Please use this identifier to cite or link to this item:
https://hdl.handle.net/10321/2348
DC Field | Value | Language |
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dc.contributor.author | Paliathanasis, Andronikos | en_US |
dc.contributor.author | Krishnakumar, K. | en_US |
dc.contributor.author | Tamizhmani, K. M. | en_US |
dc.contributor.author | Leach, P. G. L. | en_US |
dc.date.accessioned | 2017-03-10T05:48:38Z | - |
dc.date.available | 2017-03-10T05:48:38Z | - |
dc.date.issued | 2016-05-03 | - |
dc.identifier.citation | Paliathanasis. A. 2016. Lie symmetry analysis of the Black-Scholes-Merton Model for European options with stochastic volatility. Mathematics. 4(28): 1-14. | en_US |
dc.identifier.issn | 2227-7390 (print) | - |
dc.identifier.uri | http://hdl.handle.net/10321/2348 | - |
dc.description.abstract | We perform a classification of the Lie point symmetries for the Black-Scholes-Merton Model for European options with stochastic volatility, σ, in which the last is defined by a stochastic differential equation with an Orstein-Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2) evolution partial differential equation in which the price of the option depends upon two independent variables, the value of the underlying asset, S, and a new variable, y. We find that for arbitrary functional form of the volatility, σ(y), the (1 + 2) evolution equation always admits two Lie point symmetries in addition to the automatic linear symmetry and the infinite number of solution symmetries. However, when σ(y) = σ0 and as the price of the option depends upon the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black-Scholes-Merton Equation, the model admits five Lie point symmetries in addition to the linear symmetry and the infinite number of solution symmetries. We apply the zeroth-order invariants of the Lie symmetries and we reduce the (1 + 2) evolution equation to a linear second-order ordinary differential equation. Finally, we study two models of special interest, the Heston model and the Stein-Stein model. | en_US |
dc.format.extent | 14 p | en_US |
dc.language.iso | en | en_US |
dc.publisher | MDPI | en_US |
dc.relation.ispartof | Mathematics (Basel) | en_US |
dc.subject | Lie point symmetries | en_US |
dc.subject | Financial Mathematics | en_US |
dc.subject | Stochastic volatility | en_US |
dc.subject | Black-Scholes -Merton equation | en_US |
dc.title | Lie symmetry analysis of the Black-Scholes-Merton Model for European options with stochastic volatility | en_US |
dc.type | Article | en_US |
dc.publisher.uri | http://www.mdpi.com/2227-7390/4/2/28 | en_US |
dc.dut-rims.pubnum | DUT-005582 | en_US |
item.fulltext | With Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.languageiso639-1 | en | - |
item.openairetype | Article | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
Appears in Collections: | Research Publications (Applied Sciences) |
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Paliathanasis_Mathematics_Vol4#2#28_Pgs1-14_2016.pdf | 830.13 kB | Adobe PDF | View/Open |
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