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Financial modelling with mean reversion through jumps

Siyanko, S; (2016) Financial modelling with mean reversion through jumps. Doctoral thesis , UCL (University College London).

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My research is on derivatives pricing in the presence of jumps and, in particular, when jumps are directed towards, what market participants believe, is the true, intrinsic value of an asset defined by its company fundamentals. I consider geometric Brownian motion as a model for the asset price dynamics and introduce jumps towards a deterministic exponential function. The function represents the fundamental value and jumps are here to model a market’s response to the risk of price corrections. I will solve the problem of pricing derivatives and obtain results that include the interpretation of the volatility smile and skew as the market’s aversion to risk. I will derive an efficient algorithm that would allow for realistic shapes of the volatility surface and include parameters one can interpret and estimate independently of the model. The objective is not only to introduce an alternative pricing algorithm but, more importantly, to have an algorithm that explicitly prices and measures the risk of price corrections assumed by the market. As a technical spin-off of this work, I will develop and introduce an asymptotic series expansion for the price of Asian derivatives which allows to calculate as many terms as necessary for a good, high-precision agreement with other methods.

Type: Thesis (Doctoral)
Title: Financial modelling with mean reversion through jumps
Language: English
Keywords: mean reversion through jumps, asymptotic methods for pricing Asian derivatives
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1476644
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