scholarly journals Representation of exchange option prices under stochastic volatility jump-diffusion dynamics

2019 ◽  
Vol 20 (2) ◽  
pp. 291-310 ◽  
Author(s):  
Gerald H. L. Cheang ◽  
Len Patrick Dominic M. Garces
Keyword(s):  
Stochastic Volatility ◽  
Jump Diffusion ◽  
Option Prices ◽  
Diffusion Dynamics ◽  
Exchange Option

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.

STOCHASTIC VOLATILITY AND JUMP-DIFFUSION — IMPLICATIONS ON OPTION PRICING

1999 ◽  
Vol 02 (04) ◽  
pp. 409-440 ◽  
Author(s):  
GEORGE J. JIANG
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Dynamic Properties ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
Pricing Errors ◽  
Volatility Model ◽  
Random Jump

This paper conducts a thorough and detailed investigation on the implications of stochastic volatility and random jump on option prices. Both stochastic volatility and jump-diffusion processes admit asymmetric and fat-tailed distribution of asset returns and thus have similar impact on option prices compared to the Black–Scholes model. While the dynamic properties of stochastic volatility model are shown to have more impact on long-term options, the random jump is shown to have relatively larger impact on short-term near-the-money options. The misspecification risk of stochastic volatility as jump is minimal in terms of option pricing errors only when both the level of kurtosis of the underlying asset return distribution and the level of volatility persistence are low. While both asymmetric volatility and asymmetric jump can induce distortion of option pricing errors, the skewness of jump offers better explanations to empirical findings on implied volatility curves.

scholarly journals Correction: Exchange Option under Jump-diffusion Dynamics

2014 ◽  
Vol 22 (1) ◽  
pp. 99-103 ◽  
Author(s):  
Ruggero Caldana ◽  
Gerald H. L. Cheang ◽  
Carl Chiarella ◽  
Gianluca Fusai
Keyword(s):  
Jump Diffusion ◽  
Diffusion Dynamics ◽  
Exchange Option

scholarly journals APPROXIMATE HEDGING OF OPTIONS UNDER JUMP-DIFFUSION PROCESSES

2015 ◽  
Vol 18 (04) ◽  
pp. 1550024 ◽  
Author(s):  
KARL FRIEDRICH MINA ◽  
GERALD H. L. CHEANG ◽  
CARL CHIARELLA
Keyword(s):  
Diffusion Processes ◽  
Option Price ◽  
Jump Diffusion ◽  
Option Prices ◽  
Jump Diffusion Processes ◽  
Complete Market ◽  
Diffusion Dynamics ◽  
Risk Neutral ◽  
Delta Hedging ◽  
Risk Neutral Measures

We consider the problem of hedging a European-type option in a market where asset prices have jump-diffusion dynamics. It is known that markets with jumps are incomplete and that there are several risk-neutral measures one can use to price and hedge options. In order to address these issues, we approximate such a market by discretizing the jumps in an averaged sense, and complete it by including traded options in the model and hedge portfolio. Under suitable conditions, we get a unique risk-neutral measure, which is used to determine the option price integro-partial differential equation, along with the asset positions that will replicate the option payoff. Upon implementation on a particular set of stock and option prices, our approximate complete market hedge yields easily computable asset positions that equal those of the minimal variance hedge, while at the same time offers protection against upward jumps and higher profit compared to delta hedging.

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