1. Calculate the value of a $40-strike at-the-money European call option expiring in 18 months. The risk-free rate is equal to 4% per annum, with continuous compounding, The stocks volatility is equal to 50%. Construct a three-period binomial lattice to value this option.

2. Calculate the price of a $55-strike European put option expiring in 9 months when the

stock is trading for $50. The risk-free rate is equal to 5% per annum, with continuous

compounding, and the stocks volatility is equal to 35%. Use a four-date binomial lattice

to value this option.

3. Calculate the price of a three-year $40-strike in-the-money American call option on a

stock that is trading for $50. The stocks volatility, its dividend yield, and the risk-free

rate are equal to 40%, 3%, and 5%, respectively. Rates are expressed with continuous

compounding. Use a four-date binomial lattice to value this option and spell-out the

value of its early-exercise privilege.

4. Calculate the price of a $35-strike American put option expiring in 6 months when the

stock is trading for $30. The stock will not pay dividends during this period. The

risk-free rate is equal to 5% per annum, with continuous compounding, and the stocks

volatility is equal to 40%. Use a three-period binomial lattice to value this option. Will

the option ever be exercised prematurely given that the stock pays no dividends? If so,

determine the value of its early exercise privilege.

5. Calculate the price of a $78-strike out-of-the-money American call option on a stock that

is trading for $75. The option will expire in 18 months. The stocks volatility is equal to

30%, the risk-free rate is equal to 5% per annum, and the stocks dividend yield is equal

to 2%. Both rates are expressed with continuous compounding. Using a three-period

binomial lattice, determine the value of this options early-exercise privilege. Explain

your result.

6. A stock is trading for $75 on the NYSE and at-the-money options on this stock expiring

in 18 months are currently trading at an implied volatility of 50% on the CBOE. The

risk-free rate is equal to 2% per annum, continuously compounded. Using a three-period

binomial lattice:

(a) Estimate the value of a European call option on this stock, along with the value of its

American counterparts early exercise privilege, should the stock pay no dividends

during the options life.

(a) $20.3172, $0.0000

(b) Estimate the value of a European call option on this stock, along with the value

of its American counterparts early exercise privilege, should the stock pay a single

dividend of $2.25 in 9 months.

(b) $18.8769, $0.0000

(c) Estimate the value of a European call option on this stock, along with the value

of its American counterparts early exercise privilege, should the stock pay a single

dividend of $2.25 in 15 months.

(c) $18.8912, $0.2660

(d) What does this analysis teach us about what drives the value American call options

early exercise privilege?

(d)

Discuss

7. A stock is trading for $75 on the NYSE and at-the-money options on this stock expiring

in 18 months are currently trading at an implied volatility of 50% on the CBOE. The

risk-free rate is equal to 2% per annum, continuously compounded. Using a four-date

binomial lattice:

(a) Estimate the value of a European put option on this stock, along with the value of its

American counterparts early exercise privilege, should the stock pay no dividends

during the options life.

(b) Estimate the value of a European put option on this stock, along with the value

of its American counterparts early exercise privilege, should the stock pay a single

dividend of $2.25 in 9 months.

(c) Estimate the value of a European put option on this stock, along with the value

of its American counterparts early exercise privilege, should the stock pay a single

dividend of $2.25 in 15 months.

(d) What does this analysis teach us about what drives the value American put options

early exercise privilege?

8. An at-the-money call option on the Euro will expire in three months. The spot exchange

rate is $2 per Euro. The domestic interest rate is equal to 5% and the interest rate in

the Eurozone is equal to 6%. The exchange rate volatility is equal to 10%. Calculate

the value of this option without and with early exercise privilege using a binomial lattice

consisting of three periods of equal length.

9. Construct a four-date binomial tree to value a European and an American call option on

the U.S. dollar using Rendelman and Bartters equal probability method. The relevant

inputs are provided in the table below.

Parameter input

Value

Spot exchange rate (USD/CAD)

1.34

Strike

1.30

Tenor (in years)

0.75

Risk-free rate (CAD)

0.0450

Risk-free rate (USD)

0.0472

Volatility

0.15

10. Using the Black-Scholes-Merton (BSM) formula, calculate the price of a 50-strike, at

the-money European call option on a stock trading at an implied volatility of 50%. The

option will expire in one year and the risk-free rate is equal 3% per year. Using put-call

parity, calculate the price of the corresponding put option

11. Using the BSM formula, calculate the price of an $80-strike European put option on

a stock that is trading for $70. The option will expire in 9 months and it is trading

at a 60% implied volatility. The risk-free rate is equal to 2% per year, continuously

compounded. Using put-call parity, calculate the price of the corresponding call option