Tree on paths method and system for modeling securities
First Claim
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1. A electronic programmed computer implemented method for approximating distribution of a Stochastic process for modeling derivative securities, the method comprising the steps of:
- specifying a stochastic process for an underlying state variable;
using Monte Carlo simulations, by a computer, to generate a plurality of paths corresponding to the underlying state variable, each of the plurality of paths comprising states that represent future evolutions of the underlying state variable for a given time period through a given maturity date;
generating a tree using a computer, based upon the plurality of paths, the tree comprising a recombining of states of the plurality of paths at each of a plurality of time layers, wherein the recombining for a given time layer determines a set of closest generated states for the given time layer as compared to a previous time layer, and applies a transition probability to link the set of closest generated states for the given time layer to a previous state; and
wherein the underlying state variable is a primary state variable having a corresponding secondary state variable, and wherein specifying the stochastic process, using the Monte Carlo simulations, and generating the tree implement the primary state variable and the secondary state variable and using the generated tree to evaluate derivative securities.
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Abstract
A system for implementing a tree on paths method for generating a recombining interest rate tree from previously generated paths. The inventive method is a tree on paths method whereby a tree is created from previously generated paths. The tree on paths method uses Monte Carlo simulations to generate paths and uses a recombining algorithm to obtain a computationally efficient tree from the generated paths.
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Citations
11 Claims
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1. A electronic programmed computer implemented method for approximating distribution of a Stochastic process for modeling derivative securities, the method comprising the steps of:
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specifying a stochastic process for an underlying state variable; using Monte Carlo simulations, by a computer, to generate a plurality of paths corresponding to the underlying state variable, each of the plurality of paths comprising states that represent future evolutions of the underlying state variable for a given time period through a given maturity date; generating a tree using a computer, based upon the plurality of paths, the tree comprising a recombining of states of the plurality of paths at each of a plurality of time layers, wherein the recombining for a given time layer determines a set of closest generated states for the given time layer as compared to a previous time layer, and applies a transition probability to link the set of closest generated states for the given time layer to a previous state; and
wherein the underlying state variable is a primary state variable having a corresponding secondary state variable, and wherein specifying the stochastic process, using the Monte Carlo simulations, and generating the tree implement the primary state variable and the secondary state variable and using the generated tree to evaluate derivative securities. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A non transitory computer-readable medium having program code stored therein for approximating distribution of a stochastic process in modeling derivative securities, the program code including instructions which, when executed by a computer, perform operations comprising:
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specifying a stochastic process for an underlying state variable; using Monte Carlo simulations, by a computer, to generate a plurality of paths corresponding to the underlying state variable, each of the plurality of paths comprising states that represent future evolutions of the underlying state variable for a given time period; generating a tree, using a computer, based upon the plurality of paths, the tree comprising a recombining of states of the plurality of paths at each of a plurality of time layers, wherein the recombining for a given time layer determines a set of closest generated states for the given time layer as compared to a previous time layer, and applies a transition probability to link the set of closest generated states for the given time layer to a previous state; and
wherein the underlying state variable is a primary state variable having a corresponding secondary state variable, and wherein specifying the stochastic process, generating the Monte Carlo simulations, and generating the tree implement the primary state variable and the secondary state variable and using the tree to evaluate the derivative security. - View Dependent Claims (10, 11)
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Specification