代写Calibration and Empirical Analysis of the Vasicek Model for AUD Swaptions代写留学生Matlab语言程序

1. Project Topic

Title: Calibration and Empirical Analysis of the Vasicek Model for AUD Swaptions.

Overview: This project implements the single-factor Vasicek model to price a matrix of at-the-money (ATM) Australian Dollar (AUD) interest rate swaptions. The core work involves calibrating the model to the AUD yield curve and swaption market data. We will then compare the model's prices and implied volatilities to market data to identify systematic pricing biases and discuss the model's practical limitations and utility as a diagnostic tool.

2. Data Availability

All data will be sourced from the Bloomberg Terminal:

Yield Curve: AUD zero-coupon curve bootstrapped from par swap rates (ADSWP).

Swaption Volatilities: ATM volatilities for a matrix of expiries (1M, 3M, 6M, 1Y, 2Y, 5Y) and underlying swap tenors (1Y, 2Y, 5Y, 10Y) from SWPM.

Note: The quoting convention (Black-76 or Bachelier) for market volatilities will be recorded for accurate comparison.

3. Methodology and Model

The project will be executed in four phases using Excel/VBA:

1. Market Data Setup (Excel): Bootstrap the zero-coupon yield curve and calculate forward swap rates for all swaption contracts in the matr.

2. Model Implementation (VBA): Code the Vasicek model and its analytical formula for zero-coupon bond prices. Implement Jamshidian's (1989) decomposition to price swaptions as a portfolio of bond options. A key deliverable is a VBA function: VasicekSwaptionPrice(...).

3. Model Calibration (Excel/VBA): Use Excel Solver to find the Vasicek parameters (k, θ, σ) that minimize the sum of squared errors between model and market swaption prices.

4. Analysis (Excel):

Compare model prices vs. market prices.

Create a "Vasicek-Implied Vol Surface" by inverting the Black-76 model and compare it to the market surface.

Analyze pricing biases across expiries and tenors, and discuss the model's inability to capture volatility smiles.

Relations to Course: This work directly applies course concepts: fixed income basics (bootstrapping), swaption mechanics, implementing the Vasicek model for derivative pricing, and the practical challenges of model calibration.

4. Potential Learning Objectives

Technical Skills: Sourcing and processing market data from Bloomberg.

Quantitative Finance: Deepening understanding of term structure models and calibration.

Programming: Developing advanced financial modeling skills in Excel/VBA.

Critical Analysis: Empirically testing a financial model to understand its biases and limitations.