Options - Binomial Trees

1. A stock price is currently $\$60$. It is known that at the end of three months it will be either $\$63$ or $\$58$. The risk-free rate is $10 \%$ per annum with continuous compounding.
   What is the value of three month European call option with a strik price of $\$59$?


2. A stock price is currently $\$60$. Over each of the next two 4-months periods it is expected to go up by $7\%$ or down by $6 \%$per annum with
   continuous compounding. What is the value of a 8-month European call option with a stick price of $\$61$.


3. A stok price is currently $\$70$.It expected that at the end of 3 months it will be either $\$65$ or $\$75$. The risk-free
   interest rate is $6\%$ per annum with continuous compounding. What is the value of a 3-months European put option with a strike price of $\$70$.


4. A stock price is currently 30. It expected that at the end of 3-months it will be either $\$27$ or $\$33$.
   The risk-free interest rate is 10 per annum with continuous compounding. Suppose $S_{T}$ is the stock price at the end of 3-months. What the value of
   a derivative that pays off $(S_{T})^{3}-3(S_{T})^{2}$

Options

1. Suppose that a party wanted to enter into an FRA that expires in 47 days and is based on 129-day LIBOR.The dealer quotes a rate of 4.65 percent
   on this FRA. Assume that at expiration, the 129-day LIBOR is 4 percent and the notional principal is $\$25,000,000$.
   Calculate the FRA payoff on a long position.
2. Assume Dell expects to receive 30,000,000 Euro in 120 days. A dealer provides a quote of $\$0,885$ for a currency forward contratct to expire in 120 days.
   Suppose that at the end of 120 days, the rate is $\$0.92$. If the settlement is in cash.
   Calculate the cash flow at expiration if Dell enters into a forward contract expiring in 120 days to buy dollars at $\$0.885$
3. Calculate the payoff at expiration for a call option on the S & P 100 stock index in which the underlying price is 755.21 at expiration, the multiplier is 100, and the exercise price is
   
   
   1. 600
   2. 800
4. Calculate the payoff at expiration for a put option on the S & P 100 stock index in which the underlying price is 755.21 at expiration, the multiplier is 100, and the exercise price is
   
   
   1. 600
   2. 800
5. Calculate the payoff at expiration for a call option on the British pound in which the underlying price is 1.321 at expiration, the options are on 100,000 British pound, and the exercise price is
   
   
   1. 1.29
   2. 1.41
6. Calculate the payoff at expiration for a put option on the British pound in which the underlying price is 1.321 at expiration, the options are on 100,000 British pound, and the exercise price is
   
   
   1. 1.29
   2. 1.41
7. Calculate the payoff at expiration for a put option on the British pound in which the underlying price is 1.321 at expiration, the options are on 100,000 British pound, and the exercise price is
   
   
   1. 1.29
   2. 1.41
8. A call option with an exercise price of 50 will expire in 146 days. No cash payments will be made by the underlying asset over the life of the option. If the underlying asset price is at 55 and the risk-free rate of return is 5.0 percent, the lower bounds for an American call option and a European call option, respectively, are closest to :
   
   

   	Lower bound for American call	Lower bound for European call
   A.	5.00	5.00
   B.	5.00	5.96
   C.	5.96	5.00
   D.	5.96	5.96

9. A put option with an exercise price of 60 will expire in 146 days. No cash payments will be made by the underlying asset over the life of the option. If the underlying asset price is at 55 and the risk-free rate of return is 5.0 percent, the lower bounds for an American call option and a European call option, respectively, are closest to :
   
   

   	Lower bound for American call	Lower bound for European call
   A.	3.84	3.84
   B.	3.84	5.00
   C.	5.00	3.84
   D.	5.00	5.00

10. A call with a strike price of 60 is available on a stock currently trading for 55. The call expires in six months and the risk-free rate of return is $10 %$.
    The lower bound on this call value is :
    
    1. is zero
    2. is 5 if the call is American
    3. is 2.2 if the call is European
    4. is 3.12 if the call is European
    
    

Interest Rate

1. A trader write a June put option with a trike price of $\$20$. The price of the option is $\$3$. Under what circumstances does the trader make a gain?


2. A bank quotes you an interest rate of $13\%$ per annum with quaterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?


3. An investor receives $\$110$ in one year in return for an investment of $\$100$ now.
   
   Calculate the percentage return per annum with:
   
   
   1. Annual compounding
   2. semiannual compounding
   3. Monthly compounding
   4. Continuous compounding