URGENT

1.Which of the following statements is correct?

Please explain and justify your choice.

		A) The delta of a short position in an at-the-money European call is 0.5.
		B) The delta of a short position in a European put is between 0 and 1.
		C) The vega of a long position in an option increases as we move away from the money.
		D) The gamma and the vega of a long position in a European call is negative.

2.Which of the following statements is correct?

Please explain and justify your choice.

		A) As the time-to-expiration increases (all else remaining unchanged), European calls and puts always become more valuable.
		B)Only the buyer of an option has the obligation to post a margin.
		C)All in-the-money American puts have positive intrinsic value, while all out-of-the-money American puts have a zero intrinsic value.
		D)In a bear market, the holder of a put gains more than then holder of a short position in the underlying asset.

3. Which of the following statements is correct?

Please explain and justify your choice.

		A) A long position in a European call is delta-hedged with a long position in the underlying asset.
		B) A delta-neutral portfolio needs to be rebalanced less frequently as the gamma increases to maintain delta-neutrality.
		C) The delta hedging error increases as the curvature of the relation between the option prices and the stock price increases.
		D) To change the gamma of a portfolio, we need to trade the portfolios underlying asset.

Which of the following statements is correct?

		A) To estimate implied volatility, we do NOT need to change the arbitrary guess of volatility, when the Black-Scholes option price which is based on our arbitrary guess of volatility is greater than the option price observed in the market.
		B) Implied volatility decreases as option prices increase.
		C) Implied volatility is backward looking, i.e. standing at time t, it is the expected volatility under the real probability measure between t and (t - T), where T is the time-to-maturity.
		D) According to Black-Scholes implied volatility should be constant across both the strike price K and the time-to-maturity T.