A variance swap lets you bet on "realized" variance. The exchange automatically calculates realized variance for each day, so if you bet the total realized variance over the next 3 days will

[1] which means 80% vol (annualized), or roughly 5% daily realized vol (un-annualized)

Standard var swap PnL is defined as

*average*to exceed 0.64 [1], then you can buy this contract. If it turns out to be 0.7812, you earn the difference of 0.1412 notional which would mean $141,200 on a million dollar notional.[1] which means 80% vol (annualized), or roughly 5% daily realized vol (un-annualized)

Standard var swap PnL is defined as

(sigma_r

^{2}- K) N ….. ...(1)where

N denotes notional amount like $1,000,000

K denotes strike, which is always in terms of annualized variance

sigma_r is annualized realized Vol over the n days, actually over n-1 price relatives sigma_r

^{2}is annualized realized Variance, and calculated as 252/(n-1) [ ln

^{2}(S2/S1) + ln^{2}(S3/S2)^{ }+ … + ln^{2}(S_{n}/S_{n-1}) ]where

S2 denotes the Day 2 closing price.

ln

ln(S2/S1) is known as daily realized Vol un-annualized, or DRVol^{2}(S2/S1) is known as daily realized Variance un-annualizedIn other words, take the n-1 values of ln(PriceRelative) and find the stdev assuming 0 mean, then annualize.

A more intuitive interpretation -- take the

*average of the n-1 daily realized variances, then multiply by 252*.

Now, trading often work with DRVol rather than the S2 stuff above, so there’s an equivalent PnL formula to reveal the contribution of "today’s" DRVol to a given var swap position, and also track the cumulative contribution of each day’s DRVol. Formula (1) becomes PnL ==

252N/(n-1)*[ ln

^{2}(S2/S1)-K/252 + ln^{2}(S3/S2)-K/252 + .. + ln^{2}(S_{n}/S_{n-1})-K/252 ], orN/(n-1)*[ 252ln

^{2}(S2/S1)-K + 252ln^{2}(S3/S2)-K + .. + 252ln^{2}(S_{n}/S_{n-1})-K ]where

N/(n-1) represents the notional amount allocated to each day.

252ln

√252 ln(S2/S1) represents the annualized DRVol, but is omitted from the formula due to clutter^{2}(S2/S1) represents the annualized daily realized Variance on Day 2closing | PR | ln PR | sqrt(252) ln PR | spread over K | daily PnL contribution |

$1,200 | |||||

$1,250 | 1.041667 | 0.040822 | 64.8029% | 0.32994168 | $1,374,757 |

$1,240 | 0.992 | -0.00803 | -12.7507% | -0.073742023 | -$307,258 |

$1,275 | 1.028226 | 0.027835 | 44.1864% | 0.105243561 | $438,515 |

$1,200 | 0.941176 | -0.06062 | -96.2386% | 0.836186882 | $3,484,111 |

You can then add up the daily contributions, which would add up to the same total PnL by Formula in (1).

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