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Task Use the expected value of the discounted payoff under the risk-neutral density V for the appropriate form of payoff, to consider: 1. Arithmetic Sampling - fixed and floating strike 2. Geometric Sampling - fixed and floating strike In both cases use the Euler-Maruyama scheme for simulating the underlying stock price using the following set of data Today's stock price S. - 100 Strike E - 100 Time to expiry (T - t) - 1 year volatility o - 20% constant risk-free interest rate 7 - 5% This is an open ended exercise and marking will be based on initiative shown and willingness to experiment, but your completed assignment should centre on a short report (and computer code separately) to include: Outline of the numerical procedure used Results - appropriate tables, comparisons and error graphs (e.g. changing number of simulations). Any interesting observations and problems encountered. Conclusion and references Do not include code as an appendix to the report, this should be in a separate file.

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I. Introduction

In this paper we will solve for the market value of an Asian call and put option for both European-style (where the holder of the contract can only exercise at maturity) and American-style (where the holder can exercise at any day until maturity) using Monte Carlo Simulation utilizing the Euler-Maruyama scheme in determining the evolution of the asset price from day zero to maturity. Also, we solve for the case where the Asian option has fixed strike and the case where it has a floating strike with the additional case where the average...
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