BSM Model and Financial Derivatives Quiz

BSM Model and Its Applications in Financial Derivatives

The Black-Scholes-Merton (BSM) model, a pivotal concept in financial theory, offers a framework to evaluate and price standard financial derivatives, notably options. Developed by renowned economists Fischer Black, Myron Scholes, and Robert Merton in the 1970s, this model has been instrumental in shaping the modern finance landscape.

BSM Model Overview

The BSM model relies on several assumptions:

1. The underlying asset follows a geometric Brownian motion, meaning its price fluctuates log-normally over time.
2. The underlying asset's price follows a continuous process.
3. Frictionless markets with zero transaction costs and no arbitrage opportunities.
4. Constant volatility.

The model's equations provide values for call and put options prices, and they are independent of the underlying asset's price distribution.

Financial Derivatives and BSM Model

Derivatives such as options and futures are financial contracts based on the value of an underlying asset. The BSM model has been instrumental in pricing and understanding these contracts, with applications spanning:

1. Call options: A contract that gives the buyer the right to purchase an underlying asset at a predetermined price (strike price) for a specific period.
2. Put options: A contract that grants the buyer the right to sell the underlying asset at a predetermined price (strike price) for a specific period.
3. Futures contracts: Agreements to buy or sell an asset for a future delivery date.

Risk Types and BSM Model

The BSM model, despite its simplifying assumptions, can be used to understand and assess three essential risks associated with derivatives and financial markets:

1. Credit risk: The potential loss arising from a counterparty's default on a contractual obligation. This risk is not directly addressed by the BSM model, but it is crucial to consider when structuring financial contracts.

2. Market risk: The risk that the value of an asset or portfolio will decrease due to unfavorable market movements. The BSM model helps understand the sensitivity of option prices to market factors, such as the underlying asset's price, volatility, and interest rates.

3. Liquidity risk: The risk associated with the inability to sell an asset or contract quickly at a fair price. This risk is not directly addressed by the BSM model, but it is a critical consideration when designing financial contracts and trading strategies. Liquidity risk can also influence market risk by increasing the volatility of asset prices.

Shortcomings of BSM Model

Despite its revolutionary impact, the BSM model has several limitations:

1. Disregards stochastic volatility: The BSM model assumes constant volatility, whereas option prices are often affected by time-varying volatility.
2. Does not consider dividend payments: The model neglects dividend payments in the underlying asset's price.
3. Limited to European-style options: Black-Scholes model only applies to European-style options (options that can only be exercised at expiration).

Notwithstanding these shortcomings, the BSM model remains a powerful tool for understanding and pricing standard financial derivatives. Its contributions to the finance industry have been profound, and its applications continue to evolve, driving innovations in financial engineering and product design.