# Erratum: “Solutions for Problem Set 8…”

HT to TJ Brooks for identifying various typos in my solutions for Problem Set 8. In the solutions for the 3rd and 4th questions, I mistakenly identified the put payoff at the down node having a value of 16, which is incorrect; the correct value is 12. However, all of the answers are correct and are based upon p(d) having a value of 12. I have corrected these typos so the version of the solutions for this problem set are now error-free.

# Midterm exam 2 information…

Midterm 2 will be given during class on Tuesday, April 3. This test consists of 4 problems. You are only required to complete 3 problems. At your option, you may complete all 4 problems, in which case I will throw out the problem on which you receive the lowest score.

The questions pertain to topics which we have covered since the first midterm exam. Topics covered include 1) demand for insurance, 2) adverse selection, 3) portfolio/capital market theory, and 4) financial derivatives (calls and puts specifically).  I have posted the formula sheet that will appear as the back page of the exam booklet at the following location: http://fin4335.garven.com/spring2018/formulas_part2.pdf.

Tomorrow’s class meeting will be devoted to a review session for the midterm exam. If you haven’t already done so, I highly recommend that you review Problem Sets 5-8 and also try working the Sample Midterm 2 Exam (solutions are also provided) prior to coming to class tomorrow.  I will come to class prepared to work through the solutions for Problem Set 8 and the sample exam, as well as address any questions or concerns that y’all may have.

# Finance 4335 extra credit opportunity

I have decided to offer the following extra credit opportunity for Finance 4335. You can earn extra credit by attending and reporting on Dr. P. J. Hill’s upcoming lecture entitled “Saving the Environment Through Prices and Property Rights”:

If you decide to take advantage of this opportunity, I will use the grade you earn to replace your lowest quiz grade in Finance 4335 (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. Hill’s lecture. In order to receive credit, the report must be submitted via email to risk@garven.com in either Word or PDF format by no later than Monday, March 26 at 5 p.m.

# On the role of replicating portfolios in the pricing of financial derivatives

Replicating portfolios play a central role in terms of pricing financial derivatives. Here is a succinct summary from yesterday’s class meeting:

1. Buying forward is equivalent to buying the underlying on margin, and selling forward is equivalent to shorting the underlying and lending money. Like options, forwards and futures are priced by pricing the replicating portfolio and invoking the “no-arbitrage” condition. If the forward/futures price it too low, then one can earn positive returns with zero risk and zero net investment by buying forward, shorting the underlying and lending money. Similarly, if the forward futures price is too high, one can earn positive returns with zero risk and zero net investment by selling forward and buying the underlying with borrowed money. This is commonly referred to as “riskless arbitrage”; it’s riskless because you’re perfectly hedged, and it’s arbitrage because you are buying low and selling high.
2. The replicating portfolio for a call option is a margined investment in the underlying. During yesterday’s class meeting, we priced a one timestep call option where the price of the underlying asset is $100, the exercise price is also$100, u = 1.05, d = .95, the interest rate r = 5%, and the timestep $\delta t = 1/12$. Given these parameters, the payoff on the call is $5 at the up (u) node and$0 at the down (d) node.  The replicating value consists of half a share that is financed by a margin balance of $47.30; thus the “arbitrage-free” price of the call option is (.5(100) – 47.30) =$2.70.
3. Since the replicating portfolio for a call option is a margined investment in the underlying, it should come as no surprise that the replicating portfolio for a put option consists of a short position in the underlying combined with lending. Thus, in order to price the put, we need to determine and price the components of the replicating portfolio. We will begin class tomorrow by completing our analysis of the replicating portfolio approach to pricing calls and puts, and move on to other pricing methods such as delta hedging and risk neutral valuation.