Question #15

The yield curve is assumed to be flat so that the risk-free rate of interest is known and constant over the term of the option. Having a fixed yield curve does not necessarily imply that the yield curve is flat. BSM assumptions include that markets are frictionless (no taxes, transactions costs) and that the options are European-style, meaning that early exercise is not allowed. (Module 31.6, LOS 31.f) Frank Potter, CFA, a financial adviser for Star Financial, LLC has been hired by John Williamson, a recently retired executive from Reston Industries. Over the years Williamson has accumulated $10 million worth of Reston stock and another $2 million in a cash savings account. Potter has a number of unconventional investment strategies for Williamson's portfolio; many of the strategies include the use of various equity derivatives. Potter's first recommendation involves the use of a total return equity swap. Potter outlines the characteristics of the swap in Table 1. In addition to the equity swap, Potter explains to Williamson that there are numerous options available for him to obtain almost any risk return profile he might need. Potter suggest that Williamson consider options on both Reston stock and the S&P 500. Potter collects the information needed to evaluate options for each security. These results are presented in Table 2. Table 1: Specification of Equity Swap Term 3 years Notional principal $10 million Settlement frequency Annual, commencing at end of year 1 Fairfax pays to broker Total return on Reston Industries stock Broker pays to Fairfax Total return on S&P 500 Stock Index Table 2: Option Characteristics Reston S&P 500 Stock price $50.00 $1,400.00 Strike price $50.00 $1,400.00 Interest rate 6.00% 6.00% Dividend yield 0.00% 0.00% Time to expiration (years) 0.5 0.5 Volatility 40.00% 17.00% Beta Coefficient 1.23 1 Correlation 0.4 Table 3: Regular and Exotic Options (Option Values) Reston S&P 500 European call $6.31 $6.31 European put $4.83 $4.83 American call $6.28 $6.28 American put $4.96 $4.96 Table 4: Reston Stock Option Sensitivities Delta European call 0.5977 European put –0.4023 American call 0.5973 American put –0.4258 Table 5: S&P 500 Option Sensitivities Delta European call 0.622 European put –0.378 American call 0.621 American put –0.441 Potter has also been asked to evaluate the interest rate risk of an intermediate size bank. The bank has a large floating rate liability of $100,000,000 on which it pays the MRR on a quarterly basis. Potter is concerned about the significant interest rate risk the bank incurs because of this liability: since most of the bank's assets are invested in fixed rate instruments there is a considerable duration mismatch. Some of the bank's assets are floating rate notes tied to MRR, however, the total par value of these securities is significantly less than the liability position. Potter considers both swaps and interest rate options. The interest rate options are 2-year caps and floors with quarterly exercise dates. Potter wishes to hedge the entire liability. Potter has obtained the prices for an at-the-money 6 month cap and floor with quarterly exercise. These are shown in Table 6. Table 6: At-the-Money 0.5 year Cap and Floor Values Price of at-the-money Cap $133,377 Price of at-the-money Floor $258,510