Jerace, Carmelo (A.A. 2023/2024) Rigorous mathematical derivations for option pricing and Monte Carlo analysis: from black-scholes to local volatility model. Tesi di Laurea in Probabilità e applicazioni alla finanza, Luiss Guido Carli, relatore Hlafo Alfie Mimun, pp. 153. [Master's Degree Thesis]

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Abstract/Index

The dynamics of financial derivatives: instruments, applications, and market impact. Forward contracts. Futures contracts. Swaps contracts. Option contracts. Put-call parity. Mathematical foundations of stock price modeling and derivatives pricing. The lognormal model for the stock price. Risk neutrality and no-arbitrage principle. The black-scholes model. Greeks. Delta Δ. Gamma Γ. Vega V. Theta Θ. Rho ρ. Use of Delta, Gamma and Vega. Pathwise estimators and analytical methods for greeks calculation. Pathwise method. Delta Δ estimator. Gamma Γ estimator. Vega V estimator. Theta Θ estimator. Rho ρ estimator. Monte Carlo simulations for option pricing and greeks. Bloomberg terminal data extraction. Call option valuation and greek metrics: results. Put option valuation and greek metrics: results. Advanced option pricing: the CEV and Local Volatility Models. The CEV model. The volatility surface. Local volatility model: the dupire formula. Relationship between CEV and local volatility models.

References

Bibliografia: pp. 131-132. Sitografia: pp. 133-134.

Thesis Type:	Master's Degree Thesis
Institution:	Luiss Guido Carli
Degree Program:	Master's Degree Programs > Master's Degree Program in Economics and Finance (LM-56)
Chair:	Probabilità e applicazioni alla finanza
Thesis Supervisor:	Mimun, Hlafo Alfie
Thesis Co-Supervisor:	Biagini, Sara
Academic Year:	2023/2024
Session:	Summer
Deposited by:	Alessandro Perfetti
Date Deposited:	28 Jan 2025 17:23
Last Modified:	28 Jan 2025 17:23
URI:	https://tesi.luiss.it/id/eprint/41076

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