Representation and Numerical Approximation of American Option Prices under Heston

2014 ◽  
pp. 93-139
Keyword(s):  
Numerical Approximation ◽  
American Option ◽  
Option Prices

New Bounds on American Option Prices

2007 ◽  
Author(s):  
In Joon Kim ◽  
Geun Hyuk Chang ◽  
Suk-Joon Byun
Keyword(s):  
American Option ◽  
Option Prices

scholarly journals Randomized Binomial Tree and Pricing of American-Style Options

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hu Xiaoping ◽  
Cao Jie
Keyword(s):  
American Option ◽  
Option Prices ◽  
Occurrence Probability ◽  
Binomial Tree ◽  
No Arbitrage ◽  
Complete Market ◽  
Cubic Polynomial ◽  
American Style ◽  
The Impact ◽  
And Storage

Randomized binomial tree and methods for pricing American options were studied. Firstly, both the completeness and the no-arbitrage conditions in the randomized binomial tree market were proved. Secondly, the description of the node was given, and the cubic polynomial relationship between the number of nodes and the time steps was also obtained. Then, the characteristics of paths and storage structure of the randomized binomial tree were depicted. Then, the procedure and method for pricing American-style options were given in a random binomial tree market. Finally, a numerical example pricing the American option was illustrated, and the sensitivity analysis of parameter was carried out. The results show that the impact of the occurrence probability of the random binomial tree environment on American option prices is very significant. With the traditional complete market characteristics of random binary and a stronger ability to describe, at the same time, maintaining a computational feasibility, randomized binomial tree is a kind of promising method for pricing financial derivatives.

Generalized Analytical Upper Bounds for American Option Prices

2007 ◽  
Vol 42 (1) ◽  
pp. 209-227 ◽  
Author(s):  
San-Lin Chung ◽  
Hsieh-Chung Chang
Keyword(s):  
Interest Rates ◽  
American Options ◽  
General Theorem ◽  
Upper Bounds ◽  
American Option ◽  
Option Prices ◽  
Dividend Yield ◽  
Strike Price ◽  
Risky Assets ◽  
The Interest Rate

AbstractThis paper generalizes and tightens Chen and Yeh's (2002) analytical upper bounds for American options under stochastic interest rates, stochastic volatility, and jumps, where American option prices are difficult to compute with accuracy. We first generalize Theorem 1 of Chen and Yeh (2002) and apply it to derive a tighter upper bound for American calls when the interest rate is greater than the dividend yield. Our upper bounds are not only tight, but also converge to accurate American call option prices when the dividend yield or strike price is small or when volatility is large. We then propose a general theorem that can be applied to derive upper bounds for American options whose payoffs depend on several risky assets. As a demonstration, we utilize our general theorem to derive upper bounds for American exchange options and American maximum options on two risky assets.

Analytical Upper Bounds for American Option Prices

2002 ◽  
Vol 37 (1) ◽  
pp. 117 ◽  
Author(s):  
Ren-Raw Chen ◽  
Shih-Kuo Yeh
Keyword(s):  
Upper Bounds ◽  
American Option ◽  
Option Prices

MESHLESS COLLOCATION METHOD FOR OPTION PRICING BY VARIANCE GAMMA MODEL

2013 ◽  
Vol 10 (03) ◽  
pp. 1350004
Author(s):  
Y. J. ZHENG ◽  
Z. H. YANG ◽  
Y. C. HON
Keyword(s):  
Analytical Solution ◽  
Collocation Method ◽  
American Option ◽  
Optimal Choice ◽  
Numerical Comparison ◽  
Option Prices ◽  
Variance Gamma ◽  
Computational Region ◽  
Meshless Collocation ◽  
Leave One Out

Based on the use of radial basis functions (RBFs), we present in this paper a meshless collocation method to compute both European and American option prices by solving the variance gamma (VG) model. The valuation of the financial derivatives is performed by solving a corresponding partial integro-differential equation (PIDE). In the case of European option, numerical comparison with the analytical solution shows that the proposed scheme achieves a higher accurate approximation than most existing numerical methods. When analytical solution is not available in the case of American option, we use a dividend process to obtain an alternative characterization of the American option so that solution to the PIDE can be achieved in the entire computational region. Since the RBFs used in this paper are infinitely differentiable, the approximation of the derivatives of option prices can be obtained at no extra interpolation cost. In addition, the leave-one-out cross validation (LOOCV) algorithm is generalized for obtaining a local optimal choice of the shape parameter contained in the RBFs for superior convergence. Several numerical examples are given to verify the efficiency and stability of the proposed method.

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