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The lattice approaches for pricing path-dependent mortgage-related products

Liou, Ching-Pin
http://rave.ohiolink.edu/etdc/view?acc_num=case1057678646

Abstract Details

1994, Doctor of Philosophy, Case Western Reserve University, Operations Research.
Mortgages can be viewed as risk-free assets plus various contingent claims, which are frequently modeled as options. Based on arbitrage arguments, and the characteristics of the particular mortgage analyzed, one can derive a partial differential equation for the mortgage. The exact form of the valuation equation and the methods required to solve it depend on the type of stochastic process used to model the underlying uncertainties. In general, no closed-form solutions can be obtained to the partial differential equations for these mortgage-related products. Numerical methods must be employed. Numerical methods for pricing contingent claims may be classified as forward based or backward based. For example, the most common technique, Monte Carlo simulation, is forward based. However, forward based methods cannot be applied to all types of mortgage-related products, because some option features embedded in these contracts, such as termination of the contract before it matures, depend critically on assessing future cash flows. Backward based methods, such as the lattice approaches, overcome such difficulty. In particular, the lattice approaches can be readily modified to incorporate additional option like features. However, backward based methods have difficulty in dealing with path dependence sinc e cash flows depending on state variables occurring earlier in time cannot be determined. The purpose of this thesis is to develop lattice-based models for pricing the following path-dependent mortgage-related products: GNMA pass-throughs, index amortization swaps, lookback mortgages, and adjustable-rate mortgages. For these products, we show the history of the process, relevant for pricing, can be captured by a single additional state variable. Specifically, this additional statistic, together with the current interest rate is sufficient for capturing all information along the path. The usual single variable lattice based models are then adapted to handle two state variables and dynamic programming is used to obtain values.
Peter Ritchken (Advisor)
176 p.
lattice approaches; pricing; path-dependent; mortgage-related

Recommended Citations

Citations

  • Liou, C.-P. (1994). The lattice approaches for pricing path-dependent mortgage-related products [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1057678646

    APA Style (7th edition)

  • Liou, Ching-Pin. The lattice approaches for pricing path-dependent mortgage-related products. 1994. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1057678646.

    MLA Style (8th edition)

  • Liou, Ching-Pin. "The lattice approaches for pricing path-dependent mortgage-related products." Doctoral dissertation, Case Western Reserve University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=case1057678646

    Chicago Manual of Style (17th edition)

case1057678646
496
© 1994, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.