Question

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.

Three answers are needed from three questions

Answer 1

You have asked three unrelated questions. I will answer the first one. Please post the balance questions separately.

Q - 1

Current stock price, S₀ = $ 65.

The American one-year call option on the stock is trading at C = $ 20 with strike price of K = $ 65.

R = rate of interest =10% p.a. (continuously compounding)

The Call Put Parity for American Options is given by: S₀ - PV (Div) - K < C - P < S₀ - PV (K); Where PV refers to present value, Div = Dividend and P = Price of put option on the same underlying and with same matuiry as call option

Or, P + S₀ - PV (Div) - K < C < P + S₀ - PV (K)

We don't have any put option given in the question. Hence, assume P = 0

Hence, S₀ - PV (Div) - K < C < S₀ - PV (K)

Case 1: Assume no dividend.

Hence, Div = 0; PV (K) = Ke^-RT

T = 1 year, Hence, PV (K) = 65 x e^{-10% x 1} =  58.81

65 - 0 - 65 < C < 65 - 58.81

Hence, 0 < C < 6.19

C actually is $ 20

Thus, the call option is too expensive and it's not free from arbitrage.

Case 2: the stock pays a dividend of $5 in one year

Div = 5; PV (Div) = Div x e^-RT = 5 x e^{-10% x 1} = 4.52

Hence, S₀ - PV (Div) - K < C < S₀ - PV (K)

Or, 65 - 4.52 - 65 < C < 65 - 58.81

Hence, - 4.52 < C < 6.19

Since C is call price, it can't be negative. Hence, the bound should be: 0 < C < 6.19

C actually is $ 20

Thus, the call option is too expensive and it's not free from arbitrage, in this case also.

Please post the other questions separately.