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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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Ontological neighbourhood

Economics

Microeconomics: Financial economics

Related concepts (32)

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.

Put option

In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the underlying), at a specified price (the strike), by (or on) a specified date (the expiry or maturity) to the writer (i.e. seller) of the put. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.

Option style

In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging.

Mathematical finance

Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.

Binary option

A binary option is a financial exotic option in which the payoff is either some fixed monetary amount or nothing at all. The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The former pays some fixed amount of cash if the option expires in-the-money while the latter pays the value of the underlying security. They are also called all-or-nothing options, digital options (more common in forex/interest rate markets), and fixed return options (FROs) (on the NYSE American).

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