Foundations of Derivative Pricing

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Learning mathematical finance and the principles behind derivative pricing is essential for anybody working in front-office investment banking, whether a quant actively developing financial models or a quant-dev developing the infrastructure around the models.  This course provides a practical foundation in the mathematical and the computation/numerical approaches used for pricing and risk-managing derivatives.

• Understanding Financial Models: Basic mathematical finance provides the foundation for many financial models that are used in the industry. Understanding these models and the underlying mathematics is essential for any finance professional who wants to be able to analyze and interpret financial data accurately as well as to understand the limits of the models.
• Understanding Pricing/Calibration Methodology: The approach used to calibrate and price trades has an impact on their accuracy, performance and stability. It is important that all front office quant and quant-devs understand these issues. 
• Derivative Trades: Working in a front-office role, it's important to understand the range of trade types, the client requirements and the trader/risk-management considerations.
• Risk management: Basic mathematical finance provides tools for measuring and managing financial risk. Understanding these tools is essential for anyone working in or with risk management.

• Financial Mathematics: The course begins with an overview of financial mathematics, including concepts such as time value of money, discounting, and present value. History of options and derivatives.
• Probability Theory: Probability theory is an essential component of mathematical finance. We cover the basics of probability theory, including concepts such as probability distributions, expected value, and variance.
• Stochastic Calculus: Stochastic calculus is the branch of mathematics that deals with random processes. We cover the basics of stochastic calculus and how it is used to model financial instruments.
• Derivative Instruments: The course covers the most common assets and types of derivative instruments. 
• Black-Scholes Model: The Black-Scholes model is a widely used mathematical model for pricing options.
• Volatility: We cover local-volatility and stochastic volatility models, their impact on pricing and extremal events.
• Hedging: Hedging is an essential part of risk management in financial markets. This course covers the basic approaches behind hedging.
• Monte Carlo Simulations: Monte Carlo simulations are a powerful tool for modeling financial instruments. This course covers Monte Carlo simulations, correlating processes, low-discrepancy approaches.
• Lattice Methods: For backwards induction we cover lattice methods such as PDE as well as convolutional approaches.

This course would benefit junior quants coming from a non-finance background. In addition, all quant devs with a numerate background.

Course contents and duration can be modified to align with additional client needs. 

Delivery can be on-site, remote or in recorded form.