Publication: Entropía relativa y riesgo de modelo en Swaps de tipos de
interés
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2018-09
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Abstract
Las volatilidades que cotizan en el mercado para opciones "out the money" corresponden a precios más altos que los proporcionados por la fórmula de Black-Scholes. Esta característica se conoce como smile de volatilidad y conviene considerarla en los modelos de valoración de contratos financieros. Proponemos una metodología para instrumentos derivados de los tipos de interés que permite obtener una probabilidad neutral al riesgo incorporando de manera implícita la influencia del smile de volatilidad. Así, esta medida posibilita la valoración correcta de derivados mediante el Primer Teorema Fundamental de Valoración Financiera. En concreto, en este Trabajo la empleamos para valorar un "swap". Posteriormente se lleva a cabo un análisis del riesgo de modelo asociado a la no consideración del smile de volatilidad.
Market volatilities for out the money options correspond to higher market prices than those given by the Black-Scholes formula. This fact is known as volatility smile and should be considered in mathematical models for pricing fi�nancial instruments. We propose a methodology for interest rate derivatives which determines a risk-neutral measure that implicitly includes the influence of volatility smile. Thus, this probability can be used, along with the First Fundamental Theorem of Asset Pricing, to give a correct price to derivatives. In particular, in this project we price a swap. Finally, an analysis is performed to determine model risk when volatility smile is not considered.
Market volatilities for out the money options correspond to higher market prices than those given by the Black-Scholes formula. This fact is known as volatility smile and should be considered in mathematical models for pricing fi�nancial instruments. We propose a methodology for interest rate derivatives which determines a risk-neutral measure that implicitly includes the influence of volatility smile. Thus, this probability can be used, along with the First Fundamental Theorem of Asset Pricing, to give a correct price to derivatives. In particular, in this project we price a swap. Finally, an analysis is performed to determine model risk when volatility smile is not considered.
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