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#1




Asian Option Pricing Question
Here is a quote from the ACTEX MFE Fall 2017 Study manual(page M45):
"Effect of Averaging The number of averaging n has a great impact on the prices of Asian options. For average price Asian options, the price is a decreasing function of n. For average strike Asian options, the price is an increasing function of n." I fail to see how this makes any sense because the payoff for an avg price Asian call has a reciprocal relation to the avg price compared to a similar put. I also fail to see how the number of sample points can always have the same effect on price when the average is highly dependent on the profile of asset price. A concave  up function will have a lower average with more sampling and a concave  down function will have a higher average with more sampling. Any insight as to whether this paragraph makes sense or not will be greatly appreciated! 
#2




Average Price Option:
For average price option, as N increases, the average stock price, S_bar, has less volatility. This makes it less likely to have a large payoff. As a result, the value of an average price Asian option decreases as N increases. Here's another perspective to help you remember whether the value of an average price Asian option will increase or decrease as N increases. When N=1, the only observation in the average stock price is the final stock price, i.e., S_bar=S(T). Thus, the payoff of an average price Asian option equals the payoff of a corresponding European option. Recall the value of an average price Asian option is always less than or equal to that of an equivalent European option. Notice when N=1, the value of an average price Asian option is already at its maximum. Thus, when N increases, the value of the average price option cannot increase any further, so it must decrease. Average Strike Option: For average strike option, as N increases, it is more likely that the average stock price, S_bar, will be further away from the final stock price, S(T). As a result, the value of an average strike Asian option increases as N increases. Here's another perspective to help you remember whether the value of an average strike Asian option will increase or decrease as N increases. When N=1, the only observation in the average stock price is the final stock price, i.e., S_bar=S(T). Thus, the payoffs of the average strike Asian options are equal to 0. Recall an option owner can choose not to exercise an option if it produces a negative payoff. As a result, the value of an option cannot be negative, which means the minimum value of an option is 0. Notice when N=1, the value of the average strike Asian option is already at its minimum, i.e., 0. Thus, when N increases, the value of the average strike option cannot decrease further, and it will increase. Hope this helps! 
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