Finance Assignment 2

This assignment focuses on the Black Scholes model for valuing options, discussing risk measures, and analyzing a case study involving fixed and floating rates. It includes calculations for European vanilla options and the implications of investment strategies for firms A and B.

Running head: ASSIGNMENT 2 1
Assignment 2
Institution Affiliation
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ASSIGNMENT 2 2
Part A (i)
When valuing options using Black Scholes Models, the source of uncertainty is considered to
be the stock price and the option price (Fadugba, Nwozo, & Babalola, 2012). In order to
eliminate this source of uncertainty, an individual can buy delta shares of stock and a short
position on the option. This portfolio is instantaneously riskless free and thus must yield
riskless rate.
Part A (ii)
Delta is considered to be one of the four major risk measures while analyzing options. A
short call position in a European vanilla option has negative delta because it pragmatically
measures the degree to which an option is exposed to movement in the price of the
underlying asset (commodity/stock). Its values range from 1.0 to -1.0 (Valverde, & Talla,
2013). When a call is shorted, the movement of the underlying asset acts against the value of
options that is if the price of the underlying asset decreases then the value of the option
increases since the call option is short and vice versa.
Part B
Non-dividend paying asset = US$65
Riskless interest rate = 5% per annum
Maturity = 5 years
Lower boundary of the European vanilla put option on this asset with a strike price of US$80
=?
From the above formula, substitute X = 80, r = 5%, s0 = 65, T = 5
Ep0> = Max (80 – 65, 0)
(1-0.05)
Ep0> = Max (62.682 – 65, 0)
Ep0> = Max (-2.317, 0) = 0
Therefore, the lower boundary is zero (Haug, & Taleb, 2011).

ASSIGNMENT 2 3
Part C
Firm B would invest at a fixed rate and Firm A at floating rate. The net advantage
would be:
Fixed rate Floating rate Net Advantage
Firm B 8% Libor + 0.5%
Firm A 6% Libor + 0.0%
Advantage 2% -0.50% 1.50%
Fee to the intermediary 0.10%
Net Advantage 1.40%
The 1.4% is to be shared 0.7% each by A & B.
Firm B invests at 8% & Firm A invests at Libor + 0.5%
The swap arrangement and the net effect would be:
Firm B Firm A
Gets from the investment 8% Libor + 0.0%
Pays to Bank 7.30% Libor - 0.7%
Gets from Bank Libor + 0.5% 6%
Net return from swap Libor + 1.2% 6.70%
Return from direct investment Libor+ 0.5% 6%
The bank nets 7.3 + (Libor - 0.7%) - (Libor + 0.5%) - 6% = 0.1%
The rates that A and B could receive on their preferred interest rate is 0.1% (Xiu, 2014).

ASSIGNMENT 2 4
Reference
Fadugba, S., Nwozo, C., & Babalola, T. (2012). The comparative study of finite difference
method and Monte Carlo method for pricing European option. Mathematical Theory
and Modeling, 2, 60-66.
Haug, E. G., & Taleb, N. N. (2011). Option traders use (very) sophisticated heuristics, never
the Black–Scholes–Merton formula. Journal of Economic Behavior &
Organization, 77(2), 97-106.
Valverde, R., & Talla, M. (2013). Risk Reduction of the Supply Chain Through Pooling
Losses in Case of Bankruptcy of Suppliers Using the Black–Scholes–Merton Pricing
Model. Some Recent Advances in Mathematics and Statistics. World Scientific, 248-
256.
Xiu, D. (2014). Hermite polynomial based expansion of European option prices. Journal of
Econometrics, 179(2), 158-177.