Currency Variance Swap Payout Calculator
Calculate the periodic payout of a currency variance swap by comparing realized variance to the strike variance over a given tenor. Used by options traders and risk managers settling volatility positions.
About this calculator
A currency variance swap pays the difference between realized variance and a pre-agreed strike variance, scaled by a notional amount. The payout formula is: Payout = Variance Notional × (Realized Variance − Strike Variance) × (Swap Tenor / 365) / Payment Frequency. Realized variance is the actual squared daily return of the currency pair annualized over the observation period, while strike variance is the fixed level agreed at trade inception (often the square of implied volatility). If realized variance exceeds the strike, the variance buyer receives a payment; if it falls short, the buyer pays. Unlike volatility swaps, variance swaps have convex payoffs—large moves are rewarded disproportionately—because variance grows with the square of returns.
How to use
Assume Variance Notional = $1,000,000, Strike Variance = 0.04 (equivalent to 20% vol²), Realized Variance = 0.06 (equivalent to ~24.5% vol), Swap Tenor = 180 days, Payment Frequency = 2 (semi-annual). Payout = $1,000,000 × (0.06 − 0.04) × (180/365) / 2 = $1,000,000 × 0.02 × 0.4932 / 2 = $1,000,000 × 0.004932 = $4,932. The variance buyer receives $4,932 for this payment period, reflecting that the currency was more volatile than the strike implied.
Frequently asked questions
What is the difference between a variance swap and a volatility swap in FX markets?
A volatility swap pays based on the difference between realized volatility (standard deviation) and a strike volatility, while a variance swap pays based on realized variance (volatility squared) versus a strike variance. Because variance is the square of volatility, variance swaps have a convex payout profile: large market moves benefit the long variance holder disproportionately compared to a volatility swap. Variance swaps are more common in practice because they can be replicated perfectly using a portfolio of vanilla options, making them easier to hedge and price. Volatility swaps require a convexity correction.
How is realized variance calculated for a currency variance swap?
Realized variance is computed from the daily log returns of the currency pair over the swap's observation period. Each day's return is r_t = ln(S_t / S_{t-1}), and realized variance is the annualized average of these squared returns: σ² = (252 / N) × Σ r_t². The factor 252 reflects the number of trading days in a year. This value is compared to the strike variance agreed at trade inception. Disputes about realized variance calculations—especially around non-trading days, holidays, and disruption events—are governed by the ISDA definitions embedded in the swap confirmation.
Why would a trader buy or sell a currency variance swap?
A trader who expects the currency pair to be more volatile than the level priced into options (i.e., realized variance > strike variance) would buy the swap to profit from that view. Conversely, a trader who thinks the market is overpricing volatility would sell variance to collect the premium if the pair remains calm. Variance swaps are also used as pure hedges against volatility exposure embedded in an existing options book. Because their payoff is path-independent and linked directly to realized variance, they are cleaner instruments for volatility exposure than delta-hedged options positions.