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Pricing Financial Instruments: The Finite Difference Method
Curt Randall,Domingo Tavella +1 more
TLDR
The Pricing Equations. as mentioned in this paper and the Finite-difference method are the most commonly used methods for finite difference methods in the literature, and they can be found in:Abstract:
The Pricing Equations. Analysis of Finite Difference Methods. Special Issues. Coordinate Transformations. Numerical Examples. Index.read more
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Stochastic Evolution Equations in Portfolio Credit Modelling
TL;DR: A structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor is considered and the existence and uniqueness for the solution taking values in a suitable function space are established.
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Optimal Exercise of Executive Stock Options and Implications for Firm Cost
TL;DR: In this article, the optimal policy and option cost for an executive with general concave utility was analyzed, and analytically how the policy and cost vary with risk aversion, wealth and dividend, and when there exists a single stock price boundary.
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Componentwise splitting methods for pricing american options under stochastic volatility
Samuli Ikonen,Jari Toivanen +1 more
TL;DR: Efficient numerical methods for pricing American options using Heston's stochastic volatility model are proposed and the accuracy and computational efficiency of the proposed symmetrized splitting method are demonstrated by numerical experiments.
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High-order compact finite difference scheme for option pricing in stochastic volatility models
Bertram Düring,Michel Fournié +1 more
TL;DR: A new high-order compact finite difference scheme for option pricing in stochastic volatility models is derived and fourth order convergence for non-smooth payoff is observed.
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Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
TL;DR: In this article, the authors proposed a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system, and showed that the discretization on an unbounded domain is convergent of first order in the timestep and second order in spatial grid size.