Question

4. An Asian option is an option whose payoffs depend on the average price of the un- derlying asset over a certain period of time (instead of the price at maturity in the case of standard options). Early exercise of the option is not allowed. For instance, consider the payoff of an Asian Call option at maturity (in three months) on a stock ABC that does not pay dividends : Cz = max ( Si + S2 + S3 - Yo) mas ( 3 1 ,0). - A where S1, S2, and S3 are the price of the underlying asset after 1, 2, and 3 months, respectively, and X is the strike price. Assume that the one-month effective rate is 1%, and that the strike price is X = 99, what is the price of the Asian Call option if the stock price is expected to take one of the following paths in the future: 110.25 100 102.9 - 98 96.04

Answer 1

ans A There are more than one possible path , actually 4 of them . the average price across the 4 paths is roughly 101.50

we can use this to price the option .take risk free rate t =1/12 and time =1/12.

Ans B to protect my stocks i would need protection against prices falling. So i would look for an option with strike price below the current spot price. So if the stock falls i can cushion the fall to the extent of Spot - strike price However this may not protect enough is the closing price is lower than strike price. The second method is to sell a Covered Call option at a price which is at least 1% ( risk free rate ( more than spot price .This would mean the cash from selling the option is assured and will protect the stocks in hand t a certain extent.  

Ans 3 - Considering Asian options has lower volatility as it is an average of 3 data points the  prices should be lower than European which is at a fixed price and a a particular instant of time. in B&S option pricing if the Sigma value is lower the formula will throw up a smaller number so lower prices.