## Volatility Change Before Expiration

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Buy 1 SPX 1400 Straddle at $41.50 Debit

(Buy 1 SPX 1400 Call at $22.20)

(Buy 1 SPX 1400 Put at $19.30)

Say SPX index fluctuated up and down around the level of 1400, its level when the straddle was purchased, and 10 days after purchase (20 days before expiration) it was again at the level of 1400. Time decay would have its natural, negative effect on the value of both options. But assume the investor initially bought the straddle motivated more by a predicted increase in option implied volatility than an expected change in the level of SPX, and that this prediction proved true.

The straddle was originally purchased at an implied volatility level of approximately 13%, but say the volatility level is now approximately 18%. What prices might the investor expect to see in the marketplace for both the long at-the-money call and put, given no change in interest rates or dividend yield of the underlying index?

SPX 1400 call = $24.50 expected value

__SPX 1400 put = $22.50 expected value__

SPX 1400 straddle = $47.00 expected value

If the investor could sell the straddle at these expected values for both the call and put, the total received would be $47.00, or $4,700 total. The investor would make a profit:

$4,700 total sale price straddle

-__ $4,150__ total straddle cost

$550 profit

The investor’s $550 profit after owning the SPX 1400 straddle for 10 days, with the underlying index level unchanged, would come from the expected increase in option implied volatility. This $550 represents a return on the initial $4,150 investment of 13.3% over 10 days. If during this 10-day period the option implied volatility actually decreased, which was not expected by the investor, the straddle would most likely show a loss due to time decay with SPX unchanged at a level of 1400.

If the level of SPX index had increased (or decreased) dramatically while owning the straddle, a profit might have been made from a concurrent increase in value of the call (or the put) instead, without an implied volatility increase.