Question

Assignment 2 (assessment worth 15%)
Due Date 24 May at 5pm GMT+8

[Submission will be strictly observed. Make submission via Turnitin]

Question 1

Assume Alpha Ltd is currently trading on the NYSE with a stock price of $65. The American one-year call option on the stock is trading at $20 with strike price of $65. If the one-year rate of interest is 10% p.a. (continuously compounding), is the call price free from arbitrage or is it too cheap/expensive, assuming that the stock pays no dividends? What if the stock pays a dividend of $5 in one year?

Question 2

The current price of a non-dividend paying stock is $35. Use a two-step tree to value an American put option on the stock with a strike price of $33 that expires in 12 months. Each step is 6 months, the risk free rate is 6% per annum (continuously compounding), and the volatility is 15%. What is the option price? Show work in detail and use a tree diagram (Use 4 decimal places).

Question 3

Two firms X and Y are able to borrow funds as follows:

Firm A: Fixed-rate funding at 3.5% and floating rate at Libor-1%.

Firm B: Fixed-rate funding at 4.5% and floating rate at Libor+2%.

Assume A prefers fixed rate and B prefers floating rate. Show how these two firms can both obtain cheaper financing using a swap. What swap strategy would you suggest to the two firms if you were an unbiased advisor? What is the net cost to each party in the swap? Show your work in detail.

The Questions are not related to each other all of them are separate questions

Answer 1

Answer 1

There are various ways to calculate the price of a call option, viz. put-call parity, binomial interest rate tree, black scholes model, intrinsic value + time value of money model

The formula for these is as below:-

• PUT CALL PARITY =

We do not have the value of Put premium to use this formula

• Binomial Interest rate tree = we do not have volatility & risk free rate to use this formula
• Black Scholes model = we do not have risk free rate to use this formula (The question says 1 year Interest Rate, & not 1 year Risk free rate. There's a difference.)
• Finally Call Price = Intrinsic Value + Time Value of Money = (0+20) = 20

Intrinsic value is nothing but difference between the stock price of the underlying price - strike price

i.e. underlying price = 65 & strike price is also 65.

Hence, by using the above formula, the time value of money of call option should be 20.

Since, this is an American option, it can be exercised any time before or at the time of expiration.

Hence, if the time value of call is 20, it is correctly priced.

If the time value of call is less than 20, it is overpriced

If the time value of call is more than 20, it is underpriced.

Answer 2

Strike price	X	33.0000
Current stock price	S	35.0000
Risk free interest rate per annum	Rf	0.0600
Dividend yield	dy	-
Length of time step (in years)	n1	0.5000	square root =	0.7071
Volatility	σ	0.1500

Up factor	u	e to the power (σ*square root of n)	e to the power (G8*I7)	1.1119
down factor	d	1/u	1/I9	0.8994
probability (up)	p	e to the power (Rf-dy)*n-d)/(u-d)		1.0305	0.6168
probability (down)	1-p				0.3832

.

						43.2709	(put premium = IF (G3-J16>0,(G3-J16),0)	-
			38.9163	Put premium = 0	-
Stock price	35.0000					35.0000	put premium = 0	-
put premium= ANSWER	0.6486		31.4778	Put premium = 33-31.48	1.5222
				1.5200		28.3100	put premium = 33-28.310026	4.6900
				or 1.74

.

put price	0.6683		1.7972
	1.0305		1.0305
ANSWER	0.6486		1.7441
put price formula	(0*.617+1.74*.383)/dividing factor		(0*.617+4.6899737*0.383)/dividing factor
dividing factor	e to the power (Rf)*n = e to the power (0.06*0.5)		e to the power (Rf)*n = e to the power (0.06*0.5)

.

Answer 3

	fixed	floating
Firm A	3.50%	Libor - 1%
Firm B	4.50%	Libor + 2%

As per the question, the above is allowed.

The cells marked in green are the preferences of two firms.

If we simply accept this arrangement - the total cost will be = 3.5% + (LIBOR +2%)= LIBOR + 5.5%

STRATEGY
Firm A	Borrow Floating =	Pay (LIBOR -1%)
Firm B	Borrow Fixed=	Pay 4.5%
Now, apart from this above trade, they should borrow in their respective preferred rates highlighted in green, i.e.
Firm A	Borrows fixed	Pays 3.5%
Firm B	Borrows floating	Pays LIBOR +2%