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Explanation:
A call-on-a-call compound option is exercised at if the value of the underlying call option exceeds the exercise price of the compound option, which is `$1.90`.
From the table, the one-year call option is worth:
Thus, the compound option becomes worthwhile when the stock price at is **above `32.50`** (so that the underlying call is worth more than \`1.90`).
So the correct condition is B.
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729.3. Consider a compound option that gives the holder the right to pay `T_1) and purchase a call option with a strike price of \`40.00 and one year to expiration; so this is a call-on-a-call with $T_1 = +1.0$ year and $T_2 = +2.0$ years. The underlying stock price is currently \2.50` intervals:
European call option prices with stock prices
| Stock (S0) | $30.00 | $32.50 | $35.00 | $37.50 | $40.00 | $42.50 |
|---|---|---|---|---|---|---|
| Strike (K) | $40.00 | $40.00 | $40.00 | $40.00 | $40.00 | $40.00 |
| Volatility, σ | 30.0% | 30.0% | 30.0% | 30.0% | 30.0% | 30.0% |
| Riskfree rate, r | 4.00% | 4.00% | 4.00% | 4.00% | 4.00% | 4.00% |
| Time to maturity, T, years | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| BSM call price, c = | $1.16 | $1.90 | $2.87 | $4.08 | $5.50 | $7.13 |
Under what condition(s) will this compound call-on-a-call option be exercised in one year?
A
This compound call will never be exercised
B
This compound call will be exercised if the stock price, S(1.0), is above $32.50
C
This compound call will be exercised if the underlying call has positive intrinsic value at time T1; i.e., if S(1.0) >= $40.00
D
The compound call will be exercised if the underlying call has a lower bound of $1.90 at time T1; i.e., if S(1.0) >= $40.33