Apparatus and method of pricing financial derivatives
AssigneeThe Johns Hopkins University
InventorsJong-Shi Pang, Jacqueline Huang
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Abstract
An apparatus for and method of determining the price of financial derivatives such as options. One preferred embodiment of the invention employs a discretized partial differential linear complementarity problem (PDLCP) based system to determine the forward pricing of financial instruments such as vanilla American options. In this embodiment, an optimization problem in the form of a mathematical program with equilibrium constraints (MPEC) is implemented to derive implied volatilities of the assets underlying the subject derivatives. The implied volatilities thus derived are used as inputs in the PDLCP-based system to accurately determine the forward pricing of the subject derivatives.
Claims20
A method of pricing a financial derivative whose value is based on an underlying asset, the method comprising the steps of:
- retrieving input data used to generate a forward price of the financial derivative;
- using a computer to calculate implied volatility of the underlying asset, wherein said calculating step is an optimization process in the form of a mathematical program with equilibrium constraints (MPEC) used to derive the implied volatility of the underlying asset;
- generating a forward price of the financial derivative based on retrieved input data and the calculated implied volatility;
- and
- issuing a report to a user including the forward price generated.
A process of implementing a forward pricing model, the process comprising the steps of:
- using a computer to generate inputs to a forward pricing model from an inverse of said forward pricing model;
- applying said inputs to said forward pricing model;
- applying a finite difference scheme to approximate the partial differential equation of a financial derivative price model having an unknown price variable and at least one unknown input that is not said unknown price variable;
- solving said approximation to obtain a solution for said unknown price of variable;
- further solving said solution for said at least one unknown input to said solution to provide at least one known input;
- and
- applying said at least one known input to said financial derivative price model.
An apparatus for pricing a financial derivative whose value is based on an underlying asset, the apparatus comprising:
- a processing unit;
- and
- a memory, wherein a computer program is stored for execution by said processing unit to derive a forward price of the financial derivative based on a solution of an inverse pricing process, wherein the solution of the inverse pricing process produces implied volatilities of the underlying asset by minimizing an objective function.
A financial instrument engine comprising:
- a data source retrieving data from external sources;
- a user interface device inputting data from a user;
- a volatility calculator calculating volatility utilizing an optimization of a mathematical program with equilibrium constraints (MPEC);
- and
- a forward pricing unit, coupled to said data source, said user interface device, and said volatility calculator, determining forward pricing of a financial instrument based on data input to said forward pricing unit, wherein said forward pricing unit determines a projected value of the financial instrument based in part on the volatility calculated by said volatility calculator.
An article of manufacture comprising a machine-readable storage medium having stored therein indicia of a plurality of machine-executable control program steps, the control program comprising the steps of:
- (a) inputting pricing data used in the calculation of a forward price of a financial derivative, including an observed trading price;
- (b) determining an initial theoretical price based on the pricing data received in said inputting step (a);
- (c) calculating implied volatility data based on the pricing data input in said inputting step (a) and the initial theoretical price determined in said determining step (b), wherein said calculating step (c) comprises the substep of optimizing an objective function representing the difference between the observed trading price and the initial theoretical price;
- (d) generating a final theoretical price of the financial derivative based on the implied volatility data calculated in said calculating step (c);
- and
- (e) issuing user reports containing the final theoretical price generated in said generating step (d).
Dependencies are inferred from the claim text.