This study reviews techniques to estimate volatility and price Variance Swaps.
problem Estimating historical volatility and pricing Variance Swaps.
method Review of existing techniques.
result Discussion of various methods to estimate volatility and price Variance Swaps.
The paper prices swaps on generalized variance measures for multiple assets.
problem Hedging risk in financial markets with multi-asset swaps.
method Pricing generalized variance swaps using Barndorff-Nielsen and Shephard model.
result Results have implications for commodity sector risk management.
The paper develops a new hybrid model for pricing variance swaps.
problem Pricing variance swaps in a model with stochastic volatility and interest rate.
method Hybrid model combining Heston's stochastic volatility and CIR stochastic interest rate with regime-switching.
result A semi-closed form pricing formula for variance swaps is derived.
The paper proposes pricing methods for multi-asset generalized variance swaps.
problem Hedging risk in financial markets with complex asset structures.
method Proposes pricing methods for two new measures of generalized variance (maximum eigen-value and trace of covariance matrix) under Markov-modulated volatilities.
result Demonstrates pricing results for three stocks, highlighting the usefulness of these swaps in commodity risk management.
Paper generalizes pricing and hedging of volatility swaps in stochastic models.
problem Pricing and hedging of volatility swaps in stochastic volatility models.
method Generalizes zero vanna approximation to seasoned swaps, derives hedges using vanilla options and variance swaps.
result Pricing and hedging of volatility swaps are made practical and robust.
A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff can be replicated exact…
The chapter evaluates volatility and variance swap pricing under stochastic volatility models.
problem Pricing of volatility derivatives under stochastic volatility models.
method Uses convexity correction approximation, Laplace transform, and Markov chain Monte Carlo algorithm.
result Shows the impact of jumps on volatility derivatives pricing and compares different pricing approaches.
Empirical study finds variance swap rate is affine in spot variance for S&P500 data.
problem Investigating the relationship between variance swap rate and spot variance.
method Empirical analysis using S&P500 data from 2006-2018, testing different models.
result Affine relationship between variance swap rate and spot variance is supported.
This paper develops a semi-closed form formula for pricing variance swaps with stochastic volatility and interest rate correlation.
problem Pricing variance swaps with stochastic volatility and interest rate correlation under full correlation structure.
method Developed an efficient semi-closed form pricing formula for variance swaps using characteristic functions.
result The correlation between the underlying and interest rate significantly impacts the pricing of variance swaps.
We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull-White and Schobel-Zhu stochastic volatility models we give simple explicit expressions (improving Broadie and Jain (2008a) in the case of the Heston model). We give condi…
The paper prices variance swaps in incomplete markets with stochastic interest rate and volatility.
problem Pricing variance swaps in markets with stochastic interest rates and volatility.
method Equilibrium framework and joint moment generating function.
result Closed-form solution for fair delivery price of variance swaps.
This paper investigates the pricing and hedging of variance swaps under a 3/2 volatility model. Explicit pricing and hedging formulas of variance swaps are obtained under the benchmark approach, which only requires the existence of the numéraire portfolio. The growth optimal portfolio is the numéraire portfolio and u…
The paper calculates fair strike for variance swaps on time-changed Markov processes.
problem Calculating fair strike for variance swaps on time-changed Markov processes.
method Proving the fair strike equals the price of a European contract and solving the integro-differential equation.
result The fair strike for variance swaps can be computed explicitly for certain Markov processes.
Develops a novel framework for pricing variance swaps in multi-asset stochastic volatility models.
problem Pricing variance swaps in multi-asset stochastic volatility models.
method Determinant-based instantaneous generalized variance, Heston and BNS stochastic volatility frameworks.
result Analytical pricing expressions for multi-asset Heston and BNS formulations.
We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating strategies which enforce t…
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordina…
In stochastic volatility models based on time-homogeneous diffusions, we provide a simple necessary and sufficient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It extends Theorem 3.8 of Jarrow, Kchia, Larsson and Protter (2013) and gives an aff…
The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …
A new permutation method improves two-sample testing power.
problem Two-sample testing with improved power and validity.
method Structured block-restricted cross-swaps.
result Block-restricted permutations achieve higher power than full permutations.
The paper introduces a new stochastic volatility model with long-term memory and jumps.
problem Developing a model for variance and volatility swaps with long-term memory and jumps.
method Fractional Barndorff-Nielsen and Shephard model incorporating long-term memory and jumps.
result Arbitrage-free prices for variance and volatility swaps derived for the new model.
New method estimates risk-neutral density for asset prices, improving on existing techniques.
problem Estimating risk-neutral density for asset prices accurately.
method Developed a nonparametric approach reformulated as a double-constrained optimization problem.
result Our approach outperforms existing methods in estimating risk-neutral density.
In the recent years, banks have sold structured products such as worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correl…
The mixed-fractional CEV model improves CDS pricing by accounting for default risk.
problem Improving the pricing of Credit Default Swaps (CDS) by accounting for default risk.
method Using a mixed-fractional Brownian motion to model the Constant Elasticity of Variance (CEV) model.
result The mixed-fractional CEV model yields more realistic CDS spreads and default probabilities.
ARSM estimator improves gradient backpropagation for categorical variables.
problem Improving gradient backpropagation through categorical variables.
method ARSM combines variable augmentation, REINFORCE, Rao-Blackwellization, and variable swapping.
result ARSM outperforms existing estimators and provides variance reduction methods.
