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Posted: March 21st, 2023
Chapter 14. Black & Scholes Model
1.
Explain why the Black-Scholes model is inappropriate if the stock
can gap.
2. Is assuming a constant (nonstochastic) interest rate in the
Black-Scholes model a major de ciency of the model?
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3. The Black-Scholes model assumes constant volatility. How serious a
shortcoming is this?
4.
Compute the three-month (T = 1=4) forward price F of a stock
currently trading at $40 when the risk-free rate for this period is r = 4%.
Then, set the strike price K = F and
Sundaram
& Das: Derivatives - Problems and Solutions . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 193
calculate call and put values from the
Black-Scholes model if the volatility is = 0:4, assuming the stock pays no
dividends. What can you say about the call and put prices you just computed?
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21(We repeat the previous question allowing for nonzero dividends).
Assume a stock has a dividend yield of d = 2%. Compute the three-month (T =
1=4) forward price F of a stock currently trading at $40 when the risk-free
rate for this period is r = 4%. Then, set the strike price to K = F and
calculate call and put values from the Black-Scholes model if the volatility is
= 0:4. What can you say about the call and put prices you just computed?
6. Plot the price of a Black-Scholes call for a range of volatility
from 5% to 40%. Use the following parameters: S = 30, K = 33, T = 1=3, r =
0:03, and d = 0. Does the function appear concave or convex?
7. Plot the price of a Black-Scholes call for declining maturity from
three years to zero years. Does the function appear concave or convex? Use the
following parameters:
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S = 30, K = 33, = 0:3, r =
0:03, and d = 0.
8. Plot the price of a Black-Scholes call for a range of interest
rates from 1% to 20%. Use the following parameters: S = 30, K = 33, T = 3, =
0:3, and d = 0.
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