Isolating Forward Volatility with Forward Options and Variance Swaps
Summary
The document discusses ways to gain exposure to volatility over a future interval, from one future date to another. One proposed instrument is an option whose underlying payoff depends on the asset’s return between those dates. Under a diffusive price model, the ratio of the two future prices removes dependence on the initial price, leaving exposure to volatility during the later interval. The option can be viewed through implied volatility for a strike set at the asset’s level on the first date and a maturity spanning the interval.
A second approach combines variance swaps by holding one with the later maturity and shorting one with the earlier maturity. This aims to isolate realized variance accrued between the two dates, represented through squared log returns. The answer sketches these exposures but gives no pricing derivation, empirical evidence, or practical implementation details. It does not establish that either instrument solves the skew and changing at-the-money risks raised for calendar spreads, and the variance swap payoff is presented schematically.
Key ideas
- A forward option can expose a trader to volatility over an interval that begins in the future.
- The future price ratio removes dependence on the initial asset price under the stated diffusive model.
- A long later-maturity and short earlier-maturity variance swap position targets variance over the intervening period.
- The response offers a conceptual outline without pricing details or evidence on implementation risks.
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Full text
# How to trade forward volatility?
# How to trade forward volatility?
What would be the best way to trade forward volatility or term structure?
One way, I think of is through gamma neutral calendar spreads. The problem with this approach is "change of ATM" and the steep skew which near term maturity(short leg) has is hard to manage.
The other approach is through variance swap, I am not much familiar with this approach and trying to understand it. Does variance swap cover the shortcomings of "gamma neutral calendar spread"
Would high appreciate the response. Much Thanks!!
## Answer by StochasticMan (score 2)
https://quant.stackexchange.com/a/77150
A simple way to get exposure to forward volatility is by trading a call/put that strikes in future. Consider for example the payoff: $ \left(\frac{S_{T_2}}{S_{T_1}}-1 \right)^+ $ where both $T_1$ and $T_2$ lies in the future.
Without any assumption on the volatility model, just supposing that S has a diffusive dynamic i.e : $dS_t = \sigma_t dW_t$ . You can see that $ \frac{S_{T_2}}{S_{T_1}} = e^{\int_{T_1}^{T_2}\sigma_t dW_t - \frac{1}{2} \int_{T_1}^{T_2}\sigma^2_t dt }$ an thus you've killed any second order sensitivity to $S_0$ and you're only sensitive to volatility $(\sigma_t)$ for $ t \in [T_1,T_2]$ .
A way to see it is by following a gentle Black Scholes pricing, your option price will sensitive to the implied volatility $\hat{\sigma}_{(S_{T_1}, T_2 - T_1)}$ of strike $S_{T_1}$ and residual maturity $T_2 - T_1$.
Talking about variance swap, just suppose you are long a variance swap of maturity $T_2$ and short another one of maturity $T_1$ so you just have to care about accounted variance from $T_1$ to $T_2$ i.e your payoff will be driven by the following term: $ \sum_{T_1}^{T_2} \ln^2 \left(\frac{S_{T_{i+1}}}{S_{T_i}} \right)$Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.