I’d like to make an important point about the formulas provided on the formula sheet for the replicating portfolio approach to option pricing. There, I list replicating portfolio values at inception and at expiration. Keep in mind that this approach involves determining a weighting scheme such that one replicates call or put payoffs by appropriately choosing stock exposure (delta) and bond exposure (beta). At this point in the course, we only allow for two possible option payoffs at expiration; thus, there actually are two equations for the replicating portfolio at expiration. These equations reflect the fact that the value of the underlying asset is different in each possible terminal state. However, since she value of the underlying asset is known at the inception of the option, there is only one equation for the replicating portfolio at that point in time.

]]>The fourth problem in this problem set references an Excel spreadsheet template called “Derivagem” which you can download from http://fin4366.garven.com/spring2019/DG300.xls. Open DG300.xls up in Excel, and you’ll encounter a dialog box which looks something like this:

Click on “Enable Macros”, and once the spreadsheet is open, select the “Equity_FX_Index_Futures_Options” worksheet. The upper left corner of the spreadsheet is where you input the data for the problem. For this problem, “Underlying Type” is “Equity”, “Option Type” is “Black-Scholes – European”, a $.50 dividend is paid in 6 months, which corresponds to .5 year, the current stock price is $41, volatility is 35%, and the risk-free rate of interest is 6%, the option’s life is 1 year, and the strike or exercise price is $40:

Once you have input these data, select the call button for the call option price and the put button for the put option price. Depending on whether you select “Put” or “Call”, when you click on “Calculate”, the spreadsheet will report back put and call option prices based on the Black-Scholes-Merton (BSM) option pricing formula. For now, this formula may be somewhat of a black box for many (if not most) of you, which is a “problem” we will surely rectify in the not-too-distant future in Finance 4366.

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If you decide to take advantage of this opportunity, I will use the grade you earn on your report to replace your lowest quiz grade in Finance 4366 (assuming that your grade on the extra credit is higher than your lowest quiz grade). The report should be in the form of a 1-2 page executive summary in which you provide a critical analysis of Dr. Hazlett’s lecture. In order to receive credit, the report must be submitted via email to options@garven.com in either Word or PDF format by no later than Monday, February 11 at 5 p.m.

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