Question 1

A stock is currently trading at a price of 22.You observe the following prices for European put options on the stock (the strikes are in parentheses): $C ( 20 ) = 3.35$ and $C ( 22 ) = 1.95$ .Given this information,you can conclude that the minimum price of the 24-strike call consistent with no-arbitrage is

Accepted Answer

The minimum price of the 24-strike call option can be determined using put-call parity, which is $C + K e^{-rT} = P + S$, where $C$ is the call price, $K$ is the strike price, $P$ is the put price, $S$ is the stock price, $r$ is the risk-free rate, and $T$ is the time to expiration. Since we're not given $r$ or $T$, and assuming they're such that $K e^{-rT}$ is approximately $K$, we can rearrange the formula to find the call price as $C = P + S - K$. Using the information given for the put options, we can infer the price of a put option with a strike price of 24 by creating a synthetic put option through a combination of buying and selling the options and stock given. However, without direct put prices for a 24-strike, we focus on creating a no-arbitrage condition for the call option.Given the information, we don't have direct put prices for a 24-strike, but we can infer that the price of the 24-strike call option must be at least as much as the difference in the intrinsic values of the options and stock positions that could be created to mimic its payoff. The closest we can get to determining this without additional information is recognizing that the call option's price must be non-negative (choice A) and that it should provide no arbitrage opportunity when considering the prices of other options and the stock.However, the correct answer involves recognizing that the call option's price must account for the intrinsic value and the time value, which is not directly calculable from the given information. The minimum price that prevents arbitrage involves comparing the relative prices of options with different strikes but the same maturity. The question seems to aim at understanding the concept of no-arbitrage bounds rather than calculating a specific price based on a formula.Given the lack of direct calculation from the provided information, the answer hinges on understanding that the price of the 24-strike call option must be set in a way that prevents arbitrage opportunities, considering the prices of the other options and the stock. The correct choice, therefore, involves recognizing that there's a minimum value that respects the no-arbitrage condition, which is more than 0 (eliminating A) but without enough information to precisely calculate it based on the given data. The choice B (0.55) is selected based on the principle of no-arbitrage and the need for the call option's price to be consistent with the prices of other options and the stock, but the explanation provided does not accurately reflect a direct calculation from the given data.

Question 2

The FTSE index is at 5,100.You are short a straddle on the FTSE 100 struck at 5,100 and long a 5,000/5,200 strangle.If volatility were to increase,

Accepted Answer

If volatility were to increase, the value of the straddle (which is short) would increase due to higher option premiums, resulting in losses. On the other hand, the value of the strangle (which is long) would increase due to wider breakeven points, resulting in gains. However, since the straddle has a higher gamma (sensitivity to changes in the underlying asset's price) than the strangle, the overall effect would be negative, and the value of the position would decrease. Therefore, the correct answer is C.

Question 3

The FTSE index is at 5,100.You are short a straddle on the FTSE 100.struck at 5,100 and long a 5,000/5,200 strangle.You are also short a 5,000-5,100-5,200 butterfly.Ceteris paribus,an increase in the level of the FTSE

Accepted Answer

Your portfolio's payoff is flat and independent of the level of the FTSE.

Question 4

A stock is currently trading at a price of 22.You observe the following prices for European call options on the stock (the strikes are in parentheses): $C ( 20 ) = 3.25$ , $C ( 22 ) = 1.95$ ,and $C ( 24 ) = 0.40$ .You can conclude from this that

Accepted Answer

The prices of the calls are inconsistent with no-arbitrage because the value of call options should decrease as the strike price increases, which is observed, but the specific prices may not align with the expected decrease based on no-arbitrage conditions.

Question 5

Suppose you are short a call and long a put on the S&P 500 index with the same strike and same maturity.Then,you are essentially holding

Accepted Answer

Being short a call and long a put with the same strike price and maturity creates a synthetic position that mimics being short on the underlying asset, in this case, the S&P 500 index. This is equivalent to a short forward position on the index.

Quiz 8: Options: Payoffs Trading Strategies

The FTSE index is at 5,100.You are short a straddle on the FTSE 100 struck at 5,100 and long a 5,000/5,200 strangle.If volatility were to increase,

The FTSE index is at 5,100.You are short a straddle on the FTSE 100.struck at 5,100 and long a 5,000/5,200 strangle.You are also short a 5,000-5,100-5,200 butterfly.Ceteris paribus,an increase in the level of the FTSE

A stock is currently trading at a price of 22.You observe the following prices for European call options on the stock (the strikes are in parentheses) : $C ( 20 ) = 3.25$ , $C ( 22 ) = 1.95$ ,and $C ( 24 ) = 0.40$ .You can conclude from this that

Suppose you are short a call and long a put on the S&P 500 index with the same strike and same maturity.Then,you are essentially holding