5 votes
Accepted

Is variance swap long volatility of volatility?

My two cents: Let's agree that a derivative is long an underlying if the payoff of the derivative increases with the price of the underlying $S$. Then buying a variance swap is going long the ...
Frido's user avatar
  • 1,854
5 votes

Is variance swap long volatility of volatility?

What about the following argument: a variance swap can be replicated with a portfolio of vanilla options, nearly all of which are out of the money (OTM) . But it is well known that OTM options are ...
dm63's user avatar
  • 17k
5 votes
Accepted

Market price versus theoretical price of varswaps

The well-known formula expressing the price of a variance swap as a function of an (infinite) strip of European options is actually not that model-free: it assumes that the price process follows a ...
Quantuple's user avatar
  • 14.6k
4 votes

Variance Swaps for IR products

In this month's Risk magazine, there was a research paper stating precisely There is no liquidity in the variance swaps of interest rates.
siou0107's user avatar
  • 2,680
4 votes
Accepted

Structured question on mark-to-market value of a variance swap

The (undiscounted) value of any derivative is the expected value of the payoff. So the (undiscounted) value of a varswawp is: $$\mathbb{E}\left[ \mathrm{Notional} \cdot 10000 \cdot \left( K^2 - \...
will's user avatar
  • 2,571
4 votes
Accepted

Different types of swaps and generalized pricing structure - correlation swap, variance swap, volatility swap, gamma swap, etc

For Variance Swaps (and Vol swaps with some caveats), the Black Scholes model is the main tool used for pricing. It is just less obvious. Using your example, options are not priced with S-K or K-S ...
AKdemy's user avatar
  • 8,739
4 votes
Accepted

Smile wings and varswap pricing

The main concern is usually for the far wing where strikes are low. Variance swaps have a theoretical replication. The fair variance swap strike $K_{var}$ is computed as $$ K^2_{var} = \frac{2*e^{rT}}...
AKdemy's user avatar
  • 8,739
4 votes

Is variance swap long volatility of volatility?

Since the variance swap is linear in variance. Its local volatility exposure is 2σ, with second derivative = 2. If one was to hedge this local volatility exposure using options or a volatility swap, ...
Newquant's user avatar
  • 769
3 votes
Accepted

Volatility swaps hedging

Although this question seems Taylor-made for me, I shall resist promoting my own work and refer you instead to Carr and Lee's seminal paper Robust replication of volatility derivatives. Basically what ...
Frido's user avatar
  • 1,854
2 votes

Calculating PnL of Options strategies with Volatility Surface

The function that converts option prices and implied vols is bijective. So yes, you can compute the PnL given you have the volatility surface and you know the parameters that where used in its ...
Rodrigo's user avatar
  • 310
2 votes
Accepted

Impact of stochastic rates on varswaps and volswaps

I can't post this as a comment yet (not enough reputation), but for the impact of stoch rates on varswaps you can take a look at his: Horfelt & Torne, The value of a variance swap - a question of ...
p.sibuea's user avatar
2 votes
Accepted

A lower bound for variance swap strike

It is indeed perfectly correct under your working assumptions. This is actually what Gatheral also notes in his book 'The Volatility Surface: A Practioner's Guide' (Chapter 11 on Variance Swaps, pages ...
Quantuple's user avatar
  • 14.6k
2 votes

Strike of a Variance Swap in a Sticky Strike World

The fair strike computed via replication equals the integral of weighted prices of out-of-the-money options over all strikes. As you wrote correctly, these weights are being inversely proportional to ...
AKdemy's user avatar
  • 8,739
2 votes
Accepted

Smile Dynamics - forward variance

Ok, so $$ d\xi_t^T = \omega e^{-k(T-t)} \xi_t^T dW_t $$ where $W$ is standard Brownian. Then, just by applying Ito I hope you can see that $$ \log \xi_t^T / \xi_0^T = \omega \int_0^t e^{-k(T-u)} dW_u -...
Frido's user avatar
  • 1,854
1 vote

How to trade forward volatility?

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 $...
StochasticMan's user avatar
1 vote

Calendar spreads through variance swaps

No, there is no typo, just sloppy language. I don't know which book this is from, but the example concerns a forward start variance swap. The forward start variance swap strike is today's expectation ...
Frido's user avatar
  • 1,854
1 vote

Strike of a Variance Swap in a Sticky Strike World

Hi Saul5813, I've put together the variance swap fair strike as spot moves, under a linear skew model where v(k) = 0.3 - 0.1*(k/s0 - 1). For the purpose of looking at sticky strike, I fixed the vols ...
Newquant's user avatar
  • 769
1 vote
Accepted

Derive the price of log contract

Applying the Ito lemma, you prove easily that the dynamics of $F_t$ in risk-neutral measure $\Bbb Q$ is $$ \frac{dF_t}{F_t} = \sigma dW_t $$ (the drift is $0\cdot dt$, in stead of $r\cdot dt$ as in ...
NN2's user avatar
  • 1,008
1 vote

Different types of swaps and generalized pricing structure - correlation swap, variance swap, volatility swap, gamma swap, etc

I think the $^+$ was just a typo. Nice question! I'll try to make this point in the case of interest-rates, but the argument is general. To some extent it’s case by case, but the general feature of a ...
Gabriele Pompa's user avatar
1 vote

Deriving the VIX formula

The VIX formula is based on Demeterfi et. al 1999 and their final variance swap replication formula is given by: $$ \begin{align}\label{eq:rep_formula} \mathbb{E}\big[\mathbb{V}\big] &= \frac{...
Martin Georg Haas's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible