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AUTUMN TRIMESTER EXAMINATION - 2022

Academic Year - 2022/23

FIN 3008S

DERIVATIVES SECURITIES

Question 1

a)  A European call option and put option on a stock both have a strike price of $20 and an expiration date in six months. The call option sells for $1.50 and the put has a premium of $1.80. The risk free rate is 8.5% per annum (continuously compounded), and the current stock price is $18.50. Outline the procedure for a trader to exploit any arbitrage opportunity that is present. [10 marks]

b)  Using the data from Part A, describe what happens if the stock pays out a dividend of $0.3 in 1 months’ time. [15 marks]

Question 2

a)  A stock price is currently $50. Over each of the next two periods of four months, it is expected to go up by 15% or down by 10%. The risk-free interest rate is 8% per annum with continuous

compounding. What is the value of a one-year European put option with a strike price of $45? [15 marks]

b)  What is the answer if the one year put option is American instead of European? [10 marks]

Question 3

a)  What is the differences between implied volatility and historical volatility of stock prices? Is there a difference in your answer if the asset is a commodity like corn instead? [10 marks]

b)  What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5.5% per annum, the volatility is 30% per annum, and the time to maturity is 90 days? [15 marks]

Question 4

a)  A senior economist said “A bank loan has lesser default risk than a corresponding swap based on the same notional principle and that is why the subprime crisis occurred due to the implosion of credit default swaps” . Critically evaluate this statement. [10 marks]

b)  A financial institution has agreed to pay 8% per annum and receive three-month SOFR  in  return  on  a  notional  principal  of $150  million with  payments  being exchanged every three months. The swap has a remaining life of 13 months. The average of the bid and offer fixed rates currently being swapped for three-month SOFR is 9% per annum for all maturities with continuous compounding. The three- month SOFR rate two months ago was 7.5% per annum. What is the value of the swap? [15 marks]