Pricing and Hedging Volatility Derivatives

Broadie, Mark; Jain, Ashish

doi:10.3905/jod.2008.702503

Cited by 86 publications

(59 citation statements)

References 13 publications

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“…The convexity bias that arises from the above inequality leads to imperfect replication when a volatility swap is replicated using a buy-and-hold strategy of variance swaps (e.g., Broadie and Jain, 2008). Simply put, the payo¤ of variance swaps is quadratic with respect to volatility, whereas the payo¤ of volatility swaps is linear.…”

Section: Foreign Exchange Volatility Risk Premiamentioning

confidence: 99%

Volatility Risk Premia and Exchange Rate Predictability

2013

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We discover a new currency strategy with highly desirable return and diversi…cation properties, which uses the predictive capability of currency volatility risk premia for currency returns. The volatility risk premium -the di¤erence between expected realized volatility and model-free implied volatility -re ‡ects the costs of insuring against currency volatility ‡uctuations, and the strategy sells high-insurance-cost currencies and buys low-insurancecost currencies. The returns to the strategy are mainly generated by movements in spot exchange rates rather than interest rate di¤erentials, and the strategy carries a large weight in a minimum-variance portfolio of commonly employed currency strategies. We explore alternative explanations for the pro…tability of the strategy, which cannot be understood using traditional risk factors.

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Section: Foreign Exchange Volatility Risk Premiamentioning

confidence: 99%

Volatility Risk Premia and Exchange Rate Predictability

2013

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“…In terms of a precise definition of these instruments one may refer to Broadie and Jain (2008) as a rather excellent source. Since these two instruments are swaps, their structure is similar to vanilla interest rate swaps, in which there is a floating leg and a fixed leg, and also there is a notional amount that multiplied the difference of the first two terms.…”

Section: Description Of Variance and Volatility Swapsmentioning

confidence: 99%

“…Since these two instruments are swaps, their structure is similar to vanilla interest rate swaps, in which there is a floating leg and a fixed leg, and also there is a notional amount that multiplied the difference of the first two terms. According to Broadie and Jain (2008) definitions, one may describe the variance swaps as a contract over a realised variance and a fixed price, accorded by the parties, times a notional amount. With respect to the realised variance, this one is calculated from a given asset which might be a single stock or an index, depending of the level of volatility that the investor wants to be exposed.…”

Section: Description Of Variance and Volatility Swapsmentioning

confidence: 99%

Comparison of Model for Pricing Volatility Swaps

Romero

2013

SSRN Journal

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La serie Documentos de Trabajo es una publicación del Banco Central de Chile que divulga los trabajos de investigación económica realizados por profesionales de esta institución o encargados por ella a terceros. El objetivo de la serie es aportar al debate temas relevantes y presentar nuevos enfoques en el análisis de los mismos. La difusión de los Documentos de Trabajo sólo intenta facilitar el intercambio de ideas y dar a conocer investigaciones, con carácter preliminar, para su discusión y comentarios.La publicación de los Documentos de Trabajo no está sujeta a la aprobación previa de los miembros del Consejo del Banco Central de Chile. Tanto el contenido de los Documentos de Trabajo como también los análisis y conclusiones que de ellos se deriven, son de exclusiva responsabilidad de su o sus autores y no reflejan necesariamente la opinión del Banco Central de Chile o de sus Consejeros.The Working Papers series of the Central Bank of Chile disseminates economic research conducted by Central Bank staff or third parties under the sponsorship of the Bank. The purpose of the series is to contribute to the discussion of relevant issues and develop new analytical or empirical approaches in their analyses. The only aim of the Working Papers is to disseminate preliminary research for its discussion and comments.Publication of Working Papers is not subject to previous approval by the members of the Board of the Central Bank. The views and conclusions presented in the papers are exclusively those of the author(s) and do not necessarily reflect the position of the Central Bank of Chile or of the Board members. AbstractThe popularity of volatility derivatives has increased through these years of financial turmoil. In particular, variance and volatility swap seem interesting to analyse due to its growing trading volume. Hence, the aim of this work is to present a full revision of these two volatility derivatives, comparing pricing methodologies, like Taylor expansion and Heston (1993) volatility process. In addition, there will be a complete section dedicated to the study of the volatility skew and the wings or "smile". The results showed that the Taylor expansion has a reasonable level of convergence at some values of the parameters of the volatility dynamics, though the findings concluded that higher order of this expansion yielded poor results than the lower order. In the other hand, the smile and the volatility skew showed that the former may change the final value of the fair volatility strike, whereas the latter has almost null impact on this one. ResumenLa popularidad de instrumentos de volatilidad, como los swaps de volatilidad y varianza, se ha incrementado incluso durante los años de crisis financiera. El presente trabajo busca exhibir una revisión completa de estos dos derivados, comparando metodologías como la expansión de Taylor y el proceso de volatilidad descrito por Heston (1993), además de dedicar un apartado completo al estudio del skew y smile de la volatilidad. Los resultados muestran que la expansión...

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“…In the literature, there are many discussions on this quadratic hedging approach, see, e.g., Carr and Mayo (2007), Broadie andJain (2008), Liu (2010). In general, for complex nonlinear payoff f , there is no closed-form formula for u i , which have to be computed numerically.…”

Section: Algorithm 31 (Iterative Equidistribution Equation Algorithmmentioning

confidence: 99%

“…Demeterfi et al (1999) use European calls and puts with equally-spaced strikes to replicate the log payoff, which is not optimal because of the equal spacing. Broadie and Jain (2008) propose a simulation method to obtain the optimal approximation of a static replication; this minimizes the approximation error, but is computationally expensive. Liu (2010) discusses three optimal approximations of nonlinear payoffs.…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs

Deng

Zheng

2015

Quantitative Finance

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In this paper we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear payoff functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear payoff function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges, and also for a jump diffusion process allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results of the static replication and approximation in the literature.JEL classification. C, C6, C63, G, G1, G12

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Pricing and Hedging Volatility Derivatives

Cited by 86 publications

References 13 publications

Volatility Risk Premia and Exchange Rate Predictability

Volatility Risk Premia and Exchange Rate Predictability

Comparison of Model for Pricing Volatility Swaps

Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs

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