Quantitative Finance
# Option Strategies

You think that with impending news, the stock would most likely not move more than 3%, but there is a 10% chance that it would move more than 10%.

Which of the following option positions are you most likely to put on?

**True, False or It depends?**

We know that the ATM straddle price can be approximated by the formula

$Y_{ATM} = \frac{ 1}{ 2000} S \sigma \sqrt{t}.$

Since gamma is the second (partial) derivative with respect to the underlying price $S$, the gamma of the straddle is 0.

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 call on the 30 strike is trading $2.10 at $2.11, the call on the 32 strike is trading $1.34 - $1.35. Your broker calls you up and says that his market for the 31 call is $1.80 bid at $1.81.

Assuming no transaction fees (other than the bid ask spread) or execution risk , how would you trade the 31 call?