Question

Answer each question, pls TYPE answers showing the calculation processes, not taking a picture of handwriting.

1. Using the Black-Scholes options pricing model. Calculate the call option premium on a stock with an exercise price of $105, which expires in 90 days. The stock is currently trading for $100 and the monthly standard deviation on the stock return is 3%. The annual risk-free rate is 4% per year.

2. Explain why it may be better (add value) for a firm to implement risk management strategies rather than have shareholders do it for themselves.

Answer 1

Annualized Standard Deviation = Standard Deviation of Monthly Returns * Sqrt (12)

= 3% * sqrt (12)

= 10.39%

Assumes 365 days in a year

Now using the Black-Scholes options pricing model to calculate the call option premium on a stock in following manner –

INPUTS		Outputs	Value
Standard deviation (Annual) σ	10.39%	d1	-0.7285
Expiration (in Years) T	0.25	d2	-0.7801
Risk free rates (annual) r	4.00%	N(d1)	0.2331
Current stock price (S)	$100.00	N(d2)	0.2177
Exercise price (X)	$105.00	B/S call Price	0.6849
Dividend yield (annual)	0	B/S Put Price	4.6544

Call option premium is $0.6849 per stock

2. Explain why it may be better (add value) for a firm to implement risk management strategies rather than have shareholders do it for themselves.

Risk management strategies include the understanding of the potential risk of an organization and making the risk management plan accordingly to mitigate that risk. A firm faces various kinds of risk like operational risk, financial risk, market risk etc. and firm’s risk management strategies try to tackle with each separately. These risk mitigation strategies need professional skills and resources; so it may be better (add value) for a firm to implement risk management strategies rather than have shareholders do it for themselves. By making effective risk management strategies, a firm can increase its brand value.

Formuls used in excel calculation: