Explain the cash flow of the volatility, Financial Management

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1. Let's look at the cash flow of the volatility (variance) spread swap:

-(σ2Nasdaq- σ2S&P500)N2

It is noticeable from this expression that investor actually takes a long position on the S&P500 variance and a short position on the NASDAQ variance. This trade is able to be put in place by simultaneously entering into a long S&P500 variance swap and a short NASDAQ variance swap.

Pricing here is to conclude the initial variance swap spread which makes the initial value of the swap between the two indices have a value of zero. This price is specified as 21% in the question.

2. Of course we need the correlation between the two markets. If the correlation is high close to one in absolute value among these markets then this implies that most of the time volatility will move in both markets in the same direction which in return indicates that volatility (variance) spread is relatively tight in the long run this makes the position mentioned in the query reasonable. Consequently the fixed leg of the spread has to be set (relatively) higher.

If the correlation is low near to zero in absolute value which implies that these two markets move more or less independently from every other then there is no reason to believe that the volatility spread between the markets should get narrower.

It is less probable that the investor who holds a long position will end up with a positive payoff. In order to make the initial value of the swap equal to zero the fixed leg of the spread requires to be set at a lower level.

3. The smile effect is significant. Nevertheless in this present case the trade concerns realized volatility and not the Black-Scholes implied volatility.

This signifies that the pricing of the swap will make no use of the smile in any direct way. Indirectly the smile is able to be useful to calibrate a model on the other hand.

4. If the position is taken by utilizing volatility (variance) swaps then this may be less risky compared to the other ways of taking the same position. As well the pricing of the instrument may be easier.

The major risk involved here is related to the assumption that the long run dynamics of the volatility spread is stationary. If this underlying supposition is violated then the position may lose.


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