The current price of a non-dividend-paying stock XYZ is $30. The annual volatili

Question

The current price of a non-dividend-paying stock XYZ is $30. The annual volatility of XYZ price is 20%. Suppose that you have a six-month short call position with the strike price of $32. Assume the continuously compounding risk-free rate is 5%.

A) Using risk-less portfolio approach, what long position in the XYZ stock is necessary to hedge the short call position? (Calculate the number of shares you must purchase to hedge one short call)

Strategy (portfolio you use to replicate the option behavior), and Calculations:

B) What is the value the call option?

Calculations:

C) What long position in the stock s necessary to hedge a long put option when the strike price is $32. Calculate the number of shares you purchase.

Strategy (portfolio you use to replicate the option behavior), and Calculations:

D) What is the value of the put option?

Calculations:

Explanation / Answer

1. To hedge Short call we have to have a Long call with strike price of 32.

Since stock volatility is 20%, price can be in the range of 24 to 36

Short call will gives profits if stock price is less than 32 (Strike Price)

We have to hedge in order to tackle when price raises more than 32

So buy a Long call with strike price of 32

2. Value of call option is stock price - strike price = 30-32 = -2

3. To hedge Long put we have to have a Long call with strike price of 32.

Since stock volatility is 20%, price can be in the range of 24 to 36

Long put will gives profits if stock price is less than 32 (Strike Price)

We have to hedge in order to tackle when price raises more than 32

So buy a Long call with strike price of 32

4. Value of Long put is strike price – stock price = 32 - 30 = 2

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