Which of the following statements are true:I.

Delta hedges need to be rebalanced periodically because with changes in prices, delta changes, and the amount of hedge required changes as well, requiring a readjustment. The more frequent the rebalancing, the better the performance of the hedge. However, the greater the rebalancing frequency, the greater are the number of trades required, increasing the costs from trading. The trader has to balance transaction costs against the adverse effects from poorer hedge performance. Therefore rebalancing frequency is a consideration for a trader and statement I is true.

Statement II is not true. When options are granted, their future impact on the price gets priced in into the current price, and no change occurs when these are actually exercised.

Statement III is true. Consider the Black Scholes PDE

202.23.e1

and substitute delta = 0 (as this is a delta neutral portfolio), and we get the result 202.23.e. Since r is generally small, a large negative theta means a large positive gamma and vice-versa. Therefore theta can be used as a proxy for gamma and this statement is correct.

Statement IV is correct. Vega is highest closest to the strike price - look at the graph for vega to see how vega behaves with changes to spot. (Do it yourself or there is a graph in the tutorial too.)