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Topic Title: jump diffusion models (thesis)
Created On Mon May 12, 08 11:04 AM
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zwader
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Mon May 12, 08 11:04 AM
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Hi,

currently I am writing on my thesis about option valuation and I want to include some jump diffusion models. I've already read papers from Merton, Bates, Kou... and I am reading the Cont/Tankov book. I was wondering if somebody could tell me the most important models or literature for jump diffusion models cause I don't wanna miss the most important ones.

Greetz, Thanks for any help
 
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zhouqj
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Wed May 14, 08 06:01 AM
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Maya Briani's PHD Thesis, "Numerical methods for option pricing in jump-diffusion markets".
=>Here you can find more detail about numerical method

I find many useful things from here to help me implementing jump diffusion model for exotic options.
Hope this help.

 
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jfuqua
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Wed May 14, 08 04:21 PM
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There are many papers on this. Here are a few in the last year or so.
By consulting the bibliographies of books/papers you will find all you need.

Duffie, Pan, Singleton, 2000, Transform Analysis and Asset Pricing for Affine Jump Diffusions, Econometrica, 68(6)
Eberlein Ernst, Dilip Madan 'Sato Processes and the Valuation of Structured Products' 7/07
Espinosa Fernando, Josep Vives 'A Volatility-Varying and Jump-Diffusion Merton Type Model of Interest Rate Risk' V38 #1 Feb. 06 Insurance: Mathematics and Economics
Feng Liming, Vadim Linetsky 'Pricing Options in Jump-Diffusion Models: An Extrapolation Approach' Operations Research March 08, SSRN 6/07 <Bermuda, Barrier, V-G, PIDE>
Fink Jason, Michael Albert 'Adaptive Mesh Modeling and Barrier Option Pricing Under a Jump-Diffusion Process' SSRN 2/07
Forster Barbara, Eva Lütkebohmert, Josef Teichmann 'Calculation of Greeks for Jump-Diffusions' (Arxiv/0509016),
Gapeev Pavel 'Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes' J. of Applied Probability V. 4, #3 Sept 07
Gapeev Pavel 'Perpetual Barrier Options in Jump-Diffusion Models' Stochastics V. 79 #1 & 2 2007
Gapeev Pavel 'Pricing and Hedging Perpetual American Options In Jump-Diffusion Models:Barrier Lookback Switching and Credit Options'
Hanson Floyd 'American Put Option Pricing for Stochastic-Volatility Jump-Diffusion Models' 2006
Hanson Floyd 'Applied Stochastic Processes and Control for Jump Diffusions:Modeling, Analysis and Computation' SIAM Press 2007
Hanson Floyd 'Stochastic Processes and Control for Jump-Diffusions' SSRN 10/07
Krutchenko R.N., A.V. Melnikov 'Quantile Hedging for a Jump-Diffusion Financial Market Model' in Trends in Mathematics 2001 Birkhauser Verlag
Lindset Snorre 'Pricing American Exchange Options in a Jump-Diffusion Model' Journal of Futures Markets March 2007


Edited: Sat May 17, 08 at 03:46 PM by jfuqua
 
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Cuchulainn
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Wed May 14, 08 04:41 PM
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Quote

Originally posted by: zhouqj
Maya Briani's PHD Thesis, "Numerical methods for option pricing in jump-diffusion markets".
=>Here you can find more detail about numerical method




Maya B. was a PhD student of Roberto Natalini who is active in this area.

Some time ago, someone from UMD did a thesis on this PIDE. (FDM for the PDE and FEM for the 'I', if you get my drift)

google/search.

-------------------------
www.datasimfinancial.com

Edited: Wed May 14, 08 at 05:23 PM by Cuchulainn
 
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drift00
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Thu May 15, 08 11:24 AM
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You seriuosly should look at the research paper of Phd Roberto Reno. Innovative and very advanced stuff regarding jump diffusion models
 
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zwader
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Sat May 17, 08 04:31 PM
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Thank you all for the help, I appreciate it a lot.
Is it correct that there are 4 different types of models for jump diffusions:

1. complete capital market with asset - specific jumps like Merton
2. incomplete capital market with asset - specific jumps like Chang
3. complete capital market with market - jumps like Mercurio/Rumggaldier and
4. incomplete capital market with market - jumps like Bates or Kou

And is it right that I have to use equilibrium concepts if the capital market is incomplete an that I can use arbitrage Arguments if the market is complete?

Thanx again
 
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atakami
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Tue May 20, 08 10:59 PM
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I'm looking for a new model with jump diffusion to use to quote options on Fed Bonds. We know that at a certain date the rate will have discrete numbers.
 
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