ECONM3017 Derivatives UOB Assignment Answer UK

ECONM3017 Derivatives course delve into the fascinating world of derivatives and explore their role in modern financial markets. Whether you are a finance enthusiast, an aspiring trader, or a student aiming to build a strong foundation in economics, this course will provide you with a comprehensive understanding of derivatives and their applications.

Derivatives are financial instruments that derive their value from an underlying asset, such as stocks, bonds, commodities, or currencies. They play a crucial role in managing risks, hedging investments, and speculating on price movements. As the global financial landscape becomes increasingly interconnected and complex, a solid grasp of derivatives and their underlying principles becomes essential for anyone seeking to navigate this intricate terrain.

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Here, we will describe some assignment briefs. These are:

Assignment Brief 1: Understand how financial derivatives are valued based on no-arbitrage pricing and risk-neutral valuation, and how these instruments can be used to implement risk management strategies.

Financial derivatives are valued using two main approaches: no-arbitrage pricing and risk-neutral valuation. Both methods aim to determine the fair value of a derivative instrument based on the underlying assets and their expected future behavior.

No-Arbitrage Pricing: No-arbitrage pricing relies on the principle that in an efficient market, there should be no opportunity for risk-free profit. This principle ensures that the prices of related securities are properly aligned. To value derivatives using no-arbitrage pricing, the following steps are typically followed:
a. Replication: The derivative’s payoffs are replicated using a combination of the underlying asset and a risk-free investment. This replication eliminates any arbitrage opportunity by creating a portfolio that replicates the derivative’s cash flows.
b. Risk-Neutral Probability: The probabilities used in the valuation are adjusted to account for risk. The risk-neutral probability is derived by assuming a risk-neutral world where investors are indifferent to risk and the expected return on the risk-free rate is used as a discount rate.
c. Valuation: The present value of the derivative’s expected cash flows, computed using the risk-neutral probabilities, is determined. The discounted value of the replicated portfolio is compared to the derivative’s value to ensure no arbitrage opportunities exist.

Risk-Neutral Valuation: Risk-neutral valuation is a technique used to value derivatives by assuming that the expected return on the derivative is equal to the risk-free rate. In this approach, the valuation is based on the assumption that the market prices the derivative based on its expected future value. The steps involved in risk-neutral valuation are as follows:
a. Risk-Neutral Probability: Similar to no-arbitrage pricing, the risk-neutral probability is derived by assuming a risk-neutral world where investors are indifferent to risk. The probabilities are adjusted to make the expected return on the derivative equal to the risk-free rate.
b. Valuation: The expected future cash flows of the derivative are discounted back to the present using the risk-free rate. The sum of these present values represents the fair value of the derivative.

Derivatives can be used as risk management tools to hedge against price fluctuations, manage portfolio risk, or speculate on market movements. Some commonly used strategies include:

  1. Hedging: Derivatives can be used to offset the risks associated with an underlying asset. For example, a commodity producer can use futures contracts to lock in a specific price to sell their products in the future, protecting themselves from adverse price movements.
  2. Speculation: Derivatives allow investors to take positions on the future direction of an asset’s price. For instance, an investor expecting an increase in the price of a stock may buy call options to profit from the potential upside without owning the underlying stock.
  3. Arbitrage: Derivatives can be used to exploit pricing discrepancies between related securities in different markets. Traders can simultaneously buy and sell derivatives to take advantage of these pricing inefficiencies.
  4. Portfolio Diversification: By incorporating derivatives into a portfolio, investors can enhance diversification and manage risk exposure. For instance, options can be used to protect a portfolio against potential market downturns.

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Assignment Brief 2: Critically discuss the practical usefulness of the Black-Scholes-Merton option pricing model.

The Black-Scholes-Merton (BSM) option pricing model is a widely used mathematical model for valuing options. Developed by economists Fischer Black and Myron Scholes in collaboration with mathematician Robert Merton, the model revolutionized the field of quantitative finance when it was introduced in 1973. While the BSM model has had a significant impact on option pricing and risk management, its practical usefulness is subject to critical analysis.

One of the main advantages of the BSM model is its simplicity and elegance. It provides a closed-form solution for valuing European-style options, which allows for quick and efficient calculations. The model assumes that the underlying asset follows geometric Brownian motion and that market conditions are efficient, assuming no transaction costs or restrictions on short selling. These assumptions make the model mathematically tractable and facilitate widespread adoption.

