Spelling suggestions: "subject:"early exercise boundary"" "subject:"early exercise foundary""
1 |
A Comparative Study of American Option Valuation and ComputationRodolfo, Karl January 2007 (has links)
Doctor of Philosophy (PhD) / For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.
|
2 |
Pricing American options in the jump diffusion modelChang, Yu-Chun 21 July 2005 (has links)
In this study, we use the McKean's integral equation to evaluate the American option price for constant jump di
|
3 |
Pricing American options using approximations by Kim integral equationsSheludchenko, Dmytro, Novoderezhkina, Daria January 2011 (has links)
The purpose of this thesis is to look into the difficulty of valuing American options, put as well as call, on an asset that pays continuous dividends. The authors are willing to demonstrate how mentioned above securities can be priced using a simple approximation of the Kim integral equations by quadrature formulas. This approach is compared with closed form American Option price formula proposed by Bjerksund-Stenslands in 2002. The results obtained by Bjerksund-Stenslands method are numerically compared by authors to the Kim’s. In Joon Kim’s approximation seems to be more accurate and closer to the chosen “true” value of an American option, however, Bjerksund-Stenslands model is demonstrating a higher speed in calculations.
|
4 |
A Comparative Study of American Option Valuation and ComputationRodolfo, Karl January 2007 (has links)
Doctor of Philosophy (PhD) / For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.
|
5 |
American option prices and optimal exercise boundaries under Heston Model–A Least-Square Monte Carlo approachMohammad, Omar, Khaliqi, Rafi January 2020 (has links)
Pricing American options has always been problematic due to its early exercise characteristic. As no closed-form analytical solution for any of the widely used models exists, many numerical approximation methods have been proposed and studied. In this thesis, we investigate the Least-Square Monte Carlo Simulation (LSMC) method of Longstaff & Schwartz for pricing American options under the two-dimensional Heston model. By conducting extensive numerical experimentation, we put the LSMC to test and investigate four different continuation functions for the LSMC. In addition, we consider investigating seven different combination of Heston model parameters. We analyse the results and select the optimal continuation function according to our criteria. Then we uncover and study the early exercise boundary foran American put option upon changing initial volatility and other parameters of the Heston model.
|
6 |
Numerical methods for pricing American put options under stochastic volatility / Dominique JoubertJoubert, Dominique January 2013 (has links)
The Black-Scholes model and its assumptions has endured its fair share of criticism.
One problematic issue is the model’s assumption that market volatility is constant.
The past decade has seen numerous publications addressing this issue by adapting the
Black-Scholes model to incorporate stochastic volatility. In this dissertation, American
put options are priced under the Heston stochastic volatility model using the Crank-
Nicolson finite difference method in combination with the Projected Over-Relaxation
method (PSOR). Due to the early exercise facility, the pricing of American put options
is a challenging task, even under constant volatility. Therefore the pricing problem under
constant volatility is also included in this dissertation. It involves transforming the
Black-Scholes partial differential equation into the heat equation and re-writing the pricing
problem as a linear complementary problem. This linear complimentary problem is
solved using the Crank-Nicolson finite difference method in combination with the Projected
Over-Relaxation method (PSOR). The basic principles to develop the methods
necessary to price American put options are covered and the necessary numerical methods
are derived. Detailed algorithms for both the constant and the stochastic volatility
models, of which no real evidence could be found in literature, are also included in this
dissertation. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013
|
7 |
Numerical methods for pricing American put options under stochastic volatility / Dominique JoubertJoubert, Dominique January 2013 (has links)
The Black-Scholes model and its assumptions has endured its fair share of criticism.
One problematic issue is the model’s assumption that market volatility is constant.
The past decade has seen numerous publications addressing this issue by adapting the
Black-Scholes model to incorporate stochastic volatility. In this dissertation, American
put options are priced under the Heston stochastic volatility model using the Crank-
Nicolson finite difference method in combination with the Projected Over-Relaxation
method (PSOR). Due to the early exercise facility, the pricing of American put options
is a challenging task, even under constant volatility. Therefore the pricing problem under
constant volatility is also included in this dissertation. It involves transforming the
Black-Scholes partial differential equation into the heat equation and re-writing the pricing
problem as a linear complementary problem. This linear complimentary problem is
solved using the Crank-Nicolson finite difference method in combination with the Projected
Over-Relaxation method (PSOR). The basic principles to develop the methods
necessary to price American put options are covered and the necessary numerical methods
are derived. Detailed algorithms for both the constant and the stochastic volatility
models, of which no real evidence could be found in literature, are also included in this
dissertation. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013
|
Page generated in 0.0692 seconds