What Are The Strengths And Weaknesses Of The Black-Scholes Option Pricing Model

Valuation is the estimation of an asset’s value, whether real or financial, based on variables perceived to be related to future investment returns, on comparison with similar assets, or, when relevant, on estimates of immediate liquidation proceeds (Pinto, Henry, Robinson, Stowe; 2010). Correct valuation of real assets can present challenges to financial analysts. Different models can be used to arrive at the closest estimate of value and yet certain issues will always arise. This case attempts to tackle two approaches in real asset valuation: Discounted Cash Flow (DCF) analysis and the issues surrounding such, as well as the Black-Scholes Model for Real Options. Questions to be addressed in the study are:

Week 1 – Introduction – Financial Accounting (Review) Week 2 – Financial Markets and Net Present Value Week 3 – Present Value Concepts Week 4 – Bond Valuation and Term Structure Theory Week 5 – Valuation of Stocks Week 6 – Risk and Return – Problem Set #1 Due Week 7* – Midterm (Tuesday*) Week 8 - Portfolio Theory Week 9 – Capital Asset Pricing Model Week 10 – Arbitrage Pricing Theory Week 11 – Operation and Efficiency of Capital Markets Week 12 – Course Review – Problem Set #2 Due

Mr. Brown readily admitted that he was not at ease discussing the most recent approaches to risk reduction or hedging. He had received his MBA from Harvard in the 1960s and had spent most of his career working for a company that had little international exposure. Moreover, he was not familiar with derivatives such as currency options, which until recently were not widely traded. However, Mr. Brown had recently hired an assistant, Mr. Dan Pross, who had some knowledge of hedging and derivatives. As a student at UCLA, Mr. Pross had traded various types of derivatives for his own portfolio and was familiar with how they were traded. Although Mr. Pross did not have a finance background, he was, in Mr. Brown’s opinion, extremely intelligent and highly capable. Mr. Brown suggested that Mr. Pross make a presentation to the senior management on the use of derivatives to reduce risk.

The goal of this paper is to explain why CCM’s aggressive program is a good alternative to any investor looking to diversify its portfolio. The paper will be divided into three distinct parts: the operational analysis, the quantitative analysis and a comparison against its peers (including the impact of CCM in a traditional portfolio).

This case attempts to tackle two approaches in real asset valuation: Discounted Cash Flow (DCF) analysis and the issues surrounding such, as well as the Black-Scholes

I have pursued my interest and knowledge of financial markets through analyst positions on Limestone Capital and Queen’s Private Capital Group, two student-run finance clubs at Queen’s. As part of my involvement, I completed training in financial modelling, developing the necessary skills to perform valuations. I also

Firstly, there are some simplifications to be done to get all the necessary inputs for the Black & Scholes model. One approximation to be made is the estimation of the

This document is authorized for use only by Yen Ting Chen in FInancial Markets and Institutions taught by Nawal Ahmed Boston University from September 2014 to December 2014.

The BSM model is used to determine fair prices of European options only following a formula (as shown below) with the first basic assumption that the underlying commodity, stock, or option pay zero dividend to its shareholders group being purchased during the option life (CFA, 2015).

William Sharpe presented several assumptions without which a valid CAPM cannot be obtained . These assumption are discussed below –

From the results we observe that early exercise premium increases at different maturity dates for the same strike price and when varying strike price with the same maturity date the early exercise premium increases non linearly in an upward trend. The shift in the trending from options 1, 2, 3 can be explained by the maturity, as maturity increases an American option is more worthwhile because more node exist where it is possible for us to exercise early. From the results early exercise price as a function of strike price, maturity and interest rate, increases when we hold maturity constant and vary the other two. The shift in trending can be explained by the increase in interest rates for options 1, 2, 3 respectively. When interest rate is increased the present value of the underlying drops and the likeliness of the option being in the money increases and therefore the value of put option increases.

As our payoff estimates are changing favourability of options too close to the base case scenario, we cannot make sound recommendations at this time. A slight change in the probability of the lease being granted or our ability to develop or good reputation reverses our optimal decision.

The success of the model is attributed to Yale’s ability to combine both quantitative analysis (mean-variance analysis) with market judgments to structure its portfolio. In addition, Yale also uses statistical analysis to actively test their models with factors affecting the market, therefore understanding the sensitivity of their portfolio in response to various market changes. Yale also follows and forecasts the cash flow of private equity and real assets in its portfolio to decide the need for hedging.

The analysis of this paper will derive the validity of the Fama and French (FF) model and the efficiency of the Capital Asset Pricing Model (CAPM). The comparison of the Fama and French Model and CAPM (Sharpe, 1964 & Lintner, 1965) uses real time data of stock market to practise its efficacy. The implication of the function in realistic conditions would justify the utility of the CAPM theory. The theory suggests that the expected return demanded by investors on a risky asset depends on the risk-free rate of interest, the expected return on the market portfolio, the variance of the return on the market portfolio, and

Ever since Ross (1976) proposed the Arbitrage Pricing Theory (APT) as an alternative to the capital pricing model, many economists and investors have applied APT across different markets. Whereas the traditional capital pricing model explained asset returns with one beta, sensitivity to the market return, APT decomposes the return with a multiple number of factors. This idea became particularly popular for investors who aim to gain systematic risk other than market risk. However, the model specification aspect has been challenging to many practitioners as the theory does not require any specific sets of variables to be used (Azeez 2006).