The goal of this thesis is to compute the price of a first touch digital option using the hybrid method presented in the paper published by Oleg Kudryavtsev and Vasily Rodochenko. Assuming that the stock and the variance dynamics are described by the Heston model, to reduce the dimension of the problem, a recombining tree that approximates the stochastic variance process is built. A recursive formula is obtained by using the Carr's randomization technique and finally the Wiener-Hopf factorization is used to derive the final formula.
L’obiettivo di questa tesi è quello di calcolare il prezzo di una first touch digital option usando il metodo ibrido presentato nel paper pubblicato da Oleg Kudryavtsev e Vasily Rodochenko. Supponendo che le dinamiche dello stock e della varianza siano descritte dal modello di Heston, per ridurre la dimensione del problema si costruisce un albero ricombinante che approssima il processo stocastico della varianza. Si ricava una formula ricorsiva usando la tecnica di Carr’s randomization ed infine, si usa la Wiener-Hopf factorization per ricavare la formula finale.
A numerical realization of the Wiener-Hopf method for the Kolmogorov backward equation
JUGGOO, SONIA
2019/2020
Abstract
The goal of this thesis is to compute the price of a first touch digital option using the hybrid method presented in the paper published by Oleg Kudryavtsev and Vasily Rodochenko. Assuming that the stock and the variance dynamics are described by the Heston model, to reduce the dimension of the problem, a recombining tree that approximates the stochastic variance process is built. A recursive formula is obtained by using the Carr's randomization technique and finally the Wiener-Hopf factorization is used to derive the final formula.File | Dimensione | Formato | |
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https://hdl.handle.net/10589/166763