# Questions tagged [variance-swap]

Variance swaps are over-the-counter financial derivatives that allow investors to hedge their exposure to the magnitude of possible price movements of underliers, such as exchange rates, interest rates, or stock indexes. [Wikipedia: Variance Swap](https://en.wikipedia.org/wiki/Variance_swap)

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### 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 ...
92 views

### Calendar spreads through variance swaps

Please refer to this image from the famous paper JUST WHAT YOU NEED TO KNOW ABOUT VARIANCE SWAPS by Bossu et al. 2005 (page 6). The underlined part, is there a typo? "if the 2-year IV is above 20....
313 views

### Strike of a Variance Swap in a Sticky Strike World

Imagine there exists a typical negative skew for some underlying I want to price a variance swap on. Critically, let’s say we are in a sticky strike world (the vols of each strike will not change with ...
118 views

### Smile Dynamics - forward variance

I was reading Smile Dynamics II by Lorenzo Bergomi. It is clear to me that on page 2 $$V_t^{T_1,T_2}=\frac{(T_2-t)V^{T_2}_{t}-(T_1-t)V^{T_1}_{t}}{T_2-T_1}$$ is the fair strike of a forward-starting ...
146 views

### Upvar downvar swap $i, i-1, i\land i-1$ conventions

Upvar and downvar swaps are examples of conditional variance swaps. For example a downvar swap only accrues variance for day $i$ (the day whose logarithmic return is $\log S_i/S_{i-1}$) if the ...
43 views

As stated in the title, who first derived the formula $$\text{Varswap strike} = \int_{\mathbb R} I^2(d_2) n(d_2) \, \mathrm d d_2$$ where $d_2$ is the Black-Scholes quantity $$d_2 = \frac{ \log S_t/... 1 vote 0 answers 227 views ### How do banks and dealers effectively hedge a variance swap? It is known that a variance swap can be replicated by a strip of options. However, it is costly to trade that many OTM options and there is not enough liquidity to trade the wings in the quantity that ... 2 votes 0 answers 129 views ### Barrier on realized volatility I am trying to understand the risk exposures of vanilla options that also have a European barrier on realized volatility. For example, the option could knock out if the realized volatility over the ... 7 votes 3 answers 1k views ### Is variance swap long volatility of volatility? In JPM's note on variance swaps, on page 29, they say "... a long variance swap is also long volatility of volatility". In Bennett's book Trading Volatility, on page 115, he says "... a ... 2 votes 1 answer 230 views ### Volatility swaps hedging I have heard that traders use a straddle to hedge volatility swaps (in the FX context), although I could not figure out the specifics. Is this type of hedge used in practice? And if yes, how does it ... 0 votes 1 answer 208 views ### Smile wings and varswap pricing Is it true that far wings of the volatility smile have an outsized influence on the price of a variance swap? Is there a mathematical argument demonstrating this idea? What do we generally refer as ... 0 votes 1 answer 138 views ### Calculating PnL of Options strategies with Volatility Surface New to Vol trading - wondering if there are any good references on calculating PnL from options strategies if I only have a volatility surface (delta or moneyness) and no individual options prices. ... 1 vote 1 answer 113 views ### Impact of stochastic rates on varswaps and volswaps Let us consider that we are looking at issuing some varswaps or volswaps on some FX rate. By longer term I mean something longer than 3 months. Different from this time two years ago, now the interest ... 2 votes 1 answer 191 views ### Initial forward variance curve calibration Let V_t^{T_1, T_2} be the forward variance swap rate for the period [T_1, T_2], seen from t (see for instance Lorenzo Bergomi's Smile Dynamics II) and let \xi_t^T = V_t^{T,T} = \frac{\partial}{\... 2 votes 1 answer 226 views ### A lower bound for variance swap strike There is a famous formula for the variance swap strike that reads$$ K_{var}^2 = \int_{-\infty}^\infty dz\, n(z) I^2(z) $$where I(z) is the Black-Scholes implied volatility function,$$ n(z) = \... 766 views

### Derive the price of log contract

I am reading the Neuberger  Log Contract paper and really confused on the log contract. So if the payoff is $\ln(S_T)$, then we can easily solve the price of such derivative: f_t^s = e^{-r(T-t)...
362 views

### Market price versus theoretical price of varswaps

When I traded varswaps several years ago, for some indices there was a significant mismatch between market price and theoretical price. The theoretical price assumes continuous monitoring and infinite ... 843 views

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

I am very new to derivatives pricing, and I am currently trying to learn these on my own. As far as I can tell, most of the derivatives that are simple (in the sense of having a constant strike that ...
1 vote
101 views

### Practical Effect of Time-Decay on Variance Swaps?

I want to implement a long vol hedging strategy by rolling spot variance swaps every month. This would be done through replicating spot VIX using the definition of VIX as a portfolio of OTM one-month ...
891 views

### Capped Variance Swap // Fair volatility using replication portfolio

I know that the Heston volatility model should be the best approach for computing fair volatility on capped variance swap but is there a way to estimate it from replication portfolio? What I call ...
156 views

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

anyone can provide solution or some idea to the following question? thanks
1 vote
158 views

### VIX and Realised Volatility Scaling

I have calculated the VIX implied volatility according to the CBOE Whitepaper: \begin{equation*} \sigma^2 = \frac{2}{T} \left(\sum_i \frac{\Delta K_i}{K_i^2} Q(K_i) e^{rT} \right) - \frac{1}{T} \...
738 views

### Deriving the VIX formula

I am having trouble filling in a few steps in the derivation. From Martin (2017), we get the following assumptions: Constant continuously compounded rate $r$; The underlying doesn't pay dividens; ...
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### Explicit formula replication of variance swap using vanilla option under black and scholes model with nonzero risk-free rate and nonzero dividend [duplicate]

I didn't find the formula for the following portfolio (variance swap replication) with nonzero risk-free rate and nonzero dividend under black and scholes model : (1) I found formula and proof only ... 297 views

### Replication of variance swap using vanilla option under black and scholes model with nonzero risk-free rate and nonzero dividend [duplicate]

I didn't find the formula for the following portfolio (variance swap replication) with nonzero risk-free rate and nonzero dividend under black and scholes model : I found formula and proof only with ... 72 views

### Variance Swaps for IR products

Just a question here. I am aware that variance swaps for equity products are quite common in the market. However, will anyone be familiar with variance swaps on swap rates in the market? Are they ...
1 vote 