Financial Math Answers

XYZ’s stock price in $100. 1-year European-style options on XYZ are trading at an implied volatility of 15%. (Assume zero dividends and zero interest rates: q=0% and r=0%.) 

[a] Where should we set the strike price of a 1-year call to give it a delta of +0.25?   

[b] q=0% and r=0% imply that the forward price = $100. It follows from put-call parity that $100-strike call and the $100-strike put are priced equally. Are their deltas +0.50 and -0.50, respectively?

Stock ABC is currently priced at $50. Consider two 6-month options on stock ABC:

Option 1:

$60-strike call (priced at 30% implied vol). Price works out to $1.27. Delta = +0.23  

Option 2:

$40-strike put (priced at 40% implied vol). Price works out to $1.56. Delta = -0.18

(Prices and deltas have been calculated via the Black-Scholes model, assuming q=0% and r=0%.)

Suppose a trader holds:

100 units of Option 1 and 200 units of Option 2.

[a] Explain the statement: “Both options are $10 out-of-the-money.”

[b] What’s the market value of the trader’s total position?

[c] How many shares of ABC should the trader buy (or sell) in order to be delta-neutral?

[d] What’s the total gamma of her position?

The force interest is given by

(t)={0.08 - 0.001t ,0<t<3

0.025t-0.04,3<t</5

0.03, t>5

Calculate the present value at time 2 of a payment £1000 at time 10

Sabir is going to university to study to become a pharmacist.his father decided to buy him a new Toyota Augo as a reward for his wonderful grade 12 results.The Toyota Augo is currently on special for the reasonable price of R174 900 including VAT.They decided to buy the car on hire-purchase and pay of the balance in 60 montly installment.Simple interest is charged at a rate of 14% p.a. A deposit of 10% is required.what is the Loan amount after the deposit has been paid

A loan of £ 2,120,000 is repayable by equal quarterly payments for 15 years. The effective rate of interest is 6% pa.

REQUIRED

i. Find the equal quarterly payment amount.

ii. Draw the amortization schedule for the loan repayment.

iii. What is the interest portion paid on the 10th payment?

iv. What is the total interest paid after the 25th payment?

v. What is the amount of capital portion in the 54th payment?

Solve the following problems. Show your solutions to support your answer.

1. At what rate will ₱ 6,500 accumulate to ₱ 27,000 for 3 years and 6 months, if compounded every 5 

months?

2. Accumulate ₱ 25,000 for 2 years and 5 months at 6 ½%, compounded every two months.

3. Briefly explain the difference between a “ 7% compounded monthly for a year” and a “7% simple 

interest for a year.”

II. In your own understanding, explain the following terms: 

1. bonds

2. stocks

3. mutual funds

I. Show necessary solutions/explanations to support your answer. 

1. How much is the interest if you loan ₱ 350,000 for one year at a simple interest rate of 8%?

2. Which of the following is also referred as Banker’s rule? Explain your answer.

a. exact interest exact time

b. exact interest approximate time

c. ordinary interest exact time

d. ordinary interest approximate time

e. none of these

3. What is the approximate time from April 8, 1999 to October 25, 1999?

4. How many ₱500 monthly payments can be withdrawn from an account containing 

₱35,000 and invested at 8% converted monthly. The first withdraw takes place in one 

Month.

5. On November 15, 2020, Jose Boliva went to BDO Bank and made a loan of ₱100,000

At 10% ordinary interest for 90 days. What is the maturity value of the loan?

what is the irr formula

Assume that your father is now 55 years old and plans to retire after 5 years from now. He is expected to live for another 15 years after retirement. He wants a fixed retirement income of Rs. 1,00,000 per annum. His retirement income will begin the day he retires, 5 years from today, and then he will get 14 additional payments annually. He expects to earn a return on his saving @ 10% p.a. annually compounding. How much must your father save today for his retirement goal?