Answer-first summary for fast verification
Answer: As we increase ($N$) from $1$ to $252$, the value of an average price put increases from $\$2.866$ to higher values
**C is false.** Instead, the average price put behaves like the average price call: at $N = 1$, both are equal to the corresponding regular option value (i.e., $\$3.753$ and $\$2.866$), and as $N$ increases the value of both average price options (call and put) **decrease** because increasing the frequency reduces the volatility of the final average relative to the final asset price. **A is true.** If $N = 1$, there is only one observation at the end of the year, so the average price equals the ending stock price, making the Asian average price call and put equal to the corresponding regular European option values. **B is true.** As the number of observations increases, the average price call becomes less volatile and therefore less valuable. **D is true.** If $N = 1$, the average strike option values are zero because the average equals the terminal price. Increasing the observation frequency increases the value of an average strike call or put, although they generally do not become as valuable as the regular option values.
Author: Manit Arora
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Question 731.3
Below is the output of a Black-Scholes (BSM) option pricing model for a one-year () option with a strike price, K = \`30.00$, on a non-dividend-paying stock, $q = 0\%$, when the stock price, $S(0) = \, with volatility, , while the risk-free rate is $3.0%` and the corresponding put option price is \`2.86`6$
However, assume that instead of a regular option, we are pricing Asian options under the same assumptions. In this case, there are four variations on the Asian option:
Let () represent the FREQUENCY of observations in order to determine the average price or strike during the life of the option; e.g., if then there is only once observation at the end of the year, if then there is an observation at the end of each month, if there is an observation at the end of week, if there is an observation at the end of each day. In regard to these Asian options, each of the following statements is true EXCEPT which is false?
A
If , then the average price call and put are, respectively, \`3.753$ and $\
B
As we increase () from $1252$, the value of an average price call decreases from $\ to lower values
C
As we increase () from $1252$, the value of an average price put increases from $\ to higher values
D
As we increase () from $1252`$, the value of an average strike put increases from zero to higher values
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