New swap contracts avoid bias and numerical errors, offering fair values independent of monitoring.
problem Bias and numerical integration errors in standard swap contracts.
method Characterized as solutions to a second-order system of PDEs, identified as a vector space of pay-offs.
result Existence of infinite variety of discretisation-invariant swap contracts with fair values independent of monitoring.
Perfect hedging of options with a dynamic portfolio in rough volatility models.
problem Hedging options in rough volatility models.
method Presented a simple but general result showing perfect hedging with a dynamic portfolio of underlying and variance swap.
result Rough volatility models significantly reduce hedging error compared to diffusion-based models.
Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.
problem Implied volatility constraints under finite log-moments.
method Analyzes stock price martingale with finite log-moments, derives new bounds and proof.
result New bounds on implied volatility growth, relaxes moment assumptions.
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European options which are written in terms of the implied volatility are given. In particular…
Study examines factors influencing tail risk premia for long-term equity investors.
problem Determining factors affecting variance and higher-moment risk premia in equity markets.
method Empirical study using discretisation invariant swaps for log returns, focusing on skewness, kurtosis, and variance risk premia.
result Momentum is the dominant driver for skewness and kurtosis risk premia, while variance risk premium is influenced by size and growth.
The article introduces a new interest rate model using Bergomi stochastic volatility.
problem Developing a model for interest rate swaps and swaptions without requiring calibration.
method Forward variance modeling by L. Bergomi applied to co-terminal swap market model.
result The model provides simple PnL formulas and high flexibility in controlling model dynamics.
Robust, or model-independent properties of the variance swap are well-known, and date back to Dupire and Neuberger, who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the assumption that the price process is continuous. In Cox and Wang we showed that a…
We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011) to find the maximum entropy density of an asset price to the relative entropy c…
Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter γ takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in \cite{Labordere2009…
The paper develops a Fourier-based method for optimal hedging in stochastic volatility models.
problem Optimal hedging in financial markets with stochastic volatility.
method Fourier representation in a semimartingale factor model.
result A tractable formula for expected squared hedging error and optimal strategy.
New bounds for VIX derivatives pricing using LS Monte Carlo.
problem Pricing VIX derivatives due to the square root of expected realised variance.
method Least Squares Monte Carlo with stochastic duality and adjustments.
result Effective upper and lower bounds for VIX derivatives pricing.
Optimizes hedging strategy using Fourier-integration for variance-optimality.
problem Finding optimal hedging strategy under variance-optimality criterion.
method General representations and Fourier-integration for Heston model; sparse hedging selection.
result Sparse semi-static hedging strategy using Fourier-integration.
Develops new e-processes and confidence sequences for Gaussian means with unknown variance.
problem Constructing valid t-tests and confidence sequences for Gaussian means with unknown variance.
method Explores generalized nonintegrable martingales and extended Ville's inequality, developing two new e-processes and confidence sequences.
result Analyzes the width of resulting confidence sequences with a polynomial dependence on error probability, proving it to be unavoidable and even better than classical fixed-sample t-tests.
Debt swaps improve financial networks by optimizing clearing payments and stability.
problem Improving financial network stability and efficiency through debt swaps.
method Analyzing computational complexity of debt swaps, focusing on semi-positive swaps and v-improving swaps.
result Polynomial length of sequences of semi-positive v-improving swaps for ranking-based clearing, but NP-hard for arbitrary v-improving swaps.
The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
problem Calculating Bachelier option prices and variance reduction in correlated cases.
method Taylor expansions and classical Itô calculus to derive option prices, uses negative powers of future mean volatility.
result The paper provides a new method to calculate Bachelier option prices and applies it to reduce variance in Monte Carlo simulations.
A new model adds stochastic spot/volatility correlation to Heston model for better exotic pricing.
problem Improving exotic option pricing in foreign exchange markets.
method Developed a Double Heston model with stochastic spot/volatility correlation, an affine model.
result The new model increases prices of out-of-the-money knockout options and one touch options.
Swapping debt contracts can mitigate risk in financial networks.
problem Mitigating risk in financial networks through debt swaps.
method Analysis of debt swapping operations in financial networks under various conditions.
result Positive debt swaps can exist in worst-case shock models to minimize losses.
Paper solves robust optimization with expectation constraints for financial derivatives.
problem Computing robust maximization solutions with expectation constraints.
method Shows a single convex minimization problem for super-replication values.
result No-arbitrage bounds on various financial derivatives.
Paper develops efficient mechanisms for estimating variance and covariance under differential privacy in the add-remove model.
problem Estimating variance and covariance under differential privacy in the add-remove model.
method Developed mechanisms based on the Bézier mechanism, a novel moment-release framework.
result Proved minimax optimality of the Bézier-based estimator in the high-privacy regime and demonstrated its better utility in instance-wise analysis.
We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.
This study models credit default swap premiums with a stochastic recovery rate.
problem Analyzing credit default swap premiums with varying recovery rates.
method Develops a model using stochastic recovery rates.
result Models credit default swap premiums effectively with a stochastic recovery rate.
The paper introduces a method to accurately price swaps and their Value at Risk (VaR) using dynamic trading and regression/simulation.
problem Theoretical and practical concerns about uncollateralized swaps and their risk not being fully hedged.
method Dynamic trading of CCP swaps, applying discount rates based on counterparty's or own bond curves, and using Longstaff-Schwartz regression and finite difference schemes.
result The uncollateralized swap can be fully replicated, and FVA is redefined as a liquidity or funding basis component of total valuation adjustment.
F. Labourie [arXiv:1212.5015] characterized the Hitchin components for PSL(n,R) for any n>1 by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce the rank n swapping algebra, which is the quotient of the swap…