Finance assignment – risk simulation and optimization

10) What does the comparison in (8) show? How does this relate to the Capital Asset Pricing Model? 

11) Using the correlation matrix develop a model to simulate portfolio returns for solutions at 25% without risk free borrowing and without short-selling (i.e. questions 4). What is the probability that portfolio returns will fall below 20% or rise above 30%?. Question 2. Option Pricing You have been asked by a client to price out a number of possible options on a stock over a six-month period (125 days). The current stock price is $25, and its expected risk neutral drift rate is 5%/year. It is also known that the annual volatility is 35%. 

12) The first option is a straight forward vanilla European put option that will pay your client if the stock price falls below $20 as at the last trading day at the end of 6 months. 

A) What is the expected payoff to this option?______________. 

B) What price would you charge the client for this protection before any transaction fees?__________ 

 

13) Your client then asked you to price an option that would payoff only if the average price over the 6 months was less than $20 (e.g. an Asian option). 

A) What is the expected payoff to this option?______________. B) What price would you charge the client for this protection before any transaction fees?__________ 

14) The next option considered was even more exotic. Your client asked you to price an option which would trigger a European put option, with a strike price of $25, if and only if the lowest price observed in the last 30 days of trading was below $20. 

A) What is the expected payoff to this option?______________. 

B) What price would you charge the client for this protection before any transaction fees?__________ 

C) What is the probability that the option will be exercised? ___________________

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