Computation of the greeks in black-scholes-merton and stochastic volatility models using malliavin calculus

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2014

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Yılmaz, Bilgi

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The computation of the Greeks of options is an essential aspect of financial mathematics. The investors use the information gained from this aspect for hedging purposes or to decide whether to invest in an option or not. However, computation of the Greeks is not straightforward in some cases due to technical difficulties. For instance, the value function of some options are complicated or moreover in some cases they might not have a closed form solution which makes the computation of their Greeks cumbersome. If this is the case, the Greeks have to be computed numerically. In this thesis, the Greeks of European call options are computed under Black-Scholes-Merton and stochastic volatility models assumptions with Malliavin calculus in particular “infinite dimensional integration by parts formula”. Moreover, the results for Black-Scholes-Merton assumptions Greeks are compared with finite difference and pathwise methods. This thesis provides a contribution to computation of Greeks literature by means of the Malliavin calculus. The advantage of the methodology followed in this thesis is that, once the Greeks formula is obtained, it can be applied to any options with continuous and discontinuous payoffs.

Subject Keywords

Malliavin calculus., Stochastic analysis., Stochastic processes., Options (Finance).

URI

http://etd.lib.metu.edu.tr/upload/12617453/index.pdf
https://hdl.handle.net/11511/23637

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

B. Yılmaz, “Computation of the greeks in black-scholes-merton and stochastic volatility models using malliavin calculus,” M.S. - Master of Science, Middle East Technical University, 2014.