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Lecture

Applications: Markov Models and Pricing

In course

FIN-404: Derivatives

This course provides a detailed presentation of the standard models for the valuation and hedging of derivatives products such as European options, American options, forward contracts, futures contract and exotic options. ...

Description

This lecture covers the application of Markov models in finance, focusing on pricing derivatives and risk-neutralization. It discusses the generator of the process, risk-neutralization under the Equivalent Martingale Measure (EMM), Markov pricing, and hedging strategies. The lecture also delves into bond pricing, the forward measure, option pricing, and the use of Vasicek and Black-Scholes-Merton (BSM) models. Additionally, it explores topics such as foreign exchange, FX forwards, carry trades, FX options, quanto options, and hedging strategies for various financial instruments.

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Instructor

Julien Hugonnier

Official source

Ontological neighbourhood

Economics

Microeconomics: Financial economics

Business

Finance: Financial risk management

Related concepts (31)

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.

Bond option

In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC. A European bond option is an option to buy or sell a bond at a certain date in future for a predetermined price. An American bond option is an option to buy or sell a bond on or before a certain date in future for a predetermined price. Generally, one buys a call option on the bond if one believes that interest rates will fall, causing an increase in bond prices.

Hedge (finance)

A hedge is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gambles, many types of over-the-counter and derivative products, and futures contracts.

Asian option

An Asian option (or average value option) is a special type of option contract. For Asian options, the payoff is determined by the average underlying price over some pre-set period of time. This is different from the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at exercise; Asian options are thus one of the basic forms of exotic options.

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).

Related lectures (37)

Forward Measures: Interest Rate Models

Explores forward measures, option pricing, and bond option pricing in interest rate models.

Interest Rates and Contracts: Duration and Convexity

Explores duration and convexity in interest rate models for bond portfolio hedging.

Asset Pricing: Fundamental Theorems

Covers the fundamental theorems of asset pricing, including EMM, self-financing strategies, risk-neutral pricing, and completeness of markets.

Interest Rate Derivatives: Caps and Floors

Explores interest rate derivatives, specifically caps and floors, cap-floor parity, pricing formulas, and implied volatilities.

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