Option pricing and CVA calculations using the Monte Carlo-Tree (MC-Tree) method

Trinh, Yen Thuan

Option pricing and CVA calculations using the Monte Carlo-Tree (MC-Tree) method

dc.availability.bitstream	openaccess
dc.contributor.advisor	Hanzon, Bernard	en
dc.contributor.advisorexternal	Ma, Jingtang	en
dc.contributor.author	Trinh, Yen Thuan
dc.date.accessioned	2022-09-08T14:54:18Z
dc.date.available	2022-09-08T14:54:18Z
dc.date.issued	2022-07-18
dc.date.submitted	2022-07-18
dc.description.abstract	The thesis introduces a new method, the MC-Tree method, for pricing certain financial derivatives, especially options with high accuracy and efficiency. Our solution is to combine Monte Carlo (MC) method and Tree method by doing a mixing distribution on the tree, and the output is the compound distribution on the tree. The compound distribution in the tree output (after a logarithmic transformation of the asset prices) is not the ideal Gaussian distribution but has entropy values close to the maximum possible Gaussian entropy. We can get closer using entropy maximization. We introduce two correction techniques: distribution correction and bias correction to improve the accuracy and completeness of the model. The thesis presents an algorithm and numerical results for calculations of CVA on an American put option using the MC-Tree method. The MC-Tree method with the distribution correction technique significantly improves accuracy, resulting in practically exact solutions, compared to analytical solutions, at the tree depth $N=50$ or $100$ and MC-drawings $M=10^5$. The bias-correction technique makes the resulting tree model complete in the sense of financial mathematics and obtains the risk-neutral probability. Besides, we have obtained new formulae for the calculations of the entropy and the Kullback-Leibler divergence for rational densities and approximate entropy of finite Gaussian mixture.	en
dc.description.status	Not peer reviewed	en
dc.description.version	Accepted Version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Trinh, Y. T. 2022. Option pricing and CVA calculations using the Monte Carlo-Tree (MC-Tree) method. PhD Thesis, University College Cork.	en
dc.identifier.endpage	197	en
dc.identifier.uri	https://hdl.handle.net/10468/13565
dc.language.iso	en	en
dc.publisher	University College Cork	en
dc.rights	© 2022, Yen Thuan Trinh.	en
dc.rights.uri	https://creativecommons.org/licenses/by-nc-nd/4.0/	en
dc.subject	Entropy	en
dc.subject	Kullback-Leibler (KL) divergence	en
dc.subject	Optimization	en
dc.subject	MC-Tree method	en
dc.subject	Option pricing	en
dc.subject	Credit valuation adjustment	en
dc.subject	Pricing models	en
dc.subject	Finite Gaussian mixture	en
dc.title	Option pricing and CVA calculations using the Monte Carlo-Tree (MC-Tree) method	en
dc.type	Doctoral thesis	en
dc.type.qualificationlevel	Doctoral	en
dc.type.qualificationname	PhD - Doctor of Philosophy	en