a) Using an appropriate function that was developed during the course, price the following Asian average price put option:

spot price = 55, strike price = 50, maturity = 1 year, risk-free rate = 5% p.a. with continuous compounding, volatility = 40%.

Assume the option is based on weekly price sampling. For this part and the rest of Question 2, use an appropriate implementation of Monte Carlo simulation to ensure reliable numerical results. What does the complete code look like in its entirety?

b) The type of averaging in the option in a) is often referred to as continuous sampling whereby all sampled prices are used in the calculation of the average price. In reality, there are Asian option contracts whose payoff is based on discrete sampling, where only a small subset of the sampled prices is used in the calculation of the average price. An Asian tail option is an example of discrete sampling, whereby a final few sampled prices are used in the averaging. Modify an appropriate function that was developed during the course to price an Asian tail option that uses only the last 5 sampled prices in the averaging (so if the option specifies weekly sampling, only the weekly prices from the final 5 weeks are included in the calculation of the average). Name the function as Asiantailpricer.

Include Asiantailpricer in your submission Test the function using the parameters in a).

What does the complete code look like in its entirety?

c) You should see the Asian tail in b) is more expensive than the Asian option in a). Provide an intuition that explains this fact. Support your argument via a computation in the box below. Extend the analysis to European options and state, with supported computation, whether equivalent European options should cost even more.

What does the code look like in its entirety?