Hello can you help me with some question I have trouble with?

Consider the following table of available call and put options on the same stock:

Type:

Call

62 Strike

0.5Maturity

12.42 Price

0.83 Delta ()

0.016 Gamma ()

8.3 Vega (V)

Put

62 Strike

0.5 Maturity

0.46 Price

-0.17 Delta ()

0.016 Gamma ()

8.3 Vega (V)

Call

80 Strike

0.5 Maturity

1.82 Price

0.3 Delta ()

0.03 Gamma ()

17.7 Vega (V)

Put

80 Strike

0.5 Maturity

8.23 Price

-0.7 Delta ()

0.03 Gamma ()

17.7 Vega (V)

a)Suggest an estimate of the likely current stock price. Explain your reasoning.

b)Recall that a bull spread is a strategy which profits from an increase in prices, but with a cap on the possible profits. Find the cost of creating a bull spread with options above.

c)Explain the meaning of the 'Delta' of an option (or option portfolio). Why do market-makers and other traders continually monitor and manage Delta risk?

d)Suppose you have an existing portfolio with =800 and =60. You choose to trade the strike 80 put option to fully hedge your gamma risk. How many shares of the underlying stock should you now buy or sell to make your portfolio delta-neutral?

e)Suppose instead you own 150 shares of stock. Is it possible to trade only in call options to create a vega-neutral and delta-neutral portfolio? If so, show how. If not, why not?