The Current Price of a Non-Dividend-Paying Stock Is $30

question 1

Essay

The current price of a non-dividend-paying stock is $30. Over the next six months, it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero.
i) What long position in the stock is necessary to hedge a short call option when the strike price is $32? Give the number of shares purchased as a percentage of the number of options that have been sold. _ _ _ _ _ _
ii) What is the value of the call option? _ _ _ _ _ _
iii) What long position in the stock is necessary to hedge a long put option when the strike price is $32? Give the number of shares purchased as a percentage of the number of options purchased. _ _ _ _ _ _
iv) What is the value of the put option? _ _ _ _ _ _
v) What is the risk-neutral probability of the stock price moving up? _ _ _ _ _ _

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Definitions:

Countersunk

A method of setting screws or bolts in which their heads sit flush with or below the surface of the material, often used for a neat finish or in applications where a smooth surface is necessary.

Even Radius

A term describing a curve or surface where all points are equidistant from a central point, typically referring to the design and manufacture of components or spaces.

Pressure Protection Valve

A normally closed, pressure sensitive control valve. Some are externally adjustable. Can be used to delay the charging of a circuit or reservoir or to isolate a circuit or reservoir in the event of a pressure drop-off.

Maintain Pressure

The act of keeping the pressure within a system at a desired level to ensure proper operation.