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Which of the following is NOT one of the assumptions of the Black-Scholes-Merton option-
pricing model?
A) The yield curve for risk-free assets is fixed over the term of the option.
B)
There are no taxes and transactions costs are zero for options and arbitrage
portfolios.
C) Early exercise is not allowed.
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