Author: Marcellino GaudenziPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Appendix To: Efficient European and American Option Pricing Under a Jump-diffusion Process
Author: Marcellino GaudenziAmerican and Exotic Option Pricing with Jump Diffusions and Other Lévy Processes
Author: Justin KirkbyPublisher:
ISBN:
Category :
Languages : en
Pages : 33
Book Description
In general, no analytical formulas exist for pricing discretely monitored exotic options, even when a geometric Brownian motion governs the risk-neutral underlying. While specialized numerical algorithms exist for pricing particular contracts, few can be applied universally with consistent success and with general Lévy dynamics. This paper develops a general methodology for pricing early exercise and exotic financial options by extending the recently developed PROJ method. We are able to efficiently obtain accurate values for complex products including Bermudan/American options, Bermudan barrier options, survival probabilities and credit default swaps by value recursion, European barrier and lookback/hindsight options by density recursion, and arithmetic Asian options by characteristic function recursion. This paper presents a unified approach to tackling these and related problems. Algorithms are provided for each option type, along with a demonstration of convergence. We also provide a large set of reference prices for exotic, American and European options under Black-Scholes-Merton, Normal Inverse Gaussian, Kou's double exponential jump diffusion, Variance Gamma, KoBoL/CGMY and Merton's jump diffusion models.
Option Pricing Under Exponential Jump Diffusion Processes
Author: Tianren BuAmerican Option Pricing in a Jump-Diffusion Model
Author: Jeremy BerrosPublisher: LAP Lambert Academic Publishing
ISBN: 9783843356930
Category :
Languages : en
Pages : 60
Book Description
Many alternative models have been developed lately to generalize the Black-Scholes option pricing model in order to incorporate more empirical features. Brownian motion and normal distribution have been used in this Black-Scholes option-pricing framework to model the return of assets. However, two main points emerge from empirical investigations: (i) the leptokurtic feature that describes the return distribution of assets as having a higher peak and two asymmetric heavier tails than those of the normal distribution, and (ii) an empirical phenomenon called "volatility smile" in option markets. Among the recent models that addressed the aforementioned issues is that of Kou (2002), which allows the price of the underlying asset to move according to both Brownian increments and double-exponential jumps. The aim of this thesis is to develop an analytic pricing expression for American options in this model that enables us to e±ciently determine both the price and related hedging parameters.
Financial Modelling with Jump Processes
Author: Peter TankovPublisher: CRC Press
ISBN: 1135437947
Category : Business & Economics
Languages : en
Pages : 552
Book Description
WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
Numerical Solution Of The American Option Pricing Problem, The: Finite Difference And Transform Approaches
Author: Carl ChiarellaPublisher: World Scientific
ISBN: 9814452637
Category : Business & Economics
Languages : en
Pages : 223
Book Description
The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers' experiences with these approaches over the years.
Robust and Efficient IMEX Schemes for Option Pricing Under Jump-Diffusion Models
Author: Santtu SalmiPublisher:
ISBN:
Category :
Languages : en
Pages : 18
Book Description
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump diffusion process. The schemes include the families of IMEX-midpoint, IMEXCNAB and IMEX-BDF2 schemes. Each family is defined by a convex parameter c ∈ [0, 1], which divides the zeroth-order term due to the jumps between the implicit and explicit part in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint family is absolutely stable only for c = 0, while the IMEX-CNAB and the IMEX-BDF2 families are absolutely stable for all c ∈ [0, 1]. The IMEX-CNAB c = 0 scheme produced the smallest error in our numerical experiments.
Computational Option Pricing Under Jump Diffusion and Lévy Processes
Author: Eleftheria ChatzipanagouPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
An Iterative Method for Pricing American Options Under Jump-Diffusion Models
Author: Santtu SalmiPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou's and Merton's jump-diffusion models show that the resulting iteration converges rapidly.
Author: 張育群