Corporate Finance, Module 23: "Advanced Option Valuation"
Required reading:
(The attached PDF file has better formatting.)
Updated: July 7, 2005
{The Brealey and Myers textbook is excellent. We say to read certain sections and to skip others. This does not mean that certain sections are better; it means that the homework assignments and exam problems are based on the sections that you must read for this course. Some of the skipped sections are fascinating, but they are not tested.}
Review section 20.2, "Financial Alchemy with Options," on pages 570-572. You read this for Module 20; make sure the put call parity relation on page 572 is crystal clear, since we adapt this relation to value risky bonds.
Read the sub-section "Default Puts and the Difference Between Safe and Risky Bonds" on pages 573-575. Financial analysts often view the corporate shield as an option. (We discuss the corporate shield with reference to corporate form and capital structure. This topic is also treated in Butsic’s risk-based capital reading on CAS Exam 8 and SOA Course 8 Finance.)
Read the sub-section "Spotting the Option" on pages 575-576. When spotting options, ask a series of questions:
What is the risky asset or liability? (This is the underlying security of the option.)
What is the non-risky asset or liability? (This is the strike price.)
How does volatility of the risky item affect the value of the option?
What are the rights of the option holder that affect the option value?
Read section 20.3, "What Determines Option Values," on pages 577-582. Understand and memorize table 20.2 on page 581. The understanding takes time and review of problems; first memorize the table so you know what to expect. The final exam poses multiple choice questions on these relations.
Read section 21.3, "The Black-Scholes Formula," on pages 601-605, including the sub-section "Using the Black-Scholes Formula" on pages 603-605, but skipping the sub-sections "The Black-Scholes Formula and the Binomial Method" and "Using the Black-Scholes Formula to Estimate Variability" on pages 605-606. Black-Scholes has four formulas:
the value of the call option (top of page 602 and middle of page 603)
the value of the put option (derived from call option by put call parity)
the value of d1 (top of page 602 and middle of page 603)
the value of d2 (which is d1 –
σ/t)
On CAS Exam 8 and SOA Course 8 Investments, we derive the Black-Scholes formula. For the on-line corporate finance course, know how to use the formula; that is, know what each of the input parameters means. The final exam gives the equations (so you need not memorize them), but unless you have worked a few examples, you will be stumped.
Read section 21.4, "Option Values at a Glance," on pages 606-608. American put options, European call and put options on dividend paying stocks, and American call options on dividend paying stocks are increasingly hard to price, and we do not have simple formulas (like Black-Scholes) that give exact values. The final exam does not ask you to price these options, but you must understand what each one means.