$1.$

Question $1$

Background: You should build a $15-$period binomial model whose parameters are calibrated to a Black$-$Scholes geometric Brownian motion model with:

$$

$=$

$0\mathrm{.}25$

T$=0\mathrm{.}25$ years,

$$

$0$

$=$

$100$

S

$0$

$$

$=100,$

$$

$=$

$2$

$\%$

r$=2\%,$

$$

$=$

$30$

$\%$

$\backslash$sigma $=30\%$ and a dividend yield of

$$

$=$

$1$

$\%$

c$=1\%.$ Your binomial model should use a value of

$$

$=$

$1\mathrm{.}0395...$

u$=1\mathrm{.}0395....($This has been rounded to four decimal places but you should not do any rounding in your spreadsheet calculations.$)$

Compute the price of an American call option with strike

$$

$=$

$110$

K$=110$ and maturity

$$

$=$

$.$

$25$

T$=\mathrm{.}25$ years.

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$0/1$ point

$3\mathrm{.}15$

Incorrect

$2.$

Question $2$

Following the background in Question $1$

Compute the price of an American put option with strike

$$

$=$

$110$

K$=110$ and maturity

$$

$=$

$.$

$25$

T$=\mathrm{.}25$ years.

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$0/1$ point

$11\mathrm{.}54$

Incorrect

$3.$

Question $3$

Following the background in Question $1$

Is it ever optimal to early exercise the put option of Question $2?$

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$1/1$ point

Yes

No

Correct

$4.$

Question $4$

Following the background in Question $1$

If your answer to Question $3$ is "Yes", when is the earliest period at which it might be optimal to early exercise? $($If your answer to Question $3$ is $"$No$",$ then you should submit an answer of $15$ since exercising after $15$ periods is not an early exercise.$)$

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$0/1$ point

$3$

Incorrect

$5.$

Question $5$

Following the background in Question $1$

Do the call and put option prices of Questions $1$ and $2$ satisfy put$-$call parity?

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$1/1$ point

Yes

No

Correct

Put$-$call parity is only satisfied by European options

$6.$

Question $6$

Following the background in Question $1$

Compute the fair value of an American call option with strike

$$

$=$

$110$

K$=110$ and maturity

$$

$=$

$10$

n$=10$ periods where the option is written on a futures contract that expires after $15$ periods. The futures contract is on the same underlying security of the previous questions.

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$0/1$ point

$1\mathrm{.}94$

Incorrect

$7.$

Question $7$

Following the background in Question $1$

What is the earliest time period in which you might want to exercise the American futures option of Question $6?$

Round all your answers to $2$ decimal places. So if you compute a price of $12\mathrm{.}9876$ you should submit an answer of $12\mathrm{.}99.$

$0/1$ point

$10$

Incorrect