Question #74

Implication 1 is incorrect. The BSM model assumes a constant risk-free interest rate but interest rate volatility is a key factor that determines the value of options on bonds and interest rate related contracts. Hence BSM is not useful for pricing options on bond prices and interest based derivatives. Implication 2 is correct. BSM allows for constant continuously compounded dividend yield (i.e., cash flow on the underlying) by adjusting the asset value by the present value of the expected cash flows. (Module 31.6, LOS 31.f) Rachel Barlow is a recent graduate of Columbia University with a Bachelor's degree in finance. She has accepted a position at a large investment bank, but first must complete an intensive training program to gain experience in several of the investment bank's areas of operations. Currently, she is spending three months at her firm's Derivatives Trading desk. One of the traders, Jason Coleman, CFA, is acting as her mentor, and will be giving her various assignments over the three month period. One of the first projects Coleman asks Barlow to do is to compare different option trading strategies. Coleman would like Barlow to pay particular attention to strategy costs and their potential payoffs. Barlow is not very comfortable with option models, and knows she needs to be able to fully understand the most basic concepts in order to move on. She decides that she must first investigate how to properly price European and American style equity options. Coleman has given Barlow software that provides a variety of analytical information using three valuation approaches: the Black-Scholes model, the Binomial model, and Monte Carlo simulation. Barlow has decided to begin her analysis using a variety of different scenarios to evaluate option behavior. The data she will be using in her scenarios is provided in Exhibits 1 and 2. Note that all of the rates and yields are on a continuous compounding basis. Exhibit 1 Stock Price (S) $100.00 Strike Price (X) $100.00 Interest Rate (r) 7.0% Dividend Yield (q) 0.0% Time to Maturity (years) 0.5 Volatility (Std. Dev.) 20.0% Value of Put $3.9890 Exhibit 2 Stock Price (S) $110.00 Strike Price (X) $100.00 Interest Rate (r) 7.0% Dividend Yield (q) 0.0% Time to Maturity (years) 0.5 Volatility (Std. Dev.) 20.0% Value of Call $14.8445 N(d1) 0.8394 N(d2) 0.8025 Exhibit 3 Stock Price (S) $115.00 Strike Price (X) $100.00 Interest Rate (r) 7.0% Dividend Yield (q) 0.0% Time to Maturity (years) 0.5 Volatility (Std. Dev.) 20.0% Value of Call $19.2147 Value of Put $0.7753