- Options, Futures, and Other Derivatives 10th edition, John C. Hull
- Option Volatility and Pricing: Advanced Trading Strategies and Techniques (2ND), Sheldon Natenberg
- Stochastic Volatility Modeling, Lorenzo Bergomi
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Options Driven Volatility Forecasting
- some inspiration for further improvements - utilizing volatility forecasting to help in pricing. Use a regression model to get to improve pricing with other factors.
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"Which Free Lunch Would You Like Today, Sir?: Delta Hedging, Volatility Arbitrage and Optimal Portfolios
- How to profit when there's a difference between the market's implied volatility (used in option pricing) and the actual volatility of the underlying asset. Hedging options mispriced by the market.
- Which delta do you choose? Delta based on RV or IV?
- Black Scholes:
$d_1 = \frac{\ln\left(\frac{S}{E}\right) + \left(r + \frac{1}{2}\sigma^2\right)(T-t)}{\sigma\sqrt{T-t}}$ - Case 1: Hedging with Actual Volatility
- Provides a guaranteed profit equal to the difference between option values using actual vs implied volatility
- Case 2: Hedging with IV (Chosen for Optimization)
- By hedging with implied volatility we are balancing the random fluctuations in the mark-to-market option value with the fluctuations in the stock price.
- 10.1 Dynamics linked via drift rates
- Profit depends crucially on the growth rate because of the path dependence.
$dS_i = μ_i(S1,..., Sn) dt + σ_iS_i dX_i$
- Extra Notes
- Mark-to-Market vs Mark-to-Model
- Mark-to-market refers to valuing assets based on current market prices - what you could actually buy or sell them for right now.
- Mark-to-model involves valuing assets using theoretical pricing models, like Black-Scholes for options.
- Mark-to-Market vs Mark-to-Model
- References
- Pricing Options on Realized Variance by Peter Carr (2005)
- Parameter risk in the Black and Scholes model by Marc Henrard (2003)
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FAQ’s in Option Pricing Theory by Peter Carr (2005)
- IX Which volatility should one hedge at - historical or implied?