Question

In: Finance

You are given the following information. The option matures in 0.5 years and is at the...

You are given the following information. The option matures in 0.5 years and is at the money. The current stock price of the underlying stock is $90.00, and the annualized 365 day t-bill rate is 5.0%. Compute the following:

a) Use the stock price and strike price information from above. Assume that the stock price can either go up by 20% or go down by 10% per period. Set up a replicating portfolio using the stock and a risk free bond using a one-period binomial model,

b) Graphically (and clearly) show all relevant information for the Stock, Bond and the Call.

c) Calculate the relevant number of Stocks and Bonds required to replicate the call.

d) Using no Arbitrage, compute the price of the Call option using this replicating portfolio.

e) Assume that the annual sigma (or Standard Deviation) for the stock is 25%. Compute the BlackScholes-Merton value of the Call option for above.

Solutions

Expert Solution


Related Solutions

You are given the following information Bond A has a price of $ 123.78, it matures...
You are given the following information Bond A has a price of $ 123.78, it matures on Jan-2030, its coupon rate is 3.78%, and it's AAA-rated Bond B has a price of $ 117.34, it matures on Jan-2030, its coupon rate is3.65%and it's AA-rated Bond C has a price of $ 119.22, it matures on Jan-2030, its coupon rate is 3.96%, and it's BBB-rated. Bond D has a price of $ 129.3, it matures on Jan-2030, its coupon rate is...
You are given the following information: Costs Make Option Buy Option Fixed Cost SAR 62500 SAR...
You are given the following information: Costs Make Option Buy Option Fixed Cost SAR 62500 SAR 2500 Variable Cost SAR 7.5 SAR 8.5 Find the break-even quantity and the total cost at the break-even point. If the requirement is 75000 units, is it more cost-effective for the firm to buy or make the components? What is the cost savings for choosing the cheaper option?
please show formulas You have been given the following information on a call option on the...
please show formulas You have been given the following information on a call option on the stock of Puckett Industries: P = $65 X = $70 t = 0.5 rRF= 5% s = 0.50 a. Using the Black-Scholes Option Pricing Model, what is the value of the call option? First, we will use formulas from the text to solve for d1and d2. Hint: use the NORMSDIST function. (d1) = N(d1) = (d2) = N(d2) = Using the formula for option...
Select the correct option... The present value of a bond that matures in 5 years can...
Select the correct option... The present value of a bond that matures in 5 years can be best described as: a) The face value of the bond discounted 5 years back to the current period b) All coupon payments that will be received over the next 5 years discounted back to the current period c) The face value of the bond plus all future cash flows from coupons being received over the coming 5 years discounted back to the current...
You are Given the Following Information for an OECS country for the years 2005 and 2004:...
You are Given the Following Information for an OECS country for the years 2005 and 2004: GDP Component (EC$MN) 2005 2004 Personal consumption 2949.9 2920.4 Government expenditure 1098.3 933.6 Investment 629.7 623.4 Exports of goods and services 2590.7 2538.8 Imports of goods and services 2305.2 2259.1 Calculate GDP for the years 2005 and 2004.You have just calculated nominal GDP. 2.You are told that inflation in 2005 was approximately 2%,what would be your initial estimate of real GDP growth in 2025?Briefly...
Given the following information: value of a normal bond is $92, value of the option is...
Given the following information: value of a normal bond is $92, value of the option is $2, and the value of bond with embedded option is $90, the embedded option is most likely: A. Option free B. Call option C. Put option Which of the following embedded option(s) is/are granted to the issuer? A.Callable bond B.Puttable bond C.Both callable and puttable bonds
Given the following information: You are 40 years old and you would like to retire at...
Given the following information: You are 40 years old and you would like to retire at age 70 (assume social security benefits at that age will be $3,000 per month). You do not have a defined benefit plan; you are just starting to invest in a 401k , current savings are zero (you recently bought a home). You estimate your life span to 90 yrs of age, and you need annual retirement income of 100,000 per year (use todays dollars)...
You obtain the following information concerning a stock, a call option, and a put option: Price...
You obtain the following information concerning a stock, a call option, and a put option: Price of the stock $42 Strike price (both options) $40 Price of the put $3 Expiration date three months You want to purchase the stock but also want to use an option to reduce your risk of loss. a) ?Do you need to purchase or sell the put option? b) What is the cash inflow or outflow from your position when you purchase your put...
Determine the price of a 6% coupon bond that matures in 20 years, given the market...
Determine the price of a 6% coupon bond that matures in 20 years, given the market rate for a similar quality bond is 8%. (Use time value tables or a financial calculator.)
Given the following information, Economy Probability of Economy Stock A Stock B Recession 0.5 -2% 0%...
Given the following information, Economy Probability of Economy Stock A Stock B Recession 0.5 -2% 0% Neutral 0.2 0% 1% Boom ? 20% 5% a) What are the expected returns for stock A and B, respectively? b) What is the standard deviation/risk for stock A? List the formula and input the number, no calculation needed. c) What is the portfolio return given that you have $10,000 and allocate $3,000 in stock A and the rest in stock B? List the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT