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.