Question
In: Advanced Math
A stock sells for $84 and pays a continuously compounded 3% dividend. The continuously compounded risk-free...
A stock sells for $84 and pays a continuously compounded 3% dividend. The continuously compounded risk-free rate is 5%.
a. What is the price of a pre-paid forward contract for one share to be delivered six months (.5 year) from today?
b. What is the price of a forward contract that expires six months from today?
c.Describe the transactions you would undertake to use the stock and bonds (borrowing and lending) to construct a synthetic long forward contract for one share of stock.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
The IF500 stock index pays no dividends. The continuously compounded risk free rate is 5%. The...
The IF500 stock index pays no dividends. The continuously
compounded risk free rate is 5%. The spot price of the index is
2,016.00.
What is the 18-month forward price of
the IF500 stock index?
The RP3000 stock index has a current price of 1,898.60. The
two-year forward price of the index is 2,016.00. The continuously
compounded risk-free rate is 5%. The stock index pays dividends
continuously at a rate of δ per year.
Determine δ.
(a) Find a stock that pays a dividend and estimate the continuously compounded dividend payment rate...
(a) Find a stock that pays a dividend and estimate the
continuously compounded dividend payment rate (for example, .02).
Using the Black/Scholes option pricing model (including dividends),
estimate the price of an at the money call option and put option
that have the same exercise price and maturity date. Assume r=.005
and use the appropriate S0, t, K. For volatility, use 30%.
(b) Evaluate how well the Black/Scholes model worked by
comparing the results to the midpoints of the bid-ask...
he current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest...
he current price of a non-dividend paying stock is 40 and the
continuously compounded risk-free interest rate is 4%. The
following table gives call and put option premiums for three-month
European-style options of various exercise prices.
Exercise price
Call Premium
Put premium
35
5.75
0.40
40
2.29
1.90
45
0.50
5.05
A trader interested in speculating on volatility is considering
two investment strategies. The first is a long 40-strike straddle.
The second is a long strangle consisting of a long...
A futures contract on a share, which pays dividend at a continuously compounded rate of 3%,...
A futures contract on a share, which pays dividend at a
continuously compounded rate of 3%, is written when the share has a
price of $790, and the continuously compounded risk-free interest
rate is 5%. The contract is priced at $800 and expires in 3
months.
(b) Demonstrate how you could execute an arbitrage transaction
and calculate arbitrage profit. [5]
A stock currently trades at $40. The continuously compounded risk-free rate of interest is 7%, and...
A stock currently trades at $40. The continuously compounded
risk-free rate of interest is 7%, and the volatility of the stock
return is 35%. Use the Black-Scholes formula to compute each of the
following (round each answer to the nearest penny). a) The price of
a 0.25-year European call option, struck at $45. Price = $ .
------------------- b) The price of a 0.25-year European put
option, struck at $45. Price = $ .----------------------
non-dividend-paying stock sells for $110.00, and the continuously compounded interest rate is 10% per annum. There...
non-dividend-paying stock sells for $110.00, and the
continuously compounded interest rate is 10% per annum. There are
6-month European calls and put options on the stock with a strike
price of $105.00. The volatility of the stock price is 35%.
Use the two-step binomial model to find European put option.
Answers: Hint: u= ? ? √∆? and d= ? − ? √∆�
Find (1-p):
Su:
Sd:
Suu:
Sud
Sdd:
At t= 0.5: Find Puu ,
At t=0.25: Find Pu, Pd...
Consider a single-stock futures contract on Apple stock. Consider the following scenario: Annualized, continuously compounded risk-free...
Consider a single-stock futures contract on Apple stock.
Consider the following scenario:
Annualized, continuously compounded risk-free interest rate for
2-month period: r = 2.61%.
Annualized, continuously compounded risk-free interest rate for
4-month period: r = 6.8%.
Current spot price of Apple stock: $578 per share.
Dividend per share of $0.74 in 2 months.
Contract expiration: T = 4 months.
Futures price on Apple single-stock futures: $600 per
share.
An arbitrage opportunity exists. What is the net profit
per share when...
Consider a single-stock futures contract on Apple stock. Consider the following scenario: Annualized, continuously compounded risk-free...
Consider a single-stock futures contract on Apple stock.
Consider the following scenario:
Annualized, continuously compounded risk-free interest rate for
2-month period: r = 2.95%.
Annualized, continuously compounded risk-free interest rate for
4-month period: r = 5.65%.
Current spot price of Apple stock: $562 per share.
Dividend per share of $0.62 in 2 months.
Contract expiration: T = 4 months.
Futures price on Apple single-stock futures 4 months from now:
$600 per share.
An arbitrage opportunity exists. What is the net...
Consider a single-stock futures contract on Exxon-Mobil stock. Consider the following scenario: Annualized, continuously compounded risk-free...
Consider a single-stock futures contract on Exxon-Mobil stock.
Consider the following scenario:
Annualized, continuously compounded risk-free interest rate for
3-month period: r = 3.99%.
Annualized, continuously compounded risk-free interest rate for
5-month period: r = 6.55%.
Current spot price of Exxon Mobil stock: $157 per share.
Dividend per share of $0.87 in 3 months.
Contract expiration: T = 5 months.
Futures price on Exxon Mobil single-stock futures: $150 per
share.
An arbitrage opportunity exists. What is the net profit
per...
Suppose that the continuously compounded risk-free interest rates for dollars and pounds are 0.04 and 0.06,...
Suppose that the continuously compounded risk-free interest
rates for dollars and pounds are 0.04 and 0.06, respectively. A
6-month dollar-denominated European call option on pounds with
strike price 1.45 costs $0.05, and a 6-month dollar-denominated
European put option on pounds with strike price 1.45 costs
$0.02.
a) Find the spot (current) exchange rate
b) Find the 6-month forward exchange rate on pounds (in dollars
per pound).
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