Prices and Asymptotics for Discrete Variance Swaps
Prices and Asymptotics for Discrete Variance Swaps
By Carole Bernard, and Zhenyu Cui
SSRN (2012)
Abstract Paper

Carole Bernard

University of Waterloo

Canada

Coder Page  

Zhenyu Cui

brooklyn college

United States

Coder Page  

The program implements formulas for each proposition of the paper. In particular it computes the fair strike of the discrete variance swap and the continuous variance swap in the Heston and Hull-White model. It also gives asymptotics.
Created
June 29, 2012
Software:
Matlab 7.8
Visits
302
Last update
November 22, 2012
Ranking
N.A.
Runs
10
Abstract
We derive closed-form expressions for the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston and Hull-White stochastic volatility models we give simple explicit expressions (improving Broadie and Jain (2008a) for the Heston case). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than the continuous variance swap. Interest rates and correlation between underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a), Jarrow et al. (2012) and Keller-Ressel (2011).
Bernard, C., and Z. Cui, "Prices and Asymptotics for Discrete Variance Swaps", SSRN.
r
r
V0
V0
theta
theta
kappa
kappa
gamma
gamma
T
T
rho
rho
n
n
mu
mu
sigma
sigma
Waiting time

Please cite the publication as :

Bernard, C., and Z. Cui, "Prices and Asymptotics for Discrete Variance Swaps", SSRN.

Please cite the companion website as :

Bernard, C., and Z. Cui, "Prices and Asymptotics for Discrete Variance Swaps", RunMyCode companion website, http://www.execandshare.org/CompanionSite/Site135

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Variable/Parameters Description, constraint Comments
r
    Risk-free rate
    V0
      Initial variance at time 0
      theta
        theta (parameter of the Heston model: long-term mean)
        kappa
          parameter of the Heston model (speed of reversion)
          gamma
            parameter of the Heston model: volatility of volatility
            T
              Maturity of the variance swap
              rho
                correlation between underlying and volatility process
                n
                  Number of discrete time step in the discrete variance swap. The time step is T/n.
                  mu
                    parameter in the drift of the Hull-White model
                    sigma
                      volatility of the Hull-White model
                      Variable/Parameters Description Visualisation
                      r
                      V0
                      theta
                      kappa
                      gamma
                      T
                      rho
                      n (when T=1 and n=12, the time step is one month)
                      mu
                      sigma
                      Prices and Asymptotics for Discrete Variance Swaps
                      C. Bernard, and Z. Cui (2012)
                      Computing Date Status Actions
                      Coders:

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                      Ranking
                      9999
                      Runs
                      N.A.
                      Visits
                      25
                      Extracting Factors from Heteroskedastic Asset Returns
                      Abstract
                      This paper proposes an alternative to the asymptotic principal components procedure of Connor and Korajczyk (Journal of Financial Economics, 1986) that is robust to time series heteroskedasticity in the factor model residuals. The new method is simple to use and requires no assumptions stronger than those made by Connor and Korajczyk. It is demonstrated through simulations and analysis of actual stock market data that allowing heteroskedasticity sometimes improves the quality of the extracted factors quite dramatically. Over the period from 1989 to 1993, for example, a single factor extracted using the Connor and Korajczyk method explains only 8.2% of the variation of the CRSP value-weighted index, while the factor extracted allowing heteroskedasticity explains 57.3%. Accounting for heteroskedasticity is also important for tests of the APT, with p-values sometimes depending strongly on the factor extraction method used.
                      Jones, S. C., "Extracting Factors from Heteroskedastic Asset Returns", Journal of Financial Economics, 62, 293-325.
                      Authors: Jones
                      Coders: Jones
                      Last update
                      11/17/2012
                      Ranking
                      30
                      Runs
                      17
                      Visits
                      81
                      A New Approach to Comparing VaR Estimation Methods
                      Abstract
                      We develop a novel backtesting framework based on multidimensional Value-at-Risk (VaR) that focuses on the left tail of the distribution of the bank trading revenues. Our coverage test is a multivariate generalization of the unconditional test of Kupiec (Journal of Derivatives, 1995). Applying our method to actual daily bank trading revenues, we find that non-parametric VaR methods, such as GARCH-based methods or filtered Historical Simulation, work best for bank trading revenues.
                      Perignon, C., and D. Smith, "A New Approach to Comparing VaR Estimation Methods", Journal of Derivatives, Winter.
                      Authors: Smith
                      Perignon
                      Coders: Perignon
                      Smith
                      Last update
                      11/23/2012
                      Ranking
                      9999
                      Runs
                      N.A.
                      Visits
                      43
                      A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics
                      Abstract
                      This paper proposes a new class of asymmetric Student-t (AST) distributions, and investigates its properties, gives procedures for estimation, and indicates applications in financial econometrics. We derive analytical expressions for the cdf, quantile function, moments, and quantities useful in financial econometric applications such as the Expected Shortfall. A stochastic representation of the distribution is also given. Although the AST density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix. A Monte Carlo study indicates generally good finite-sample conformity with these asymptotic properties.
                      Colletaz, G., "A Generalized Asymmetric Student-t Distribution with Application to Financial Econometrics", Journal of Econometrics, 157, 297-305.
                      Authors: Zhu
                      Galbraith
                      Coders: Colletaz
                      Last update
                      05/05/2012
                      Ranking
                      38
                      Runs
                      6
                      Visits
                      95
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