex; prepared on IBM PC; to print on Laser Printers; pages: 39 ; figures: 1, inline. PDF with hyperlinks
    Contact details of provider: Web page:

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    in new window

    1. Allen Abrahamson, 2003. "A Note on Constructing 50-50 Step Probability Binomial Lattices to Replicate Wiener Diffusion," Finance 0305004, EconWPA, revised 17 May 2003.
    2. Vicky Henderson & David Hobson & William Shaw & Rafal Wojakowski, 2003. "Bounds for Floating-Strike Asian Options using Symmetry," OFRC Working Papers Series 2003mf04, Oxford Financial Research Centre.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:0305005. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.