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Answer: If the strike price, \(K1 = \$100.00\) and the trigger price, \(K2 = \$90.00\), then the gap option price is greater than $0.740
For a **gap put**, the payoff is similar to a standard put, but it is activated only if the trigger condition is met. - If **\(K1 = K2\)**, the gap put becomes the same as the vanilla put, so **A is true**. - If **\(K2 > K1\)**, the payoff can be negative in some states, so the option value **can** be lower and may even be negative in theory; thus **B is not the false statement** in this context. - If **\(K2 < K1\)**, the option is exercised less often than a vanilla put, so its price must be **less than** the vanilla put price of $0.740, not greater. Therefore **C is false**. - The highest value occurs when the trigger equals the strike, which makes the contract equivalent to the vanilla put, so **D is true**. **Correct answer: C**
Author: Manit Arora
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Q-729.1 Consider an asset with a current price of $120.00 and volatility of 16.0% while the risk-free rate is 3.0%. A regular (aka, vanilla) but deeply out-of-the-money (OTM) one-year European put option on the stock with a strike price of $100.00 has a price of $0.740; i.e., p(S = \`120.00, K = \100.00`, \sigma = 0.160, Rf = 0.030, T = 1.0\text{ year}) = \`0.74`0$.
Now consider the modification of this regular put option into a gap put option with the addition of a trigger price, denoted K2. In this case, the price of the gap put option is given by p(S = \`120.00, K1 = \.
Each of the following statements about this gap option is true EXCEPT which is false?
A
If K1 = K2 = \`100.00$, then the gap option also has a price of $0.74`0
B
If the strike price, K1 = \`100.00$ and the trigger price, $K2 = \, then the gap option has a negative price
C
If the strike price, K1 = \`100.00$ and the trigger price, $K2 = \, then the gap option price is greater than $0.740
D
Given a strike price, , among various trigger prices, the gap option has its highest price when the trigger, K2 = \`100.00`$
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