Another benefit of the BSM model is its role in providing insights into option pricing theory. The model introduced the concept of delta hedging, which involves dynamically adjusting a portfolio’s composition to replicate the risk profile of an option. This approach allows traders and investors to manage their exposure to price movements effectively. Additionally, the BSM model helped establish the principle of risk-neutral valuation, which forms the foundation for pricing derivatives in a risk-neutral framework.

However, several limitations and assumptions of the BSM model undermine its practical usefulness in certain contexts. Firstly, the BSM model assumes that asset prices follow a continuous-time process and that volatility remains constant over the life of the option. In reality, financial markets are subject to jumps, discontinuities, and changes in volatility, which the BSM model fails to capture. As a result, the model may provide inaccurate valuations for options in highly volatile markets or during significant events such as market crashes.

Moreover, the BSM model assumes that markets are frictionless and efficient, disregarding transaction costs, taxes, and market imperfections. In reality, these factors can significantly impact option prices and hinder the ability to replicate the BSM assumptions. The model also assumes that underlying assets are tradable continuously, which is not always the case. For illiquid securities or options with restricted trading hours, the BSM model may not be applicable or may yield misleading results.

Additionally, the BSM model is designed for European-style options, which can only be exercised at expiration. It does not account for American-style options, which can be exercised at any time before expiration. Although the BSM model can provide a reasonable estimate for European-style options, it may undervalue American-style options, as it does not consider the additional flexibility of early exercise.

Furthermore, the BSM model assumes that returns are normally distributed, which may not hold true in reality. Financial markets exhibit fat tails and skewness, meaning that extreme events occur more frequently than expected under normal distribution assumptions. The BSM model’s failure to account for these characteristics can lead to underestimating the true value of options, particularly during periods of market stress or when dealing with tail risk.

Assignment Brief 3: Appreciate the latest developments in derivative modelling, and understand the latest problems in pricing complex derivatives.

Derivative modeling refers to the process of creating mathematical models that describe the behavior and pricing of financial derivatives. Derivatives are financial instruments whose value is derived from an underlying asset, such as stocks, bonds, commodities, or currencies. Examples of derivatives include options, futures, swaps, and exotic derivatives.

One significant development in derivative modeling is the advancement of quantitative finance techniques, such as stochastic calculus, partial differential equations, and Monte Carlo simulations. These techniques allow for more sophisticated and accurate modeling of complex derivatives. Additionally, the growth of computational power and availability of big data have contributed to more advanced modeling approaches.

However, pricing complex derivatives remains a challenging task due to several reasons:

  1. Model Complexity: Complex derivatives often involve multiple underlying assets and intricate payoff structures. This complexity makes it difficult to develop closed-form analytical solutions, requiring the use of numerical methods or simulations.
  2. Lack of Market Data: Some complex derivatives are relatively new or tailored to specific market conditions. As a result, historical market data may be scarce or insufficient for accurate pricing. This limitation can lead to increased uncertainty and risk in pricing models.
  3. Model Calibration: Derivative pricing models require calibration to market data to accurately capture market prices. Complex derivatives may require more parameters to be calibrated, which can be challenging due to limited data availability and the risk of overfitting.
  4. Liquidity and Market Dynamics: Complex derivatives may have limited liquidity, meaning that it can be challenging to find counterparties willing to trade them. Illiquidity and market dynamics can introduce additional pricing uncertainties, especially for large trades.
  5. Risk Management: Complex derivatives can expose market participants to various risks, such as credit risk, counterparty risk, and model risk. Pricing models must adequately account for these risks to ensure accurate valuation and effective risk management.

To address these challenges, financial institutions and researchers are continuously working on developing more sophisticated pricing models, refining risk management techniques, and leveraging advanced computational methods. Additionally, regulatory bodies play a crucial role in monitoring and supervising the pricing and trading of complex derivatives to maintain market stability and investor protection.

It’s important to note that the field of derivative modeling is constantly evolving, and new developments may have emerged since my last knowledge update. Therefore, I encourage you to consult the latest research papers, industry reports, and expert opinions for the most up-to-date information on the subject.

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