The representation of American options prices under stochastic volatility and jump-diffusion dynamics

2013 ◽  
Vol 13 (2) ◽  
pp. 241-253 ◽  
Author(s):  
Gerald H. L. Cheang ◽  
Carl Chiarella ◽  
Andrew Ziogas
Keyword(s):  
Stochastic Volatility ◽  
American Options ◽  
Jump Diffusion ◽  
Diffusion Dynamics

scholarly journals Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang Li ◽  
Yanli Zhou ◽  
Xinfeng Ruan ◽  
B. Wiwatanapataphee
Keyword(s):  
Diffusion Process ◽  
Stochastic Volatility ◽  
American Options ◽  
Option Price ◽  
Jump Diffusion ◽  
Incomplete Market ◽  
American Put Option ◽  
Put Option ◽  
Jump Diffusion Process ◽  
American Put

We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.

scholarly journals THE EVALUATION OF AMERICAN OPTION PRICES UNDER STOCHASTIC VOLATILITY AND JUMP-DIFFUSION DYNAMICS USING THE METHOD OF LINES

2009 ◽  
Vol 12 (03) ◽  
pp. 393-425 ◽  
Author(s):  
CARL CHIARELLA ◽  
BODA KANG ◽  
GUNTER H. MEYER ◽  
ANDREW ZIOGAS
Keyword(s):  
Stochastic Volatility ◽  
Splitting Method ◽  
Method Of Lines ◽  
Option Price ◽  
Jump Diffusion ◽  
American Option ◽  
Computational Effort ◽  
Option Prices ◽  
The Method Of Lines ◽  
Diffusion Dynamics

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston [18], and by a Poisson jump process of the type originally introduced by Merton [25]. We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer [26] for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen and Toivanen [21]. The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation and which is taken as the benchmark for the price. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.

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