Advanced Topics in Derivative Pricing

This module contains the first part of equity derivatives. After a brief review on the binomial model, we introduce Black-Scholes model and how to utilize this model to derive so-called "Greeks." Greeks are very important indices in options, which measure the sensitivity of option value to a wide range of variables such as stock price and volatility. We are also covering risk management and hedging. Greeks play an important role in risk management and hedging, as traders and quants often use Greeks approach to hedge and construct their portfolios. Moreover, we will introduce scenario analysis and how Greeks are used to measure portfolio value change. In the end, we are covering an introduction to implied volatility and volatility smile. Implied volatility is a key link between market option prices and options prices under the framework of Black-Scholes model. We'll be covering more about this topic in the next module.

This module contains the second part of equity derivatives. Following past module, we'll continue discussing implied volatility and volatility smile. We introduce two main explanations about volatility skew: risk aversion and leverage effect. Next, we will cover how to utilize volatility surface to price derivatives, including digital options and range accruals. Meanwhile, we will introduce a method to obtain risk-neutral density of terminal stock price distribution from option prices. We will also cover two additional topics about joint distribution of two securities and dynamic replication in practice. In module 3, you will have a real-world assignment where you will use all the knowledge from previous modules to solve the problems about equity derivatives. In this assignment, you will be exposed to many think-about questions where you can jump out of the Black-Scholes framework and think in a model-free world.