Option pricing with Levy processes: an analytic approach

• Autorzy: Long Nguyen-Thanh

Warianty tytułu

Wycena opcji przy użyciu procesów Levy'ego. Podejście analityczne

• Języki publikacji: EN

Abstrakty

EN

The aim of this survey is to present the case of option pricing models based on Levy process. The auhor overviewed the use of conditional characteristic function as a efficient tool to value European options, the term structure of interest rate or even the pricing measure. Section 2 present the integro-differential equation for the contingent claim values. Section 3 devoted the theory of option pricing with the conditional characteristic function, it contains in addition some new result; for example an explicit guiadance as how to compute this transform in term of the Levy characteristic triplet. And how the conditional charactristic function facilitate in the incomplete market is made in section 4. In section 5, a pricing formula for a option written on an asset, whose state variable follows a multi-jump diffusion process, is proposed. Concluding remarks are offered in section 6.

W pracy przedstawiono analityczną metodę przy wycenie opcji typu europejskiego opiewanej na aktywa, którego wartość jest zdeterminowana przez wielowymiarowy proces Levy'ego. Model zostaje starannie zbudowany w taki sposób, aby móc wycenić opcje ze zróżnicowanymi metodami wypłaty. Celem również jest ujednolicenie sposobów wyceny struktury stóp procentowych, wyceny kontraktów forward i future opiewanych na stopy procentowe, oszacowanie prawdopodobieństwa, że opcje wygasną in-the-money oraz tzw. pricing measure na rynku niezupełnym.

Słowa kluczowe

EN

Options pricing; Levy processes; Financial mathematics

PL

Wycena opcji; Procesy Levy'ego; Matematyka finansowa

• Czasopismo: Przegląd Statystyczny
• Rocznik: 2003
• Tom: 50
• Numer: z. 2
• Strony: 7--30

Twórcy

autor

Long Nguyen-Thanh

Bibliografia

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