Path-dependent options: extending the Monte Carlo simulation approach

Article Abstract:

A method extending Monte Carlo simulation is described to make it applicable not only to European-style but also American-style options. This approach requires the use of simulation to pinpoint optimal early-exercise rules through a comparison of the exercise value and the expected discounted value of holding, at different possible early-exercise dates. This comparison is possible at any individual date since it is completely forward-oriented, which means that it relies merely on knowing the current state and the future, which is open for simulation. The early-exercise conditions should be determined in a recursive fashion because the expected discounted value of holding is based on future exercise decisions. After the early-exercise conditions have been determined at each date, the conditions can then be used in the simulation, which is used for option value.

Monte Carlo method, Monte Carlo methods

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On the evaluation of compound options

Article Abstract:

Compound option valuation formulas contribute to the summation of a set of multi-normal distribution functions. An identity on totals of nested, multi-normal distributions of arbitrary dimension is presented. This identity generalizes some familiar low order identities for the multi-normal distribution. Three applications are presented for the new identity to contingent claims valuation problems. The first two applications demonstrate that significant reduction of the number of integrals to be evaluated means that speedier and more accurate algorithms can be produced for implementing the Geske-Johnson American put variation formula and the Roll-Geske-Whaley American call formula. The third application provides new economic insights into the valuation of disaggregated coupon bonds.

Bonds, Bonds (Securities)

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A Contango-Constrained model for storable commodity prices

Article Abstract:

A model of commodity price dynamics where the spot price changes between two separate stochastic processes under the risk neutral measure is presented.

United States, Forecasts, trends, outlooks, Forecasts and trends, Stochastic analysis, Market trend/market analysis, Commodity price indexes

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