Modeling Financial Security Returns Using Levy Processes

Wu, Liuren

doi:10.2139/ssrn.871760

Cited by 13 publications

(8 citation statements)

References 73 publications

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“…Once we have the Fourier transform φ(u), we can solve the option value defined in (33) numerically through various methods of fast Fourier inversions (Wu (2008)). …”

Section: Proposition 3 the Time-t Value V T Of An European Option On mentioning

confidence: 99%

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Carr

Gabaix

2011

SSRN Journal

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We propose to use the linearity-generating framework to accommodate the evidence of unspanned stochastic volatility: Variations in implied volatilities on interest-rate options such as caps and swaptions are independent of the variations on the interest rate term structure. Under this framework, bond valuation depends only on the transition dynamics of interest-rate factors, but not on their volatilities.Thus, interest-rate volatility is truly unspanned. Furthermore, this framework allows tractable pricing of options on any bond portfolios, including both caps and swaptions. This feat is not possible under existing exponential-affine or quadratic frameworks. Finally, the framework allows sequential estimation of the interest-rate term structure and the interest-rate option implied volatility surface, thus facilitating joint empirical analysis. Within this framework, we perform specification analysis on interest-rate factor transition dynamics and its relation to the interest-rate term structure; we also analyze the interest-rate volatility dynamics and its impact on interest-rate option pricing. We estimate several specifications for the transition dynamics to ten years worth of U.S. dollar LIBOR and swap rates across 15 maturities. We also estimate several interest-rate volatility dynamics specifications using ten years of swaption implied volatilities across a matrix of ten option maturities and seven swap tenors. The estimation results show that the volatility dynamics dictate the option implied volatility variation along the option maturity dimension, whereas the interest-rate transition dynamics dictate the implied volatility variation along the underlying swap maturity dimension.JEL Classification: C13; C51; G12; G13.

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“…Once we have the Fourier transform φ(u), we can solve the option value defined in (33) numerically through various methods of fast Fourier inversions (Wu (2008)). …”

Section: Proposition 3 the Time-t Value V T Of An European Option On mentioning

confidence: 99%

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Carr

Gabaix

2011

SSRN Journal

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“…Thus, applying the stochastic time change is a convenient way of generating stochastic volatility from both Brownian motions and jumps. We refer interested readers to Carr and Wu (2004a) for the mathematical treatment of time-changed Lévy processes and Wu (2006) for a review on modeling financial security returns using time-changed Lévy processes.…”

Section: International Equity Index Volatility Co-movementsmentioning

confidence: 99%

International capital asset pricing: Evidence from options

Mo¹,

2007

Journal of Empirical Finance

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“…Analysis of asset return distributions suggests that infinite-activity jump specifications are well suited to capture the daily market value fluctuations of many financial assets (Wu, 2007). The VG model that we consider in this article is an infinite-activity pure jump process.…”

Section: Billion) In 2010 Accordingmentioning

confidence: 99%

Valuation of reverse convertibles in the variance gamma economy

Deng¹,

Dulaney²,

McCann³

2013

J Deriv Hedge Funds

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Prior research on structured products has demonstrated that equity-linked notes (ELNs) sold to retail investors in initial public offerings are typically issued at above their fair market value. A particular type of ELN -reverse convertibles -embed down-andin put options and offer investors relatively high coupon payments in exchange for bearing some of the downside risk of the equity underlying the note. We analytically study the magnitude of the overpricing of reverse convertibles -one of the most popular structured products on the market today -within a stochastic volatility model.We extend the current literature to include analytical valuation formulas within a model of stochastic volatilitythe variance gamma (VG) model. We show that these complex notes are even more overpriced than previously estimated when stochastic volatility is taken into account. As a result of their complex payoffs and the lack of a secondary market to correct the mispricing,

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Modeling Financial Security Returns Using Levy Processes

Cited by 13 publications

References 73 publications

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

International capital asset pricing: Evidence from options

Valuation of reverse convertibles in the variance gamma economy

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