scholarly journals True martingales for upper bounds on Bermudan option prices under jump-diffusion processes

2013 ◽  
Author(s):  
Helin Zhu ◽  
Fan Ye Enlu Zhou
Keyword(s):  
Diffusion Processes ◽  
Jump Diffusion ◽  
Upper Bounds ◽  
Option Prices ◽  
Jump Diffusion Processes ◽  
Bermudan Option

PRICING VULNERABLE AMERICAN PUT OPTIONS UNDER JUMP–DIFFUSION PROCESSES

2016 ◽  
Vol 31 (2) ◽  
pp. 121-138 ◽  
Author(s):  
Guanying Wang ◽  
Xingchun Wang ◽  
Zhongyi Liu
Keyword(s):  
Default Risk ◽  
Diffusion Processes ◽  
Compound Poisson Process ◽  
Jump Diffusion ◽  
Option Prices ◽  
Jump Diffusions ◽  
Put Options ◽  
Jump Diffusion Processes ◽  
American Put Options ◽  
American Put

This paper evaluates vulnerable American put options under jump–diffusion assumptions on the underlying asset and the assets of the counterparty. Sudden shocks on the asset prices are described as a compound Poisson process. Analytical pricing formulae of vulnerable European put options and vulnerable twice-exercisable European put options are derived. Employing the two-point Geske and Johnson method, we derive an approximate analytical pricing formula of vulnerable American put options under jump–diffusions. Numerical simulations are performed for investigating the impacts of jumps and default risk on option prices.

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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