Sample Paper 2

Financial Maths (Prof. Mahendra Mehta)

Question 1 – Find the area under the curve (one tail distribution) under 1.5 Sigma for a normal distributed random variable (2 Marks)

Question 2 – Find the implied interest rate of USD, given the following variables for a USD / INR forward contract? (2 Marks)….. (Answer – USD Interest Rate is 2%)

· Spot – 49.20 (USD / INR)

· Forward Rate – 52.10 (USD / INR)

· Time – 9 Months

· INR Interest Rate – 10%

Question 3 – Under what relationship between the spot and strike prices, the value of the European call would be exactly equal to the value of the European put option? (3 Marks)

(Hint: Use Put-Call Parity equation to find the relationship;

LN(S/K)=(-r)*t, where, S=Spot Price; K=Strike Price, r=Annual Interest Rate, t=Time to maturity in years, LN = Natural Log )

http://www.theoptionsguide.com/understanding-put-call-parity.aspx

Question 4 – You want to buy a USD call against INR with the following market conditions. You would be required to pay a premium to buy this call option. In order that you do not pay any premium to the seller, you also sell 2 calls on USD at some strike price. Find the strike price at which you should sell 2 calls so that your net premium is zero (what you pay for buying a call and what you receive for selling 2 calls)? (Hint: Use Goal seek function in excel)

· Spot (USD/INR) – 49.50

· Strike (USD/INR) – 50.00

· Time – 6 Months

· Volatility – 15% (Annual)

· Interest Rate – USD – 1% (Foreign Currency)

· Interest Rate – INR – 9% (Domestic Currency)

Find also the value of the above option premium?

Find the net Delta (Delta of the bought call and delta of 2 net sold calls) of the options portfolio?

(7 Marks)

Answer –

Strike price of 2 sold Call options – 53.14

Original Call option premium (For bought call option) – 2.860218 (5.78%)

Delta of 1 Call option bought = 63.13%

Delta of 2 sold call options = 40.56%