Monte Carlo Option Pricing

Our group reported on Monte Carlo Option Pricing:

Monte carlo option pricing final v3 from naojan

Notes:

Monte Carlo

• important is how to generate the random distribution.
• Do not rely on this as a black box solution..
• We can look at the historical data.
• We can do this as a project – straight forward models from hull or wilmott to generate the price setting model..to value our payoff.

Slide 3 - The Entire slides focused on Option Pricing. But for Portfolio Statistics we have 3 important concepts:

• Find an algorithm for how the most basic investments evolve randomly. 
• Equities: 
• often the lognormal random walk
• can be represented on a spreadsheet or in code as how a stock price changes from one period to the next by adding on a random return. 
• Fixed-income
• BGM model in modeling how interest rates of various maturities evolve
• Credit 
• A model that models the random bankruptcy of a company. 
• Can represent any interrelationships between investments  which can achieved through correlations.
• Understand the derivatives theory for after performing simulations of the basic investments, there is a need to have models for more complicated contracts that depend on them such as options/derivatives/contingent claims. 
• May be able to use the results in the simulation of thousands future scenarios to examine portfolio statistics 
• Ie. how classical Value at Risk can be estimated

Slide 4

Risk-neutrality assumption – We make the assumption that investors are risk neutral, i.e., investors do not increase the expected return they require from an investment to compensate for increased risk.

Cox and Ross (1976) have shown that the assumption of risk neutrality can be used to obtain solutions of option valuation problems.’ This implies that the expected return on the underlying asset is the risk-free rate and that the discount rate used for the expected payoff on an option  is the risk-free rate.

Slide 6 - Stages from Watsham book and the original Boyle paper

Slide 7 - 14 - Option pricing_monte carlo example.xls

Slide 15 -Example from Wilmott: 

Its difference from watsham is that the watsham example creates random variables with empirical data's probability distribution. Wilmotts random variables are with uniform probability distribution.

***Note: have to understand the "Antithetic and QuasiRandom.xls"