Mini Project $1$:

Title: "Real$-$World Asset Pricing and Option Valuation with State Pricing in a One$-$Period Binomial Model"

Objective: The objective of this mini$-$project is to apply asset pricing concepts to real$-$world financial data. Specifically, you will explore state pricing in a one$-$period Binomial model, numeraires, asset pricing with a continuum of states, and option pricing using actual market data.

Project Outline:

Data Collection:

Obtain historical price data for a specific financial asset, such as a stock or an index, and relevant option contract data.

Introduction to the One$-$Period Binomial Model:

Provide an overview of the one$-$period Binomial model and its relevance in financial derivatives pricing.

State Pricing:

Explain the concept of state prices and how they are used to price assets and derivatives. Calculate state prices for different states of the world using real historical data.

Pricing with Numeraires:

Introduce the concept of numeraires and discuss how they simplify asset pricing. Calculate asset prices and option values using numeraires and real data.

Asset Pricing with a Continuum of States:

Extend the Binomial model to incorporate a continuum of states, making it more realistic. Use real data to calculate asset prices in this continuous$-$state model.

Option Pricing with Real Data:

Apply the concepts learned to price European and American call and put options using realworld market data. Compare the calculated option prices with actual market prices.

Numerical Analysis:

Perform sensitivity analysis using real data by varying model parameters such as volatility and interest rates. Discuss how changes in these parameters affect option prices and hedging strategies.

Conclusion and Recommendations:

Summarize the findings of the project, emphasizing the practical application of state pricing, numeraires, and continuum state models. Provide recommendations for investors or traders based on your analysis.

Presentation:

Prepare a presentation summarizing your project's key findings, methodology, and conclusions. Present your project to the class or submit it as a written report.

By conducting this mini$-$project with real$-$world data, you can gain a deeper understanding of asset pricing concepts and option valuation in a practical context. It also allows them to appreciate the complexities of real financial markets and how theoretical models are applied in practice.