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Posted: June 3rd, 2024
Chapter 10. Early-Exercise & Put-Call Parity
Note: All
interest rates, unless stated otherwise, are assumed to be continuously
compounded.
1. A stock is trading at $100. The interest rate for one year is 5%
continuously com-pounded. If a European call option on this stock at a strike
of $99 is priced at $8.50, break down the call option value into
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(a)
Instrinsic value.
(b)
Time value.
(c)
Insurance value.
2.
In the question above, what is the insurance value of the
corresponding put option?
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Sundaram
& Das: Derivatives - Problems and Solutions . . . . . . . . . . . . . . . .
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3. Explain why a European call on a stock that pays no dividends is
never exercised early. What would you do instead to eliminate the call option
position?
4. Stock ABC pays no dividends. The current price of an American call
on the stock at a strike of 41 is $4. The current stock price is $40. Compute
the time value of the European put option if it is trading at a price of $3.
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5.
Stock ABC is trading at a price of $50. At a strike price of 55,
there is a traded six-month American put. There are no dividends on the stock,
and maturity of the option is a half year. If the half-year rate of interest is
5%, what must the minimum insurance value of the put be for the put not to be
exercised?
6. Stock XYZ is trading at a price of $105. An American-style call
option on Stock XYZ with maturity one year and strike 100 is traded in the
market. The term structure of interest rates is at at 1% and there is a
dividend payment in six months of $8. What is the maximum insurance value for
the call at which it still makes sense to exercise it?
7. Assume that the true formula for pricing options is unknown, e.g.,
Black-Scholes is not applicable. Hence, you are asked to use the following
approximation for the insurance value of a put option:
S 2
IV (P ) = exp
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K T
Sundaram
& Das: Derivatives - Problems and Solutions . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 125
where S is the current price of the stock, K is the strike price,
is the volatility of the stock return, and T is option maturity.
You are given that S = 100, K = 105, and the interest rate r = 1%.
Option maturity is T = 1 year, and there are no dividends.
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What is the maximum
volatility for which early exercise of the option is induced?
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