FINC-780 Monte Carlo Option Pricing Concept: The pricing of derivatives is one of the most complex and difficult issues in finance. In some cases, there are analytical solutions (i.e., a formula) whereas in others you need some sort of numerical method. Monte Carlo simulations are widely used when the use case is difficult. It involves simulating values of the underlying instrument (e.g., the stock price of TSLA if one is trying to value options on TSLA stock). Stochastic processes are used for such simulation. Based on the simulated prices, the derivative is valued by discounting its payoff. Requirement: 1. Write code for the functions described below and run the code as instructed. Do not use any financial packages. 2. Follow standard reporting requirements. Since this is a modeling project (and not a data analytic project), the report should include a discussion of use cases and limitations. In your writing, be sure to reflect on the importance of the simulation method for valuing financial instruments. 3. An underlying requirement is the demonstration of ability to price instruments based on available descriptions on the Internet. The idea is that, in a job situation, you are able to independently apply valuating procedures. 4. Another underlying or implicit requirement is the demonstration of superior coding ability in R – you have already done a lot of work, so the
experience must show! 5. Produce an appropriately formatted pdf file (<= 8 pages) for submission. Function 1: Stock Price Generation Input (default value in parentheses): Stock price (20), Maturity (0.25), Steps (20), Sigma (0.4), interest rate (0.03), iterations (1000), seed (12) Output: Matrix of stock prices with rows forming price path; mean ending price; mean max price; mean min price. Show results for: running function using default values. Print the first two price paths and the summary measures. Function 2: Option Price Estimation Input: All inputs from function 1 PLUS a (i) a string ‘callorput’ (call), (ii) strike (20), and (iii) a string ‘exotic’ identifying option type as one of: floatlookback (floating look back where the payoff depends on the difference between the last price and the max/min price; there is no strike price); fixedlookback (fixed look back where the payoff depends on the difference between the max/min price and the exercise price); asianarithmetic; asiangeometric (the geometric mean is used in the payoff function); assetornothing (asset or nothing option). Please consult wiki pages or other resources for formulas. Output: Value of option, along with input values used. Show results for: running function for each of the five option types. Do not show output for each run. Instead, tabulate and show all results in a unified manner.