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Friendly reminder: Optional problem set 10 due tomorrow

As we wind down the spring semester in Finance 4335, here’s a friendly reminder for Finance 4335.

There is one more problem set left for Finance 4335, which is Problem Set 10 (Corporate Risk Management), and it is due via Canvas before the start of tomorrow’s class meeting. However, completing this problem set is optional. If you choose to complete and turn it in via Canvas, the grade you earn on it will replace your lowest problem set grade for the semester, provided its grade is higher than your lowest grade received on Problem Sets 1-9.

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Source for today’s coverage of the “underinvestment” problem

During today’s Finance 4335 class meeting, the logic behind the so-called underinvestment problem (where, in the absence of risk management, it may be “rational” to reject a positive net present value investment project) is explained in the How Insurance Solves the Underinvestment Problem assigned reading. That assigned reading is an unpublished appendix based on the following published (peer-reviewed) journal article:

Garven, James R. and Richard D. MacMinn, 1993, “The Underinvestment Problem, Bond Covenants, and Insurance,” Journal of Risk and Insurance, Vol. 60, No. 4 (December), pp. 635-646.

This journal article received a “best paper” award from the journal editors in the year it was published, and according to Google Scholar, it has been cited 96 times in works by other scholars.

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Extension of Problem Set 9 deadline and plans for tomorrow’s Finance 4335 class meeting

I have extended the deadline for Problem Set 9 from tomorrow (Thursday, April 25) to Tuesday, April 30. This decision was inspired by a question from a Finance 4335 student, which also led me to publish a related blog post earlier today titled "Pricing Credit Risk Class Problem and Solutions…".

In tomorrow’s Finance 4335 class, we will begin by reviewing the solutions for the first part of the class problem included in the above-referenced blog post (also previously covered during last Thursday’s class meeting). We will complete our discussion of the credit risk topic by covering the second part of the class problem. The rest of the class tomorrow will be devoted to further discussing the topic of corporate risk management, which began in yesterday’s Finance 4335 class meeting.

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Problem Set 8 helpful hints

Here are some helpful hints to consider for Problems 1 and 2 on Problem Set 8 (Problem Set 8 is due by 11 am this Tuesday):

  • Problem 1, Part A: Since the call option described in Problem 1, Part A is initially out-of-the-money (i.e., since S = $18 and K = $20), there will be terminal nodes at which the call option expires in-the-money and others at which it expires out-of-the-money.  By solving the b = \ln (K/S{d^n})/\ln (u/d) equation and rounding to the nearest integer greater than b (referred to in the CRR equation below as the parameter “a“), this indicates the minimum number of up moves required such that this call option expires in–the–money.  Once you have this information, you can consider only those terminal nodes at which the call option expires in-the-money (which are nodes a through n) and calculate the call option price by applying the CRR call option pricing equation:  C = {e^{ - rT}}\left[ {\sum\limits_{j = a}^n {\frac{{n!}}{{j!\left( {n - j} \right)!}}{q^j}{{\left( {1 - q} \right)}^{n - j}}\left( {{u^j}{d^{n - j}}S - K} \right)} } \right]
  • Problem 1, Part B: Apply the put-call parity equation (C+Ke^{-rT} =P+S) to solve for the put option price.
  • Problem 2, (Scenario A): requires solving for call and put option prices using the Black-Scholes-Merton option pricing formulas.  See the Part 2 option pricing lecture note, page 18, for a numerical illustration of how to do this.
  • Problem 2, Scenario B requires finding the current price of the underlying asset, where the call, put, and exercise prices are all given.  Solve the put-call parity equation (C + K{e^{ - rT}} = P + S) for S.
  • Problem 2, Scenario C requires finding the exercise price, where the call, put, and underlying asset prices are all given.  Solve the put-call parity equation for K.
  • Problem 2, Scenario D requires finding \sigma for a call option worth $2.38 and a put option worth $3.60.  Feel free to use the Black-Scholes spreadsheet from the course website, or better yet, create your own Excel spreadsheet in which you solve for the call and/or the put by varying \sigma (this can be accomplished either via trial and error or better yet, by using either Solver or Goal Seek).  An important lesson you’ll learn from this part of problem 2 is that call and put option prices are positively related to \sigma .
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Extra Credit Opportunity: Barnabas Financial Forum: God and Money

I’m offering an optional extra credit opportunity that involves attending and reporting on the Barnabas Financial Forum: God and Money. It will be held on Tuesday, April 16, from 3:30-4:45pm in Foster 250. The speaker for the forum will be John Cortines, author of God and Money: How We Discovered True Riches at Harvard Business School.

If you take advantage of this opportunity, I will use the grade you earn on your report to replace your lowest quiz grade in Finance 4335. For this assignment, prepare a 2-3 page executive summary offering a thoughtful synopsis of what you learn from participating in the Barnabas Financial Forum. The report must be submitted here in PDF format via the Assignments section of Canvas no later than 5 p.m. on Friday, April 19.