ii. If \( S \) follows the geometric Brownian motion, what is the process followed by (a) \( y=2 S \). (b) \( y=S^{2} \), (c) \( y=e^{5} \), and (d) \( y=e^{r(f-6)} S \). In each case express the coefficients of \( d t \) and \( d z \) in terms of \( y \) ruther than S .
iii. Describe the various dimensions of market liquidity. Why is liquidity considered as a precondition for the stability of financial markets? Why is liquidity considered as an increasing function of stock returns? Explain with suitable examples and proper reasoning.
iv. A stock price is currently 50 . It expected retum and volatility are \( 12 \% \) and \( 30 \% \). respectively. What is the probability that the stock price will be greater than 80 in two years? (Hint \( S_{\gamma}>80 \) when \( \ln S_{r}>\ln 80 \Rightarrow \) )
V. Show that the Black-Scholes-Merton formulas for call and put options satisfy put-call parity.
vi. The market price of a European call is \( \$ 3,00 \) and its price given by Black-Scholes-Merton model with a volatility of \( 30 \% \) is \( \$ 3.50 \). The price given by this Black-Scholes-Merton model for a European put option with the same strike price and time to maturity is \( \$ 1.00 \). What should the market price of the put option be? Explain the reasons for your answer.
vii. "The Black-Scholes-Merton model is used by traders as an interpolation tool." Discuss this view.
