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Lecture# The Black-Scholes-Merton Model

Description

This lecture covers the Black-Scholes-Merton model, a continuous-time economy with a constant riskless rate and a standard Brownian motion generating uncertainty. It explains the dynamics of the discounted price, self-financing strategies, continuous trading, and the replicating strategy for call options. The lecture also delves into the Black-Scholes-Merton partial differential equation (PDE), the hedging portfolio, dividend pricing, and the Feynman-Kac representation. It concludes with insights on the put option, the replicating strategy, and the linear pricing nature of the PDE.

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Instructor

In course

FIN-404: Derivatives

The objective of this course is to provide a detailed coverage of the standard models for the valuation and hedging of derivatives products such as European options, American options, forward contract

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Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include derivative structuring or pricing, risk management, investment management and other related finance occupations. The occupation is similar to those in industrial mathematics in other industries.

Model risk

In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activities other than financial securities valuation, such as assigning consumer credit scores, real-time probability prediction of fraudulent credit card transactions, and computing the probability of air flight passenger being a terrorist.

Call option

In finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at or before a certain time (the expiration date) for a certain price (the strike price). This effectively gives the owner a long position in the given asset.

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In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

Option (finance)

In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction.

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