| 3181. |
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| 3182. |
- Nohrouzian, Hossein, 1980-
(författare)
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A Cubature Method for Solving Stochastic Equations : A Modern Monte-Carlo Approach with Applications to Financial Market
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Before the financial crisis started in 2007, there were no significant spreads between the forward rate curves constructed either using the market quotes of overnight indexed swaps or those of forward rate agreements. After the crisis, we observe such spreads in the form of forward spread curves.In a popular approach pioneered by Heath, Jarrow, and Morton, the above curves satisfy a system of infinite-dimensional stochastic integral equations. In fact, the solution is a random field, or a random function of two real variables. By fixing the value of the second variable, one obtains a finite set of random forward spread curves, one for each maturity. Varying the above value generates the curves “in motion”.A standard approach to solve such a system is to replace it by a “discrete” version in the following order: first introduce discrete space, then discrete time, and finally, a discrete set of solutions. A modern approach starts by introducing a discrete space of solutions called a “cubature formulae on Wiener space”. An advantage of the modern approach is that the obtained system of equations becomes deterministic rather than stochastic and may be easily solved by standard finite-difference or finite-element methods.The thesis contains the followings new important results. The market model under consideration is large, that is, it includes infinitely many financial instruments. We reviewed existing approaches for finding conditions of no arbitrage on such a market with only one forward spread curve. First, we extended one of the approaches to the case of multiple curves and proved sufficient conditions for absence of arbitrage on such a large market. Second, we found conditions under which the solution to our system of equations is unique and non-negative. Third, using the theory of free Lie algebra, we found new cubature formulae on Wiener space and extensively tested them using the celebrated Black–Scholes equation as an input. Forth, using the results of cubature formula of degree 5, we evaluated the forward and short rates in the Heath–Jarrow–Morton and Hull–White (one-factor) models. Finally, using the same results, we constructed a new trinomial tree model for Black–Scholes–Merton and Black models.In future research, we plan to apply the obtained formulae to solve some systems of infinite-dimensional stochastic equations describing mathematical models of spread curves. Further, we plan to use the obtained formulae to deal with backward stochastic differential equations.
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| 3183. |
- Nohrouzian, Hossein, 1980-, et al.
(författare)
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An Arbitrage-Free Large Market Model for Forward Spread Curves
- 2021
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Ingår i: Applied Modeling Techniques and Data Analysis 2. - Hoboken, NJ, USA : John Wiley & Sons. - 9781786306746 - 9781119821724 ; , s. 75-89
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Before the financial crisis started in 2007, the forward rate agreement contracts could be perfectly replicated by overnight indexed swap zero coupon bonds. After the crisis, the simply compounded risk-free overnight indexed swap forward rate became less than the forward rate agreement rate. Using an approach proposed by Cuchiero, Klein, and Teichmann, we construct an arbitrage-free market model, where the forward spread curves for a given finite tenor structure are described as a mild solution to a boundary value problem for a system of infinite-dimensional stochastic differential equations. The constructed financial market is large: it contains infinitely many overnight indexed swap zero coupon bonds and forward rate agreement contracts with all possible maturities. We also investigate the necessary assumptions and conditions which guarantee existence, uniqueness and non-negativity of solutions to the obtained boundary value problem.
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| 3184. |
- Nohrouzian, Hossein, 1980-, et al.
(författare)
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Constructing Trinomial Models Based on Cubature Method on Wiener Space : Applications to Pricing Financial Derivatives
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This contribution deals with an extension to our developed novel cubature methods of degrees 5 on Wiener space. In our previous studies, we studied cubature formulae that are exact for all multiple Stratonovich integrals up to dimension equal to the degree. In fact, cubature method reduces solving a stochastic differential equation to solving a finite set of ordinary differential equations. Now, we apply the above methods to construct trinomial models and to price different financial derivatives. We will compare our numerical solutions with the Black’s and Black–Scholes models’ analytical solutions. The constructed model has practical usage in pricing American options and American-style derivatives.
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| 3185. |
- Nohrouzian, Hossein, 1980-, et al.
(författare)
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Constructing Trinomial Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives
- 2022
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This contribution deals with an extension to our developed novel cubature methods of degrees 5 on Wiener space. In our previous studies, we studied cubature formulae that are exact for all multiple Stratonovich integrals up to dimension equal to the degree. In fact, cubature method reduces solving a stochastic differential equation to solving a finite set of ordinary differential equations. Now, we apply the above methods to construct trinomial models and to price different financial derivatives. We will compare our numerical solutions with the Black’s and Black-Scholes models’ analytical solutions. The constructed model has practical usage in pricing American options and American-style derivatives.
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| 3186. |
- Nohrouzian, Hossein, 1980-, et al.
(författare)
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Pricing Financial Derivatives in the Hull-White Model Using Cubature Methods on Wiener Space
- 2022
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Ingår i: Data Analysis and Related Applications 1. - : John Wiley & Sons. - 9781786307712 - 9781394165513 ; , s. 333-358
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In our previous studies, we developed novel cubature methods of degree 5 on the Wiener space in the sense that the cubature formula is exact for all multiple Stratonovich integrals up to dimension equal to the degree. In this paper, we apply the above methods to the modeling of fixed-income markets via affine models. Then, we apply the obtained results to price interest rate derivatives in the Hull-White one-factor model.
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| 3187. |
- Nohrouzian, Hossein, 1980-, et al.
(författare)
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Pricing Overnight Index Swap in a Large Market Model Using a Cubature Method
- 2019
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Ingår i: Booklet of abstracts SPAS 2019 2nd Edition of the International Conference on Stochastic Processes and Algebraic Structures.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Cubature is an effective way to calculate integrals in a finite dimensional space. Extending the idea of cubature to the infinite-dimensional Wiener space would have practical usages in pricing financial instruments. In this paper, we calculate and use cubature formulae of degree 5 and 7 on Wiener space to price European options in the classical Black–Scholes model. This problem has a closed form solution and thus we will compare the obtained numerical results with the above solution. In this procedure, we study some characteristics of the obtained cubature formulae and discuss some of their applications to pricing American options.
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| 3188. |
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| 3189. |
- Nolte, Thomas, et al.
(författare)
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Introducing Substitution-Queries in Distributed Real-Time Database Management Systems
- 2005
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Ingår i: IEEE International Conference on Emerging Technologies and Factory Automation, ETFA. - 9780780394025 ; , s. 707-714
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper introduces query mechanisms that allow automotive control-systems (using a distributed real-time database management system(RTDBMS)) to be queried, monitored and stimulated during run-time without violating its temporal properties. The mechanisms are completely transparent to the control application since they are handled by the RTDBMS. The COMET RTDBMS is extended with ad hoc capabilities to support the introduction of subscription and substitution queries, which are used for monitoring and stimulation. These queries are intended to be used by service and calibration tools to help in the development and maintenance of modern automotive systems. Using these queries could reduce development costs, result in higher quality of the system design and consequently yield higher reliability.
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| 3190. |
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