Quantitative Finance Book

Welcome to my problem book

• Goal of this book is to summarise key topics encountered, analyse them deeper and extend them further.

• Emphasis will be put on developing intuition and decomposing these often tricky topics in simple words.

Characteristic Function Methods

• 1. Recovering PDF/CDF from Characteristic Functions
• 2. Exact Heston Model Simulations for Characteristic Function Methods

Calibration

• 3. Heston Calibration
• 4. SSVI Implied Volatility Surface
• 5. Heston Stochastic Local Volatility: Calibration and Simulation

Pricing American Options

• 6. Intuition Behind the Longstaff-Schwartz Implementation
• 7. Pricing American Options by LSMC Method
• 8. Pricing American Options by Finite Difference
• 9. Pricing American Options with the COS Method

Hedging and Greeks

• 10. Greeks under Black-Scholes
• 11. Greeks via COS Method

Trading and Hedging

• 12. Black-Scholes: From Model to PnL
• 13. Heston Model: Hedging Under Stochastic Volatility
• 14. Heston Hedging under Stochastic Local Volatility

Volatility Forecasting

• 15. Predicting Realized Volatility

References

[AMST07]

Hansjörg Albrecher, Philipp Mayer, Wim Schoutens, and Jurgen Tistaert. The little heston trap. Wilmott Magazine, pages 83–92, January 2007.

[BK06]

Mark Broadie and Özgür Kaya. Exact simulation of stochastic volatility and other affine jump diffusion processes. Operations Research, 54(2):217–231, 2006.

[FO08]

Fang Fang and Cornelis W Oosterlee. A novel pricing method for european options based on fourier-cosine series expansions. SIAM Journal on Scientific Computing, 31(2):826–848, 2008.

[FO09]

Fang Fang and Cornelis W Oosterlee. Pricing early-exercise and discrete barrier options by fourier-cosine series expansions. Numerische Mathematik, 114(1):27–62, 2009.

[GJ14]

Jim Gatheral and Antoine Jacquier. Arbitrage-free SVI volatility surfaces. Quantitative Finance, 14(1):59–71, 2014. doi:10.1080/14697688.2013.819986.

[Hes93]

Steven L Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2):327–343, 1993.

[LS01]

Francis A Longstaff and Eduardo S Schwartz. Valuing american options by simulation: a simple least-squares approach. The Review of Financial Studies, 14(1):113–147, 2001.

[vdSGO14]

Anthonie W van der Stoep, Lech A Grzelak, and Cornelis W Oosterlee. The heston stochastic-local volatility model: efficient monte carlo simulation. International Journal of Theoretical and Applied Finance, 17(7):1450045, 2014. Available at SSRN: https://ssrn.com/abstract=2278122.