Variance swap financial definition of variance swap. Arpm lab variance swap fair value as combination of options. Variance swap rates and variance risk premiums a return variance swap has zero net market value at entry. Zhu and lian 2015 provided in a monthly frequency two analytical closedform formulae for the price of forwardstart variance swap with the realized variance being defined by the actualreturn. Since for currency variance swaps the notional amount could be given in either of the two involved currencies there are two variance swap rates. See all articles by florence guillaume florence guillaume. They compare the synthetic 30day variance swap rates to the ex post realized variance to determine the variance risk premium. Since the payoff of a variance swap contract is the difference between the realized variance and the variance swap rate, the observed negative returns for long positions on variance swap contracts for all time horizons. Since the variance swap is a linear contract in variance risk, by trading these contracts, the investor does not create additional delta exposures to the underlying stock index, as would be the case for strategies involving vanilla options. The theory of variance swaps is more straightforward. Modeling and pricing of covariance and correlation swaps. Now customize the name of a clipboard to store your clips. Variance swap pricing analysis report january 15, 2011.
The novelty of this paper with respect to 20 is that we calculate the volatility swap price explicitly, moreover we price covariance and correlation swap in a two risky assets market model. A variance swap allows the investor to speculate on volatility, just as a trader might speculate on the price of a stock. We look at the variance swap market development, the pricing of variance swaps including rules of thumb and variance swap drivers. Trading a long variance swap on one index or asset versus a short variance swap on another index or underlying. Exhibit 2 variance swaps are convex in volatility volatility swap struck at 20 variance swap struck at 21. Variance swaps are actually the more natural choice. Variance swap strikes are well correlated with standard blackscholes implied volatility derived from options variance swaps 17 november 2006 peter allen 4420 73254114 stephen einchcomb. A zero cost swap is constructed around a certain variance strike. Because of the convexity, a variance swap will always outperform a contract linear in volatility of the same strike. Now consider swaps and options written on r2 and r. At maturity, the payoff to the long side of the swap is equal to the difference between the realized variance over the life of the contract and a constant called the variance. Just what you need to know about variance swaps sebastien bossu. In this swap, the lower bound of the corridor is a preset number, while the upper bound is unlimited. Mar 24, 2011 we prove that a multiple of a log contract prices a variance swap, under arbitrary exponential levy dynamics, stochastically timechanged by an arbitrary continuous clock having arbitrary correlation with the driving levy process, subject to integrability conditions.
Clipping is a handy way to collect important slides you want to go back to later. That is, it pays at maturity the weighted variance of the underlying. Powerful instruments for trading volatility are volatility and variance swaps. We solve for the multiplier, which depends only on the levy process, not on the clock. Research which can be found at conflictmanagementpolicy. Although options market participants talk of volatility, it is variance, or volatility squared, that has more fundamental theoretical significance. We assume the given prices do not admit arbitrage and deduce noarbitrage bounds on the weighted variance swap along with super and sub replicating strategies which enforce them. Feb 11, 2002 the investor also buys single stock variance swaps on intc, txn, and amat weighting the units in each swap to reflect each stocks weight in the index for a weighted average strike price of 55%. This paper proposes a method for overhedging weighted variance using only a finite number of maturities.
Citeseerx citation query more than you ever wanted to. Analytic pricing of exotic discrete variance swaps and options. Variance swaps can be used for hedging volatility exposures. One way of trading realised skew is to combine a put with a variance swap. We then combine those results and apply them to the standard market prac. A conditional variance swap also a corridor variance swap in which realized volatility accrues when the underlying remains above a specified threshold lower bound. For example, an upvariance swap may be structured in a way that it accrues realized volatility as long as. Variance swaps are instruments which offer investors straightforward and direct exposure to the volatility of an underlying asset such as a stock or index.
The purpose of this project is to derive the theoretical fair value of a variance swap, so that it can be priced and used in practice. First method used historic volatilities, second method uses implied volatilities and third method uses direct option prices. Wu 2010 among many others, the average variance risk premium is negative and sizeable for all available horizons. Section 1 gives quick facts about variance swaps and their applications. Simple variance swaps ian martin january, 20 abstract the events of 20089 disrupted volatility derivatives markets and caused the singlename variance swap market to dry up completely. Pricing variance swaps with stochastic volatility request pdf.
Two parties agree to exchange a future payment based upon the actual realized volatility over a period of time. As we will show below, however, the cboe variance futures. This paper introduces the simple variance swap, a more robust relative of the variance swap that can be priced and. Variance and volatility swaps have been studied by swishchuk 20. Why would an investor trade a variance swap over a. A variation on variance swaps which weights the periodic squared return of the underlying by the ratio of current price to initial price. It introduced a new view on volatility not only as on. As a result, the payout on a variance swap is higher when the volatility increases. An initial margin account 3 vol point equivalent is necessary to minimise the impact of any potential insolvency. Variance swaps on timechanged levy processes springerlink.
