# What is the Fair Strike in a Var/Vol Swap and how does it relate to its price? [closed]

I am a student trying to price volatility and variance swaps.

People who price those two products usually try to get the "fair strike", and don't seem to care about the price. However, I have a hard time understanding what fair strike means. Also, if people just want to get this value, how do they get a price out of it ?

I couldn't find any good resources about my question, so I decided to ask here.

Edit: Are swaps free? Do the two entities just decide to take the swap at the "fair strike" and then the loser pays to the winner at the end?

• It is like betting on a sports team. Suppose you see the bookmakers have set the Fair Probability of Manchester United winning at p=0.50. If you think the team has a higher probability of winning than this you would bet on them to win, and vice versa. The Fair Strike plays a similar role in Volatility. If you think the volatility will be higher than this you would "buy the volswap". The odds in gambling and the fair strike in vol can be considered a kind of "price" that determines if the deal is attractive to you or not. Commented Mar 20, 2023 at 10:00
• quant.stackexchange.com/a/40768/54838 Shows the strikes. These are swaps, meaning no up front cost (the meaning of fair is that both parties are treated equally). quant.stackexchange.com/a/74354/54838 might also help. Commented Mar 20, 2023 at 10:01

Vol and Var swaps are less 'swap' and more 'forwards'. There's no intermediate transfer of interest before maturity. Contracts will specify how much margin to be posted initially, as well as the required transfer of maintenance margin when required.

The price of a variance swap is the strike. From a purely theoretical standpoint, the price of a variance swap is the price of it's replicating portfolio (OTM options weighted at 1/k^2). In reality because of liquidity and replication constraints there's a bid and offer around the fair value.

The P/L of a long position is given by:

variance notional * (realised variance - strike) * T

If realised variance was 0, then the P/L would be -strike * variance notional * T. I.E the max loss or the price of the swap at inception.

The comments of nbbo2 and AKdemy and the answer by Newquant are correct. In the following, I am trying to expand on their comments and give an explanation which might clarify some concepts for a beginner in the field.

Fair Strike

In the context of volatility and variance swaps, the "fair strike" refers to the strike level at which the swap is considered fairly priced, given the current market conditions and expectations of future volatility. It's the level at which both parties (the buyer and the seller of the swap) believe that the expected future realized volatility or variance is equal to the strike level. This means that both parties should have no advantage over each other in terms of expected returns.

Price of Volatility and Variance Swaps

Swaps are not free, and they do have a price associated with them. The fair strike is used as a starting point for pricing the swap, but there are additional factors that come into play. The price of a swap typically consists of the fair strike adjusted for factors like the risk premium (the amount one party demands for taking on the risk of the swap) and the cost of hedging the swap (which includes transaction costs, bid-ask spreads, and other market frictions).

The pricing of a volatility or variance swap can be more complex than simply looking at the fair strike because market participants may have different expectations about future volatility and risk. The ultimate price of the swap will be determined by supply and demand, and the willingness of the parties involved to accept the risk associated with the swap.

In a swap, the two parties agree to exchange cash flows based on the difference between the realized volatility or variance and the agreed-upon strike level. This exchange occurs at the end or at agreed-upon times during the lifetime of the swap, and the party that has a negative value (i.e., the "loser") pays the other party the absolute value of the difference. The net result is a transfer of risk from one party to another, with one party benefiting from increased volatility and the other benefiting from decreased volatility.