A stock is priced at $30 per share. The stocks volatility is 40% per annum. Considering the following information on the nine-month to maturity at-the-money call and put options.

The theta is measured on a per day basis. The Greeks that measure the change in option price per change in interest rate/volatility are expressed in values per one percentage point change in interest rate/volatility.

a) Suppose a trader sells 70 Puts. Assuming that the stock price remained unchanged for 17 days, estimate the dollar change on the positions value.

b) Suppose a trader issues a sufficient amount of risk-free nine-month zero coupon bond to buy 50 units of call options, estimate the change in the value of his overall leveraged position in call options if the volatility increased to 47%. (2 marks)

c) Suppose a trader owns 70 calls. Give your best estimation for the value of the traders position 35 days later assuming the stock price increased by $23 per share and all else remain the same. Explain your answer.

d) Suppose the stock price increase by $6, use elasticity to calculate the percentage change in the value of a portfolio that consists of longing 3 unit of put option. Is this an exact calculation or an approximation? Explain your answers.

e) Assume that the beta of the underlying stock is 1.70 and the excess market return is 6% per year. What is the expected rate of excess return for investing 60 units of this put option? Explain your answers and state your assumptions.

f) A trader wants to establish a position which will make money if the volatility increases. Using the call and put given above, establish a position which is immune to stock price change and have a 0.5976 increase in his position value when volatility becomes 42%. What is the gamma of this position?

g) What is the delta of a bullish straddle constructed using the call and put options above?

\begin{tabular}{|l|c|c|} \hline & Call & Put \\ \hline Price & 4.62 & 3.52 \\ \hline Delta & 0.6110 & 0.389 \\ \hline Gamma & 0.040 & ? \\ \hline Theta & 0.0092 & 0.0052 \\ \hline Vega & 0.0996 & 0.0996 \\ \hline Rho & 0.1027 & 0.1140 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|} \hline & Call & Put \\ \hline Price & 4.62 & 3.52 \\ \hline Delta & 0.6110 & 0.389 \\ \hline Gamma & 0.040 & ? \\ \hline Theta & 0.0092 & 0.0052 \\ \hline Vega & 0.0996 & 0.0996 \\ \hline Rho & 0.1027 & 0.1140 \\ \hline \end{tabular}