Observations of the ATM straddle price
Quantitative Finance
Level
2
On the week of expiry, you recorded the closing price of the ATM straddle as follows:
| Trading days left | 5 | 4 | 3 | 2 |
| Price of Straddle | 3.35 | 3.23 | 3.03 | 2.73 |
What can you conclude is happening?
The market is mispriced
There is nothing wrong
The volatility is increasing greatly
Time is passing at a slower rate
The stock price is increasing greatly
The straddle approximation formula does not hold when
days
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1 solution
From the straddle approximation formula, Y = 2 0 0 0 S σ t . Thus, if the stock price and volatility stay constant, then the ratio of the price of the straddle should be 5 : 4 : 3 : 2 . As such, if the straddle price started out at 3.35, then the corresponding prices should have been 3 . 3 5 , 2 . 9 9 . 2 . 5 9 , 2 . 1 2 .
We can see that the given prices are quite a bit higher than these calculated values, which implies that S σ must be increasing.
Looking at the 3 days left and 2 days left, we see that S σ have gone up by 17% and 29% respectively. It is somewhat unlikely that this is completely due to the stock price jumping up by those amounts, without seeing a great increase in volatility. Instead, the main reason for the price increase would be that the implied volatility of these options is increasing.
Such a scenario occurs when there is major news that is announced on the day of expiration of the straddle. In this case, the straddle is pricing in the expected movement on the last day, and that the volatility on the last day is much much higher than the volatility of the rest of the week.