Robustreplicationofvolatilityderivatives prmia award for best paper in derivatives, mfa 2008 annual. Variance swap is a derivative instrument that offers an efficient way for trading volatil ity of the underlying asset. In other words, if the price in current period crashes approaches zero, the squared return would be extremely. This means that an investor who is long a variance swap i. A type of volatility swap where the payout is linear to variance rather than volatility. The term structure of variance swap rates and optimal. The variance swaps vega that is equal to the variance notional refers to the realized variance. In order to achieve a plausible result we combine 1st contracts of the asset. Volatility derivatives variance and volatility swaps diva portal. Variance swaps at yo u nee d to kn ow a b ou t variance swaps 1. Finance and economics discussion series divisions of research. Used by clients wishing to make a focused trade on volatility, without having to take a.
A variance swap is a derivative contract which allows investors to trade fu ture realized or historical volatility against current implied volatility. A variance swap is an overthecounter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i. 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 exactly using a portfolio of puts and calls and a dynamic position in the asset. Although variance swap payoffs are linear with variance they are convex with volatility.
Section 3 investigates the historical behavior of the variance risk premiums. The fair value of the variance swap is the cost of the replicating portfolio. The gamma swap obviates the need for embedding a cap which otherwise is usually embedded in volatility swaps or variance swaps to protect the seller from the impact of volatility or variance spike, following an underlying price crash. We show how a variance swap can be theoretically replicated by a hedged portfolio of standard options with suitably chosen strikes, as long as stock prices evolve without jumps. It is only purely transitory and unexpected realized variance that. The price of variance risk ian dewbecker, stefano giglio, anh le, and marius rodriguez april 29, 2015 abstract in the period 19962014, the average investor in the variance swap market was indi erent to news about future variance at horizons ranging from 1 month to 14 years. In this note we discuss the variance swap market, mechanics, pricing and. A covariance swap is a covariance forward contact of the underlying rates s1 and s2. The variance swap rate consistent with vannavolga prices is found to be given by a simple expression, but may signi cantly underestimate the true variance swap rate. Variance risk premiums city university of new york. We analyze 3 possible pricing methods based on historic data.
The variance swap s vega that is equal to the variance notional refers to the realized variance. Variance swap pricing analysis report january 15, 2011 page 8 of 23 2. Variance swaps pricing mark ioffe abstract this article describes potential practical approaches to volatility swap pricing. This paper features a market implied methodology to infer adequate starting values for the spot and long run variances and for the mean reversion rate of a calibration exercise under the heston model.
Why would an investor trade a variance swap over a volatility. Therefore, the payout will rise at a higher rate than volatility. We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of comaturing put options are given. The payoff of a variance swap is convex in volatility, as illustrated in exhibit 1. A variance swap is a derivative with a pathdependent payoff which allows investors to take positions on the future variability of an asset. Value fairvol analytical estimate of fair volatility fairprice fair rate for variance swap, obtained from equation 27 of demeter. They are swap contracts where the parties agree to exchange a preagreed variance level for the actual amount of variance realised over a period. Payoff a variance swap is an instrument which allows investors to trade future realized or historical volatility against current implied volatility.
Volatility swap struck at 20 variance swap struck at 21. We find that market quotes for variance swaps are surprisingly close to. The weight is given by the underlying level normalized by the underlying level at initiation. Modeling and pricing of covariance and correlation swaps for. For example, an up variance swap may be structured in a way that it accrues realized volatility as long as. Now we can combine the two previous equations, putting together the. Once the underlying drops below this price, the swap stops accumulating volatility. This is so because the correct way to value a swap is to value the portfolio that. Volatility and dispersion strategies in finance core. Analysis of the models used in variance swap pricing. T, kvar is the annualized delivery price for the variance swap, which is set to make the value of a variance swap equal to zero for both long and short positions at the time the contract is. Efficient pricing and superreplication of corridor variance swaps and related products.
Analytic pricing of exotic discrete variance swaps and options yue kuen kwok department of mathematics hong kong university of science and technology hong kong this is a joint work with wendong zheng. Therefore, for completeness, a digression into the theory of stochastic volatility models is done. Cash flows are exchanged at expiry on the basis of daily realised variance versus the strike variance. The blackscholes vega refers to the market implied volatility now if you want, you can estimate the realized variance at expiry from the volatility of the options for instance taking the atm variance arbitrarily, and thats often what people do. Using the url or doi link below will ensure access to this page indefinitely. Asset pricing the large asset price jumps that took place during 2008 and 2009 disrupted volatility derivatives markets and caused the singlename variance swap market to dry up completely. Arbitrage bounds for prices of weighted variance swaps. A corridor variance swap, with corridor c, on an underlying y is a weighted variance swap on x.
Credit default swap spreads and variance risk premia hao wang, hao zhou, and yi zhou 201102 note. A cap can be introduced into the trade so that the writer of the variance swap can limit the maximum loss usually 2. In fact, a variance swap is not really a swap at all but a forward contract on the realized annualized variance. Carr and wu show that we can replicate the payoff from the variance swap rate in which the contracted payoff depends on the difference between the prefixed variance swap rate and the realized return variance that is computed ex post by using outofmoney option prices. As explained later in this document, only variance the squared volatility can be replicated with a static hedge.