## Volatility Change Before Expiration

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Buy 1 XYZ 100 Call at $1.70

Buy 1 XYZ 100 Put at $1.50

Say index XYZ fluctuated up and down around the level of 100, its level when the straddle was purchased, and 10 days after purchase (20 days before expiration) it was again at the level of 100. 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 XYZ, and that this prediction proved true.

The straddle was originally purchased at an implied volatility level of approximately 14%, but say the volatility level is now approximately 19%. 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?

XYZ 100 call = $1.85 expected value

__ XYZ 100 put = $1.70 expected value__

XYZ 100 straddle = $3.50 expected value

If the investor could sell the straddle at these expected values for both the call and put, the total received would be $3.50, or $350 total. The investor would make a profit:

$3.50 straddle sale price

__-$3.20__ straddle cost

$0.30 profit

The investor’s $0.30 profit ($30 total) after owning the XYZ 100 straddle for 10 days, with the underlying index level unchanged, would come from the expected increase in option implied volatility. This $30 represents a return on the initial $320 investment of 9.4% 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 XYZ unchanged at a level of 100.

While holding the straddle in anticipation of an implied volatility increase, the investor was in a sense protected from a significant move in XYZ, up or down, which was not part of his prediction. In fact, if the level of index XYZ 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.