Question 1 (9 marks)

Part A: (5 marks)

Consider the option on currency CNY against the USD:

• Current spot rate is CNY 6.50 for 1 USD

• Risk-free CNY rate of interest is 4% p.a.

• Risk-free USD rate of interest is 2% p.a.

• Volatility (σ) of the currency returns is 20% p.a.

• Maturity of the option is 6 months.

• Strike rate of the option is CNY 7.00 for 1 USD

• The currency options are European in nature

Answer the following questions.

(i)        How much does it cost to hold (i.e., buy) a call-CNY option? Use the Garman Kohlhagen model. [2 marks]

(ii)       How  much  does  it  cost to  hold  (i.e.,  buy)  a  put-CNY  option?  Do  not  use the  Garman Kohlhagen model. [2 marks]

(iii)     What is the maximum profit that the holder of the put-CNY option can realize on terminal date? [1 mark]

Question 1

Part B: (4 marks)

Note that Part A and B are not related.

The table below shows the premiums for several currency options (all the options are maturing in 6 months):

The current and 6-month spot currency rates are given below.

i.         Calculate the current premium for a 6-month maturity put option on USD with strike price of USD 0.85 for 1 AUD. Show your working.                                                                [2 marks]

ii.        Calculate the terminal payoff for a 6-month maturity call option on USD with strike price of USD 0.70 for 1 AUD.           [2 marks]

Question 2

Part A: 4 marks

(11 marks)

Assume that a company pays no dividends over the life of European call and put options. Both call and put options mature in 1 year (i.e., they have the same expiry date), and both are currently at-

the-money.

In a no-arbitrage condition, should the call option be priced higher than/lower than/equal to the put option? Clearly prove your answer.

Question 2

Note that Part A and B are not related.

Part B: 4 marks

Consider the following information:

•   The price of a 6-month maturity European put option is $2.70.

•   The put strike price is $55.

•   The current stock price is $60.

•    Dividends received 2 months from today and 8 months from today are projected to be $1.20 and $1.40, respectively.

•   The risk-free rate and σ are not provided (and hence, you must not make any assumptions regarding the values of these variables).

• The table below shows the current prices of zero-coupon bonds with different maturities but all are with a face value of $1:

Required:

Calculate the fair price of the corresponding 6-month European call stock option with the same strike price.

Question 2

Note that Part C are not related to Part A or B.

Part C: 3 marks

A derivative (which is neither a call nor a put) is structured such that it replicates the features of a forward contract with a forward price of X. A derivative trader is tasked to derive an analytical formula to price this derivative. The pricing formula includes, among others, the familiar N(d2 ) term of the Black-Scholes model.

Assuming no default risk, the N(d2 ) of this unique derivative is __________

(i)          Almost equal to 100% (ii)          High at around 80%    (iii)        Around 50%                 (iv)         Low at around 20%

(v)         Almost equal to 0%

Fill in the blank with one of above choices. Then, clearly justify your selection in no more than three sentences.

Question 3              (10 marks)

The current price of the underlying stock is $25. We model the evolution of the stock price using a Binomial model. Over any four-month period, the stock price will rise by 18.91% and will fall by 15.90%, as illustrated in the figure below. The risk-free rate of interest is 6% p.a. compounded     continuously.

An exotic derivative with one year to maturity is written on this stock. The payoff structure of the derivative is specified as:

Required:

Use the risk-neutral Binomial approach to calculate the current value of the exotic derivative, assuming it is Bermudan-style which can be exercised at t = 8 months and at t = 12 months. Use continuous compounding for all present value calculations. Show all working.

Question 4   (10 marks)

Part A: (5 marks)

Company A entered into a semi-annual interest rate swap agreement a few months ago as the fixed rate payer, paying a 4.4% p.a. fixed swap rate and receiving floating rate equivalent to the 6- mth LIBOR. Currently, this agreement (which is termed as “swap A” in this question) will mature in 1.5 years. The following LIBOR rates (with continuous compounding) are currently available to you:

Required: what is the current value of swap A to company A? Show all of your workings.

Question 4

Part B: (5 marks)

Note that Part A and B are not related.

Consider an exotic fixed income security with 1 year remaining to maturity. On maturity, the security holder will receive $100 face value. Coupons are paid quarterly to the security holder according to the 3-month LIBOR rate. In addition, on maturity and only on maturity, the exotic security holder will have to pay a variable interest that equals to the 4-month LIBOR rate.

The  following  table  shows  the  current  LIBOR  continuously  compounded  rate  with  different maturities:

For example, the 1-mth LIBOR is 5.0% p.a. compounded continuously. You can treat the LIBOR rates  presented  in  table  above  as  the  discount  rates/spot  rates  with  different  maturities.

Required: What is the current price of the exotic fixed income security? Show all of your workings.

Question 5              (10 marks)

Several months ago, Buddy Inc. issued a unique fixed income security. As of today, the security is maturing in 10 months.

The security pays semi-annual interest, which is equal to X% minus 3% p.a., where X is equal to the sum of the 6-month and 3-month LIBOR rates. That is, in every six months, the interest is defined as:

「L6 L3] 3%

|L 2   +  4 」| − 2

where L6 (quoted on an annual basis, in %) is the 6-month LIBOR and L3 (also quoted on an annual basis, in %) is the 3-month LIBOR. Assume that the 6-month LIBOR is always greater than the 3- month LIBOR and the 3-month LIBOR is always greater than 3% p.a. At maturity, the company will pay $100 as the face value of the security. Also, assume all other bonds and floating rate notes have a face value of $100, respectively.

Table 1 shows the 3-month and 6-month LIBOR rates observed several months ago: Table 1

For example, two months ago, the 3-month LIBOR rate was observed at 4.0% p.a.

Table 2 shows the predicted 3-month and 6-month LIBOR rates over the next few months: Table 2

For example, four months from today, the 3-month LIBOR rate is predicted equal to 6.0% p.a.

Table  3  shows  the current LIBOR  rates  (assume  continuous  compounding)  with  different maturities over the next 10 months:

Table 3