Forward Volatility Agreement (FVA) & Forward Variance Lab

Price institutional Forward Volatility Agreements (FVA) and forward starting variance swaps. Model calendar variance replication, forward convexity drag, and term structure roll-down carry.

Volatility Term Structure Presets:
Forward Vol Strike

23.2%

$F_{\text{vol}} = \sqrt{K_{\text{var}}(T_1, T_2)}$
FVA Fair Strike

22.8%

Convexity-Adjusted
Forward Convexity Drag

-0.42 pts Drag

Jensen's Inequality Gap
Expected FVA P&L

+$47.8k

Long Forward Position
Roll-Down Carry

+5.2 pts / yr

Forward vs Near Spot Vol
Forward Window

3M → 12M (9m Window)

Maturity Horizon
Term Structure & Contract Parameters
Start of the forward volatility window.
End and settlement of the forward contract.
%
Fair variance strike volatility to maturity $T_1$.
%
Fair variance strike volatility to maturity $T_2$.
$
Dollar payoff per 1.0 percentage point in forward vol.
%
Volatility of forward variance for convexity drag.
%
Benchmark forecasted volatility realized in $[T_1, T_2]$.
%
Spot Volatility Curve & Forward Volatility Segment Calendar Identity: $K_{\text{var}}(T_1, T_2) = \frac{K_2 T_2 - K_1 T_1}{T_2 - T_1}$

The dashed segment represents the forward volatility implied by the term structure curve between near maturity $T_1$ and far maturity $T_2$. In contango, forward volatility trades above near spot volatility; in backwardation, forward volatility drops sharply.

Terminal Payoff: Linear FVA vs Convex Forward Variance Swap ($k) Payoff: $N_{\text{vega}} \times (\sigma - K_{\text{fwd}})$ vs $N_{\text{var}} \times (\sigma^2 - K_{\text{var}})$

A Forward Volatility Agreement (FVA) delivers pure linear exposure to realized forward volatility, while a forward variance swap produces a parabolic payoff with positive convexity during extreme forward volatility spikes.

Holding Period Carry: Cumulative Roll-Down P&L ($k) Contango Roll-Down Bleed

When trading forward volatility, holding a long forward position in an upward sloping term structure incurs negative roll-down carry as time passes towards $T_1$ without a market volatility shock.

Near Vol vs Far Vol: Fair Forward Vol Strike Matrix
Evaluates Fair Forward Implied Volatility ($F_{\text{vol}} \%$)
Realized Forward Vol vs Vega Notional: P&L Matrix
Evaluates Expected Long FVA Dollar P&L ($k)

Institutional Theory & Market Mechanics

1. Calendar Replication of Forward Variance

By the additivity of quadratic variation, total integrated variance from today ($t=0$) to far maturity $T_2$ decomposes into variance accumulated to near maturity $T_1$ plus forward variance over the window $[T_1, T_2]$:

$K_{\text{var}}(0, T_2) \cdot T_2 = K_{\text{var}}(0, T_1) \cdot T_1 + K_{\text{var}}(T_1, T_2) \cdot (T_2 - T_1)$

Solving for the forward variance strike $K_{\text{var}}(T_1, T_2)$:

$K_{\text{var}}(T_1, T_2) = \frac{K_{\text{var}}(T_2) \cdot T_2 - K_{\text{var}}(T_1) \cdot T_1}{T_2 - T_1}$

This identity allows desks to statically synthesize forward starting variance swaps by buying $T_2$ variance swaps and selling $T_1$ variance swaps in exact calendar hedge ratios.

2. Forward Convexity Drag (Jensen's Inequality)

While a forward variance swap pays on squared returns, a Forward Volatility Agreement (FVA) pays linearly on annualized forward volatility:

$\text{Payoff}_{\text{FVA}} = N_{\text{vega}} \cdot \left(\sigma_{\text{realized}}(T_1, T_2) - K_{\text{fwd, vol}}\right)$

Because the square root function is strictly concave, Jensen's inequality dictates that expected forward volatility is strictly less than the square root of expected forward variance: $\mathbb{E}[\sigma_{T_1, T_2}] < \sqrt{K_{\text{var}}(T_1, T_2)}$.

The fair strike $K_{\text{fwd, vol}}$ incorporates a second-order forward convexity drag proportional to forward vol-of-vol $\xi^2$ and the forward horizon length $T_2 - T_1$.

3. Term Structure Roll-Down & Carry

In upward-sloping (contango) volatility term structures, forward volatility trades above near-term spot volatility: $F_{\text{vol}}(T_1, T_2) > \sigma_1$.

$\text{Roll Carry} = F_{\text{vol}}(T_1, T_2) - \sigma(T_1)$

Investors who buy forward volatility suffer from negative roll-down carry if spot volatility remains suppressed. Conversely, forward volatility sellers harvest this roll yield in calm market regimes.

4. Forward Event Volatility Pricing

Corporate earnings releases, FOMC interest rate announcements, and political elections represent discrete volatility catalysts.

Because these events occur inside specific calendar windows, option markets concentrate implied variance directly into the forward period $[T_1, T_2]$, creating localized forward volatility spikes even when spot volatility appears subdued.

Quantitative Forward Volatility Mastery Quiz

1. What formula calculates the fair forward variance strike between $T_1$ and $T_2$?

2. What happens to a long forward volatility position in a steep contango term structure?

3. How is a forward starting variance swap replicated statically?

4. What characterizes the forward volatility curve during an acute market panic?

Frequently Asked Questions

A Forward Volatility Agreement (FVA) is a forward contract on future realized volatility over a forward window [T1, T2] whose payoff is strictly linear in realized volatility: Payoff = N_vega * (sigma_realized - K_fwd_vol). In contrast, a forward variance swap pays on realized variance: Payoff = N_var * (sigma_realized^2 - K_var_fwd), which exhibits quadratic positive convexity.

By the additivity of integrated variance, the total variance to maturity T2 equals the variance to T1 plus the forward variance from T1 to T2: K_var(0, T2) * T2 = K_var(0, T1) * T1 + K_var(T1, T2) * (T2 - T1). Solving for forward variance gives K_var(T1, T2) = [K_var(T2) * T2 - K_var(T1) * T1] / (T2 - T1). This can be statically synthesized by going long a T2 variance swap and short a T1 variance swap.

By Jensen's Inequality, because the square root function is strictly concave, the expected value of future realized volatility is strictly less than the square root of expected future variance: E[sigma_{T1, T2}] < sqrt(E[sigma_{T1, T2}^2]). Consequently, the fair strike for a linear FVA is lower than the square root of forward variance, with the gap representing forward convexity drag.

Forward roll-down carry is the difference between forward volatility and near-term spot volatility: Carry = F_vol(T1, T2) - sigma(T1). In an upward-sloping (contango) term structure, forward volatility trades at a premium; holding long forward volatility incurs negative roll carry as the contract matures without a volatility shock. In backwardation, forward volatility trades at a discount, offering positive roll yield.

When a major discrete catalyst (such as an FOMC interest rate decision, election, or earnings announcement) occurs in a forward window [T1, T2], option traders bid up options expiring after the event relative to those expiring before it. This concentrates high expected variance in the forward period, causing forward implied volatility F_vol(T1, T2) to decouple from the broader term structure.
Related Volatility & Derivatives Simulators:
VIX Futures & Options Lab Corridor Variance Swap Lab Volatility Swap Lab Variance Swap Lab Correlation Swap Lab CBOE VIX Index Lab Implied Vol Surface Lab