Var Swap 662x2b

VARIANCE SWAP

Volatility • Volatility is a measure of the rate & magnitude of the change of prices (up or down) of the underlying. • Volatility is not concerned with the direction of the change,positive or negative but with the amount of change. • IMPLIED VOLATILITY—It is the market prediction of future volatility, calculated based on the actual stock price, the option's strike (contract) price, time to expiration and other known variables

• REALIZED VOLATILITY-- also known as historic volatility and is the actual variance in the price of an option over time. It is measured in of the standard deviation of the price from an average.

Variance Swap •

A var-swap is an OTC derivative contract in which two parties agree to buy or sell the realized volatility of an index or single stock on a future date.

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Var-swap contracts were first mentioned in 1990.

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VAR-SWAP CASHFLOWS—

Key .. •

SWAP expiration date : The date on which contract expires.

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Observation Days: All trading days which are not disrupted.

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Contract Period: The most liquid variance swap maturities are generally from 3 months to around 2 years, although indices and more liquid stocks have variance swaps trading out to 3 or even 5 years and beyond.

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SWAP-STRIKE : Pre-determined price ,represents the level of volatility bought or sold & is set at trade inception.(volatility is scaled by a factor of 100, for example a strike of 20 represents a volatility of 20%.)

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Variance SWAP Vega : It is the dollar-change in swap value for each percentage –point movement in volatility,trade size is generally expressed in of vega.

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For eq. $ 100,000 vega exposure means that the swap value will change by $ 100,000 for each percentage point change in the volatilty of the underlying index.

VEGA = 2*Volatility(strike)* Notional

Calculation • Buyer Payoff= Notional*(Realized volatility2- Strike Level2)

• Seller Payoff= Notional*(Strike Level2 - Realized volatility2 )

Realized Volatility=

252=Annualization Factor n= no. of observations excluding the initial observation on trade date but including valuation date.

Indexi= Closing level of underlying index.

Mark to Market Variance SWAP • If an investor wishes to close out a variance swap position before maturity they must also consider any change in value of the exposure to volatility over the remainder of the variance swap term.

• Calculation :-

Example :1. One Year Var_swap with STRIKE 20% & Vega Notional $100,000 2. Var Notional = 10,0000/(20*2)= $ 2500 3. Volatility realised over first 3 months= 15% 4. Volatility realised over following 9 months = 25% Variance = [ ¼ x 152 ] + [ ¾ x 252 ] = 525 (≈22.9 volatility) At expiry,Payoff= 2,500 x (22.92 – 202) = $312,500 Note :- We are realising this pay-off now i.e after 3 months & before 9 months ,therefore we need to apply an appropriate INTEREST RATE DISCOUNT FACTOR.

So,If after 3-months, 9-month LIBOR is 4%, the discount factor applied would be 1/(1+¾ x 0.04) = 0.97 Variance = [ ¼ x 152 ] + [ (¾ x 252)*0.97 ] = 22.60

Var SWAP Contract Specifications 1. Margins and collateral :- Variance swaps are usually margined in a similar manner to options, with an initial amount to be posted as collateral, Further margin calls will be made during the course of the trade as necessary. Settlement is calculated at maturity and cash-flows exchanged shortly afterwards.(T+2). 2 . Disrupted days :- The realised variance used in a variance swap payout is calculated from closing (or official observed) prices on observation dates (scheduled trading days which are not disrupted) over a specified period. 15th day- 16,800(Index Close) 16th day- 16,300 17th day-16,600 (Here, 2.9% loss is followed by 1.84% gain(Net-loss1.06%)if 16th day is declared as disrupted,(net loss 1.19%))

3. Index reconstitution risk :- Variance swaps on indices are defined to pay out on the returns of the index and not on the weighted returns of the basket of current constituents. This means that index variance swaps (especially longdated ones) will be exposed to the risk of index reconstitution, and the variance swap may end with an exposure to a very different set of stocks, potentially with different volatility characteristics than when it was originally traded. 4. Dividend adjustments :- Variance swaps on single names are typically adjusted for dividends,i.e the return on the ex-dividend date is calculated after adjusting for the dividend. (By convention index variance swaps are not usually adjusted for dividends) Eq-If a stock is worth $100 on the day before dividend ,pays a dividend of $5 & closes at $94, on its ex-dividend day,the return used in calculating realized volatility for var-swap payout will be 94/95-1= -1.05% & NOT (94/100-1=-6%)

5. Variance swap caps :- Variance swaps, especially on single-stocks (and sector indices), are usually sold with caps. These are often set at 2.5 times the strike of the swap capping realised volatility above this level. Variance swap caps are useful for short variance positions, where investors are then able to quantify their maximum possible loss.

Max Loss for short=

Advantages • Variance swaps offer investors a means of achieving direct exposure to realized variance without the path-dependency issues associated with delta-hedged options. • variance swaps are convex in volatility: a long position profits more from an increase in volatility than it loses from a corresponding decrease.