Authors: Xinyi Shen and Shaofeng Kang
Description:
This report explores pricing an American put option using a variation of the Cox-Ross-Rubinstein (CRR) model. Key topics include:
- Deriving branching probabilities under the risk-neutral measure.
- Determining the exercise boundary for American options.
- Simulating stock price paths for early and non-exercised options.
- Computing hedging strategies and analyzing profit and loss (P&L) distributions.
- Investigating stopping time distributions under various volatility (σ) and risk-free rate (r) settings.
Key Methods:
- Risk-neutral valuation.
- Binomial tree model for pricing and hedging.
- Python simulations for option valuation.
Authors: Xinyi Shen and Zhuolin Zhou
Description:
This report examines delta-gamma hedging strategies within the Black-Scholes framework, focusing on minimizing risk when managing an at-the-money call option. Topics include:
- Construction of delta-neutral and delta-gamma-neutral portfolios.
- Incorporation of transaction costs in hedging strategies.
- Monte Carlo simulations with 5,000 paths to evaluate P&L distributions.
- Comparison between delta and delta-gamma hedging under varying drift parameters (μ).
- Impact of volatility misestimation on hedging effectiveness.
Key Methods:
- Black-Scholes model.
- Delta and gamma hedging techniques.
- Monte Carlo simulations for risk analysis.
Author: Xinyi (Cynthia) Shen
Description:
Comprehensive lecture notes for the MMF1928 Pricing Theory course. This document covers theoretical foundations and practical applications of pricing financial derivatives. Topics include:
- Binomial and Black-Scholes models.
- Martingales and risk-neutral pricing.
- Fundamental Theorems of Asset Pricing (FTAP I & II).
- Ito's Lemma and stochastic calculus.
- Pricing exotic options and interest rate derivatives.
- Advanced topics such as the Feynman-Kac theorem and Girsanov’s theorem.
Key Concepts:
- Stochastic Differential Equations (SDEs).
- Risk-neutral valuation approaches (probability and PDE-based methods).
- Numerical methods in derivative pricing.
These documents serve as valuable resources for students and professionals interested in quantitative finance, specifically in option pricing and risk management. They provide theoretical explanations and practical implementations using Python simulations.
University of Toronto – Master of Mathematical Finance Program Course: Applied Probability for Mathematical Finance & Pricing Theory
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