Two call options (with the same time to maturity) with strike prices of $36 and $42 cost $7 and $5.5 respectively. Then the maximum possible gain and loss from a bull spread formed using the two calls are respectively

Group of answer choices

$4.5 and $2.5.

$12.5 and infinity.

$12.5 and infinity.

$6 and $12.5.

$4.5 and $1.5.

We have a 4-month European call option on index futures where the current futures price is 200, the exercise price is 205, the risk-free interest rate is 8% p.a. (continuous compounding) and the continuous dividend yield of the index is 2.5%. The futures contract underlying the option matures in six months. The delta of this futures option is 0.5469. Then the option's delta with respect to the index level itself is

Group of answer choices

0.5469.

0.5621.

0.5321.

0.5519.

0.5419.

A 20-month European put option is written on a stock whose current price is $21. The stock will pay a dividend of $1 three months from now and another $1 one and half years from now. The strike price is $24, and the riskfree interest rate is 8%. Then the tightest lower bound for the put option value is,

Group of answer choices

$1.871.

$5.000.

$3.194.

$4.535.

$1.867.

A European call is written on a stock that pays semi-annual dividends of $1.5 each. The last dividend was paid two months ago. The options maturity is five months and its exercise price is $20. The current stock price is $22 and the continuously compounded interest rate is 6% p.a.. Then the call options

Group of answer choices

maximum value is $2.494.

tightest lower bound is $1.024.

tightest lower bound is $2.000.

maximum value is $1.024.

tightest lower bound is $2.494.

Nine-month European put options with strike prices of $30, $40, and $50 cost $1, $3, and $7 respectively. John bought one of each put with exercise prices $30 and $50 and wrote two puts with exercise price $40. The maximum possible net gain and loss for Johns position after nine months are

Group of answer choices

$11 and infinity

$11 and $0

$8 and $0

$11 and $11

$8 and $2