Question

A European call option written on one share of Ponce de Leon Foods, Inc. has the following parameter values: S = $118, X = $108, r = 5% p.a., sigma = 21% p.a., T = 7 months. Find the value of d1, rounded to 4 decimals (e.g., 0.0712).

QUESTION 2 A European call option written on one share of Crook & Crook, Inc. has the following parameter values: S = $34, X = $36, r = 5% p.a., sigma = 20% p.a., T = 7 months. Find the value of d2, rounded to 4 decimals (e.g., 0.0712).

QUESTION 3 A European call option written on one share of Medident Corp. has the following parameter values: S = $220, X = $200, r = 5% p.a., sigma = 30% p.a., T = 9 months. Find the call option's premium, rounded to 2 decimals (e.g., 3.24).

QUESTION 4 Consider three at-the-money (ATM) European call options (i.e., S = X for each of them) written on the same underlying asset, with the following common parameter values: r = 0% p.a. and sigma = 100% p.a. However, one of the options matures in T = 12 months, another in T = 24 months, and the last one matures in 36 months. Based on the premiums of these three call options, what do you conclude regarding the relationship between the call premium and time to maturity? The relationship between the call option's premium and its time to maturity is U-shaped. There is no relationship between the call option's premium and its time to maturity. The call option premium increases as time to maturity increases. The call option premium remains the same as time to maturity increases. The call option premium decreases as time to maturity increases. 3 points

QUESTION 5 Consider three at-the-money (ATM) European PUT options (i.e., S = X for each of them) written on the same underlying asset, with the following common parameter values: r = 0% p.a. and sigma = 100% p.a. However, one of the options matures in T = 12 months, another in T = 24 months, and the last one matures in 36 months. Based on the premiums of these three put options, what do you conclude regarding the relationship between the put premium and time to maturity? The put option premium remains the same as time to maturity increases. The put option premium increases as time to maturity increases. The put option premium decreases as time to maturity increases. There is no relationship between the put option's premium and its time to maturity. The relationship between the put option's premium and its time to maturity is U-shaped. 3 points Q

QUESTION 6 You buy a 1-year put option and sell the corresponding call option. Both options are written on 1 share of IBM stock and both have an exercise price of $119. In addition, you also buy 1 share of IBM stock. What is the net payoff you receive from this 3-asset portfolio if at expiration the price of each share of IBM stock is $18? 5 points

QUESTION 7 Consider two "corresponding" options, consisting of a call and a put with the exact same parameter values. For this pair, the call premium is $7.1. If the current price of the underlying asset is $79 and the present value of the exercise price is $79, what is the premium of the put option, P? Write the answer with one decimal; e.g., 3.2. Do NOT use the $ symbol in your answer; just write a numerical value.

Answer 1

Ans.1).

Current stock price (S)	118.00
Strike price (K)	108.00
Time until expiration(in years) (t)	0.583
volatility (s)	21.0%
risk-free rate (r)	5.00%

d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))

= {ln(118/108) + (5% + (21%^2)/2)*0.583}/(21%*(0.583^0.5))

= (0.0886 + 0.0420)/0.1604 = 0.8142

Ans.2).

Current stock price (S)	34.00
Strike price (K)	36.00
Time until expiration(in years) (t)	0.583
volatility (s)	20.0%
risk-free rate (r)	5.00%

Using the above formula, d1 = {ln(34/36) + (5% + (20%^2)/2)*0.583}/(20%*(0.583^0.5))

d1 = -0.1069

d2 = d1 - (s(t^0.5)) = -0.1069 - (20%*(0.583^0.5)) = -0.2596

Ans.3).

Current stock price (S)	220.00
Strike price (K)	200.00
Time until expiration(in years) (t)	0.750
volatility (s)	30.0%
risk-free rate (r)	5.00%

Formulae:
d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))
d2 = d1 - (s(t^0.5))
N(d1) - Normal distribution of d1
N(-d1) - Normal distribution of -d1
C = S*N(d1) - N(d2)*K*(e^(-rt))

Values for the Black-Scholes model are:

d1	0.6411
d2	0.3813
N(d1)	0.7393
N(d2)	0.6485

Call premium = (220*0.7393) - (0.6485*200*(e^(-5%*0.750)) = 37.71

Ans.4). The call option premium will increase as time to maturity increases.

This can be deduced by analyzing the formula for d1, d2 and call premium.

d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))

Since S = K, ln(S/K) = ln(1) = 0

Everything else remaining same, the numerator will increase with t and the denominator will decrease, so d1 will increase with time. So, N(d1) will increase with increasing value of d1.

d2 = d1 - (s(t^0.5)), so with increasing d1 and t, d2 will decrease and so, N(d2) will decrease, as well.

C = S*N(d1) - N(d2)*K*(e^(-rt))

Call premium will consequently increase with time, as value of N(d1) increases and N(d2) decreases.