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Nonlinear option pricing

Nonlinear option pricing (2회 대출)

Guyon, Julien. Labordere, Henry.
서명 / 저자사항
Nonlinear option pricing / by Julien Guyon, Henry Labordere.
Boca Raton, Florida :   CRC Press,   2014.  
xxxviii, 445 p. : ill. ; 25 cm.
Chapman & Hall/CRC financial mathematics series
Includes bibliographical references and index.
Options (Finance) -- Mathematical models. Nonlinear pricing -- Mathematical models. Business mathematics.
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001 000045789722
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008 140305s2014 flua b 001 0 eng
020 ▼a 9781466570337
040 ▼a 211009 ▼c 211009 ▼d 211009
082 0 4 ▼a 332.6453 ▼2 23
084 ▼a 332.6453 ▼2 DDCK
090 ▼a 332.6453 ▼b G989n
100 1 ▼a Guyon, Julien.
245 1 0 ▼a Nonlinear option pricing / ▼c by Julien Guyon, Henry Labordere.
260 ▼a Boca Raton, Florida : ▼b CRC Press, ▼c 2014.
300 ▼a xxxviii, 445 p. : ▼b ill. ; ▼c 25 cm.
490 1 ▼a Chapman & Hall/CRC financial mathematics series
504 ▼a Includes bibliographical references and index.
650 0 ▼a Options (Finance) ▼x Mathematical models.
650 0 ▼a Nonlinear pricing ▼x Mathematical models.
650 0 ▼a Business mathematics.
700 1 ▼a Labordere, Henry.
830 0 ▼a Chapman & Hall/CRC financial mathematics series.
945 ▼a KLPA


No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고6층/ 청구기호 332.6453 G989n 등록번호 111713494 도서상태 대출가능 반납예정일 예약 서비스 B M



Option Pricing in a Nutshell
The super-replication paradigm
Stochastic representation of solutions of linear PDEs

Monte Carlo
The Monte Carlo method
Euler discretization error
Romberg extrapolation

Some Excursions in Option Pricing
Complete market models
Beyond replication and super-replication

Nonlinear PDEs: A Bit of Theory
Nonlinear second order parabolic PDEs: some generalities
Why is a pricing equation a parabolic PDE?
Finite difference schemes
Stochastic control and the Hamilton-Jacobi-Bellman PDE
Viscosity solutions

Examples of Nonlinear Problems in Finance
American options
The uncertain volatility model
Transaction costs: Leland’s model
Illiquid markets
Super-replication under delta and gamma constraints
The uncertain mortality model for reinsurance deals
Credit valuation adjustment
The passport option

Early Exercise Problems
Super-replication of American options
American options and semilinear PDEs
The dual method for American options
On the ownership of the exercise right
On the finiteness of exercise dates
On the accounting of multiple coupons
Finite difference methods for American options
Monte Carlo methods for American options
Case study: pricing and hedging of a multi-asset convertible bond
Introduction to chooser options
Regression methods for chooser options
The dual algorithm for chooser options
Numerical examples of pricing of chooser options

Backward Stochastic Differential Equations
First order BSDEs
Reflected first order BSDEs
Second order BSDEs

The Uncertain Lapse and Mortality Model
Reinsurance deals
The deterministic lapse and mortality model
The uncertain lapse and mortality model
Path-dependent payoffs
Pricing the option on the up-and-out barrier
An example of PDE implementation
Monte Carlo pricing
Monte Carlo pricing of the option on the up-and-out barrier
Link with first order BSDEs
Numerical results using PDE
Numerical results using Monte Carlo

The Uncertain Volatility Model
The model
The parametric approach
Solving the UVM with BSDEs
Numerical experiments

McKean Nonlinear Stochastic Differential Equations
The particle method in a nutshell
Propagation of chaos and convergence of the particle method

Calibration of Local Stochastic Volatility Models to Market Smiles
The calibration condition
Existence of the calibrated local stochastic volatility model
The PDE method
The Markovian projection method
The particle method
Adding stochastic interest rates
The particle method: numerical tests

Calibration of Local Correlation Models to Market Smiles
The FX triangle smile calibration problem
A new representation of admissible correlations
The particle method for local correlation
Some examples of pairs of functions (a, b)
Some links between local correlations
Joint extrapolation of local volatilities
Price impact of correlation
The equity index smile calibration problem
Numerical experiments on the FX triangle problem
Generalization to stochastic volatility, stochastic interest rates, and stochastic dividend yield
Path-dependent volatility

Marked Branching Diffusions
Nonlinear Monte Carlo algorithms for some semilinear PDEs
Branching diffusions
Marked branching diffusions
Application: Credit valuation adjustment algorithm
System of semilinear PDEs
Nonlinear PDEs



Exercises appear at the end of each chapter.

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