URENT PLEASE ANSWER

Consider an investor with $50 budget who has access to the stock that currently trades at $5 and who can buy or write call options on this stock. The investor is not affecting the price of the stock or the option by his deals. The call option is currently priced at $:5 (50 cents) and has the strike price of $6. Tomorrow the option expires. and the investor believes that the stock will be priced either at $7 or at $4 with. equal probabilities. Suppose further that the investor values his wealth y according. to v(y) = ln y.

a: (2 marks) What are the .nancial assets here? Write their payo. matrix.

b: (1 mark) Further denote with s the number of stocks and with c the number

of options purchased. Write the investor.s budget constraint.

c: (1 marks) Write the state contingent levels of wealth that are feasible to

achieve by holding a portfolio (s; c):

d: According to the investor.s preferences what is the optimal portfolio? Write

this question as an optimization problem with the Lagrangean (2 marks). Solve it,

that is .nd the optimal portfolio (s; c). (4 marks).

e: (3 marks) Suppose the investor is so risk-averse that she wants to perfectly

insure herself against the stock market .uctuations. Is it possible given the assets

she has? How many stocks and how many options does she have to hold (or write)

to achieve this? Your answer, should, of course, respect the budget constraint.

f: (2 marks) What are stochastic discount factors (SDF) in general and what

role do they play?