a) Consider a call option on a stock with an exercise price of X=100 USD. It has a remaining maturity of 6 months. Plot the pay-off function of a long-position in this option as a function of the spot price at maturity date.

b) You want to speculate on rising prices. Would you rather have long position in put or in call options? Provide a brief rationale.

c) The underlying asset has an annual volatility of = 0, 2. The annual riskfree interest rate is 1%. The current spot price of the asset is 80 USD. Use Black-Scholes equation to price the call on a European option. Also give the general equation and the intermediate values.

d) Once again, assume a volatility of = 0, 2. Price a put option on the same asset with an execution price of X=100 USD and a remaining maturity of 6 months using Black-Scholes equation. All other values are like above. Also give the general equation.

e) Plot both the price of the call and the put as a function of the standard deviation 0, 01 0, 5 (resolution step size 0,01).

Discuss your findings briefly. [Hint: In Excel the cumulative standard normal distribution is given by Normal.Dist(X;0;1;TRUE)]