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Non-parametric Causal Discovery for EU Allowances Returns Through the Information Imbalance
Salvagnin C +4 more
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FORWARD AND FUTURE IMPLIED VOLATILITY
International Journal of Theoretical and Applied Finance, 2011We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities.
PAUL GLASSERMAN, QI WU
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Common Forward Rate Volatility
SIAM Journal on Financial Mathematics, 2010Statistical analyses of forward interest rate behavior provide evidence that these rates share a common volatility. We develop a risk-neutral term structure model based on this assumption. The main feature of this model is that each discounted bond price is both an explicit local martingale and a diffusion.
Victor Goodman, Kyounghee Kim
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From Spot Volatility to Forward Volatility
SSRN Electronic Journal, 2012The purpose of this note is to design a very simple algorithm to link the spot and the forward volatility representations. The impact of dividend volatility is stripped out from the forward volatility thanks to an analytic appraoch.
Adil Reghai, Gilles Boya
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Managing Forward Volatility and Skew Risk
SSRN Electronic Journal, 2021The forward start dual volatility swap is introduced. It can be regarded as the analog for volatility of what the entropy contract is for variance. Under the risk neutral measure it is shown that the difference between the forward start volatility swap and its dual is approximately the difference between two specific forward start implied volatilities.
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2015
For path-dependent and forward starting options, it is important to assess Vega, the sensitivity of the option’s value to changes in volatility, and in particular to assess these sensitivities for forward buckets. A first step in this process is to determine how forward volatilities for these forward buckets are calculated from the spot volatilities ...
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For path-dependent and forward starting options, it is important to assess Vega, the sensitivity of the option’s value to changes in volatility, and in particular to assess these sensitivities for forward buckets. A first step in this process is to determine how forward volatilities for these forward buckets are calculated from the spot volatilities ...
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PPlya-Based Approximation for the ATM-Forward Implied Volatility
SSRN Electronic Journal, 2017We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this approximation is uniformly bounded for all option maturities and implied volatilities. The approximation is extremely precise, having relative error less than [Formula: see text] for all options with integrated volatility less than ...
Ivan Matić +2 more
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Pricing Electricity Forwards Under Stochastic Volatility
SSRN Electronic Journal, 2001Based on the peculiarities of electricity as underlying commodity of forward contracts we develop a time-continuous pricing model for short-term electricity forwards. The suggested stochastic volatility model utilizes the non-tradeable spot price of electricity and its variance rate as state variables.
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Forward at the Money Forward Implied Volatility and Forward Underlying Move Estimations
SSRN Electronic Journal, 2016Ahead of the 23rd June UK referendum on "Brexit", this note provides a technique for estimating the Forward (at referendum date) At The Money Forward (ATMF) implied volatility for equity or FX Indexes. We provide a closed form formula for the forward underlying expected moves (for short terms maturities) post the referendum date.
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TRIVARIATE SUPPORT OF FLAT-VOLATILITY FORWARD LIBOR RATES
Mathematical Finance, 2010Extending the author's previous work [Math. Finance 18, No. 3, 427--443 (2008; Zbl 1141.91452)], where the bivariate support has been investigated, the present paper provides a description of the trivariate support of a flat-volatility Libor market model. More precisely, the author considers a Libor rate model \(L^1, \ldots, L^n\), where the last three
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